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Diffstat (limited to 'operations')
178 files changed, 65875 insertions, 0 deletions
diff --git a/operations/conversions/axisswap.html b/operations/conversions/axisswap.html new file mode 100644 index 00000000..ada19f35 --- /dev/null +++ b/operations/conversions/axisswap.html @@ -0,0 +1,214 @@ +<!DOCTYPE html> +<html class="writer-html5" lang="en" > +<head> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" /> + + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> + <title>Axis swap — PROJ 9.0.0 documentation</title> + <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" /> + <link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" /> + <link rel="shortcut icon" href="../../_static/favicon.png"/> + <link rel="canonical" href="https://proj.orgoperations/conversions/axisswap.html"/> + <!--[if lt IE 9]> + <script src="../../_static/js/html5shiv.min.js"></script> + <![endif]--> + + <script data-url_root="../../" id="documentation_options" 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href="../../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="../projections/index.html">Projections</a></li> +<li class="toctree-l2 current"><a class="reference internal" href="index.html">Conversions</a><ul class="current"> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Axis swap</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#usage">Usage</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="cart.html">Geodetic to cartesian conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="geoc.html">Geocentric Latitude</a></li> +<li class="toctree-l3"><a class="reference internal" href="latlon.html">Lat/long (Geodetic alias)</a></li> +<li class="toctree-l3"><a class="reference internal" href="noop.html">No operation</a></li> +<li class="toctree-l3"><a class="reference internal" href="pop.html">Pop coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l3"><a class="reference internal" href="topocentric.html">Geocentric to topocentric conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" 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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Conversions</a> »</li> + <li>Axis swap</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/conversions/axisswap.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="index.html" class="btn btn-neutral float-left" title="Conversions" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cart.html" class="btn btn-neutral float-right" title="Geodetic to cartesian conversion" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="axis-swap"> +<span id="axisswap"></span><h1>Axis swap<a class="headerlink" href="#axis-swap" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Change the order and sign of 2,3 or 4 axes.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>axisswap</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D, 3D or 4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<p>Each of the possible four axes are numbered with 1–4, such that the first input axis +is 1, the second is 2 and so on. The output ordering is controlled by a list of the +input axes re-ordered to the new mapping.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Reversing the order of the axes:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=axisswap +order=4,3,2,1 +</pre></div> +</div> +<p>Swapping the first two axes (x and y):</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=axisswap +order=2,1,3,4 +</pre></div> +</div> +<p>The direction, or sign, of an axis can be changed by adding a minus in +front of the axis-number:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=axisswap +order=1,-2,3,4 +</pre></div> +</div> +<p>It is only necessary to specify the axes that are affected by the swap +operation:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=axisswap +order=2,1 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-order"> +<span class="sig-name descname"><span class="pre">+order</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-order" title="Permalink to this definition">¶</a></dt> +<dd><p>Ordered comma-separated list of axis, e.g. <em>+order=2,1,3,4</em>. +Adding a minus in front of an axis number results in a change of direction +for that axis, e.g. southward instead of northward.</p> +<p><em>Required.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="index.html" class="btn btn-neutral float-left" title="Conversions" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cart.html" class="btn btn-neutral float-right" title="Geodetic to cartesian conversion" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
\ No newline at end of file diff --git a/operations/conversions/cart.html b/operations/conversions/cart.html new file mode 100644 index 00000000..080354e4 --- /dev/null +++ b/operations/conversions/cart.html @@ -0,0 +1,203 @@ +<!DOCTYPE html> +<html class="writer-html5" lang="en" > +<head> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" /> + + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> + <title>Geodetic to cartesian conversion — PROJ 9.0.0 documentation</title> + <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" /> + <link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" /> + <link rel="shortcut icon" href="../../_static/favicon.png"/> + <link rel="canonical" href="https://proj.orgoperations/conversions/cart.html"/> + <!--[if lt IE 9]> + <script src="../../_static/js/html5shiv.min.js"></script> + <![endif]--> + + <script data-url_root="../../" 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href="../../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="../projections/index.html">Projections</a></li> +<li class="toctree-l2 current"><a class="reference internal" href="index.html">Conversions</a><ul class="current"> +<li class="toctree-l3"><a class="reference internal" href="axisswap.html">Axis swap</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Geodetic to cartesian conversion</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#usage">Usage</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="geoc.html">Geocentric Latitude</a></li> +<li class="toctree-l3"><a class="reference internal" href="latlon.html">Lat/long (Geodetic alias)</a></li> +<li class="toctree-l3"><a class="reference internal" href="noop.html">No operation</a></li> +<li class="toctree-l3"><a class="reference internal" href="pop.html">Pop coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l3"><a class="reference internal" href="topocentric.html">Geocentric to topocentric conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Conversions</a> »</li> + <li>Geodetic to cartesian conversion</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/conversions/cart.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="axisswap.html" class="btn btn-neutral float-left" title="Axis swap" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="geoc.html" class="btn btn-neutral float-right" title="Geocentric Latitude" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="geodetic-to-cartesian-conversion"> +<span id="cart"></span><h1>Geodetic to cartesian conversion<a class="headerlink" href="#geodetic-to-cartesian-conversion" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Convert geodetic coordinates to cartesian coordinates (in the forward path).</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>cart</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geocentric cartesian coordinates</p></td> +</tr> +</tbody> +</table> +<p>This conversion converts geodetic coordinate values (longitude, latitude, +elevation above ellipsoid) to their geocentric (X, Y, Z) representation, where +the first axis (X) points from the Earth centre to the point of longitude=0, +latitude=0, the second axis (Y) points from the Earth centre to the point of +longitude=90, latitude=0 and the third axis (Z) points to the North pole.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Convert geodetic coordinates to GRS80 cartesian coordinates:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 17.7562015132 45.3935192042 133.12 2017.8 | cct +proj=cart +ellps=GRS80 +4272922.1553 1368283.0597 4518261.3501 2017.8000 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="axisswap.html" class="btn btn-neutral float-left" title="Axis swap" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="geoc.html" class="btn btn-neutral float-right" title="Geocentric Latitude" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="cart.html" class="btn btn-neutral float-left" title="Geodetic to cartesian conversion" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="latlon.html" class="btn btn-neutral float-right" title="Lat/long (Geodetic alias)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="geocentric-latitude"> +<span id="geoc"></span><h1>Geocentric Latitude<a class="headerlink" href="#geocentric-latitude" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Convert from Geodetic Latitude to Geocentric Latitude (in the forward path).</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>geoc</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geocentric angular coordinates</p></td> +</tr> +</tbody> +</table> +<p>The geodetic (or geographic) latitude (also called planetographic latitude +in the context of non-Earth bodies) is the angle between the equatorial plane +and the normal (vertical) to the ellipsoid surface at the considered point. +The geodetic latitude is what is normally used everywhere in PROJ when angular +coordinates are expected or produced.</p> +<p>The geocentric latitude (also called planetocentric latitude in the context of +non-Earth bodies) is the angle between the equatorial plane and a line joining +the body centre to the considered point.</p> +<a class="reference internal image-reference" href="../../_images/geocentric_latitude.png"><img alt="Geocentric latitude" class="align-center" src="../../_images/geocentric_latitude.png" style="width: 437.0px; height: 257.0px;" /></a> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>This conversion must be distinguished from the <a class="reference internal" href="cart.html#cart"><span class="std std-ref">Geodetic to cartesian conversion</span></a> +which converts geodetic coordinates to geocentric coordinates in the cartesian +domain.</p> +</div> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the conversion are taken from <span id="id1">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span> +(equation 3-28)</p> +<p>Let <span class="math notranslate nohighlight">\(\phi'\)</span> to be the geocentric latitude and <span class="math notranslate nohighlight">\(\phi\)</span> the +geodetic latitude, then</p> +<div class="math notranslate nohighlight"> +\[\phi' = \arctan \left[ (1 - e^2) \tan \left( \phi \right) \right]\]</div> +<p>The geocentric latitude is consequently lesser (in absolute value) than the geodetic +latitude, except at the equator and the poles where they are equal.</p> +<p>On a sphere, they are always equal.</p> +</section> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Converting from geodetic latitude to geocentric latitude:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=geoc +ellps=GRS80 +</pre></div> +</div> +<p>Converting from geocentric latitude to geodetic latitude:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +step +proj=geoc +inv +ellps=GRS80 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="cart.html" class="btn btn-neutral float-left" title="Geodetic to cartesian conversion" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="latlon.html" class="btn btn-neutral float-right" title="Lat/long (Geodetic alias)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="../projections/index.html">Projections</a></li> +<li class="toctree-l2 current"><a class="current reference internal" href="#">Conversions</a><ul> +<li class="toctree-l3"><a class="reference internal" href="axisswap.html">Axis swap</a></li> +<li class="toctree-l3"><a class="reference internal" href="cart.html">Geodetic to cartesian conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="geoc.html">Geocentric Latitude</a></li> +<li class="toctree-l3"><a class="reference internal" href="latlon.html">Lat/long (Geodetic alias)</a></li> +<li class="toctree-l3"><a class="reference internal" href="noop.html">No operation</a></li> +<li class="toctree-l3"><a class="reference internal" href="pop.html">Pop coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l3"><a class="reference internal" href="topocentric.html">Geocentric to topocentric conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li 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+</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="conversions"> +<span id="conversions-list"></span><h1>Conversions<a class="headerlink" href="#conversions" title="Permalink to this headline">¶</a></h1> +<p>Conversions are coordinate operations in which both coordinate reference systems +are based on the same datum. In PROJ projections are differentiated from +conversions.</p> +<div class="toctree-wrapper compound"> +<ul> +<li class="toctree-l1"><a class="reference internal" href="axisswap.html">Axis swap</a></li> +<li class="toctree-l1"><a class="reference internal" href="cart.html">Geodetic to cartesian conversion</a></li> +<li class="toctree-l1"><a class="reference internal" href="geoc.html">Geocentric Latitude</a></li> +<li class="toctree-l1"><a class="reference internal" href="latlon.html">Lat/long (Geodetic alias)</a></li> +<li class="toctree-l1"><a class="reference internal" href="noop.html">No operation</a></li> +<li class="toctree-l1"><a class="reference internal" href="pop.html">Pop coordinate value to pipeline stack</a></li> +<li class="toctree-l1"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l1"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l1"><a class="reference internal" href="topocentric.html">Geocentric to topocentric conversion</a></li> +<li class="toctree-l1"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</div> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="../projections/wintri.html" class="btn btn-neutral float-left" title="Winkel Tripel" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="axisswap.html" class="btn btn-neutral float-right" title="Axis swap" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="../projections/index.html">Projections</a></li> +<li class="toctree-l2 current"><a class="reference internal" href="index.html">Conversions</a><ul class="current"> +<li class="toctree-l3"><a class="reference internal" href="axisswap.html">Axis swap</a></li> +<li class="toctree-l3"><a class="reference internal" href="cart.html">Geodetic to cartesian conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="geoc.html">Geocentric Latitude</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Lat/long (Geodetic alias)</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="noop.html">No operation</a></li> +<li class="toctree-l3"><a class="reference internal" href="pop.html">Pop coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l3"><a class="reference internal" href="topocentric.html">Geocentric to topocentric conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Conversions</a> »</li> + <li>Lat/long (Geodetic alias)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/conversions/latlon.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="geoc.html" class="btn btn-neutral float-left" title="Geocentric Latitude" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="noop.html" class="btn btn-neutral float-right" title="No operation" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="lat-long-geodetic-alias"> +<span id="latlon"></span><h1>Lat/long (Geodetic alias)<a class="headerlink" href="#lat-long-geodetic-alias" title="Permalink to this headline">¶</a></h1> +<p>Passes geodetic coordinates through unchanged.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Aliases</strong></p></td> +<td><p>latlon, latlong, lonlat, longlat</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +</tbody> +</table> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>Can not be used with the <strong class="program">proj</strong> application.</p> +</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<p>No parameters will affect the output of the operation if used on it’s own. +However, the parameters below can be used in a declarative manner when used with +<strong class="program">cs2cs</strong> or in a <a class="reference internal" href="../pipeline.html#pipeline"><span class="std std-ref">transformation pipeline</span></a> .</p> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-datum"> +<span class="sig-name descname"><span class="pre">+datum</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-datum" title="Permalink to this definition">¶</a></dt> +<dd><p>Declare the datum used with the coordinates. Available options are: +<code class="docutils literal notranslate"><span class="pre">WGS84</span></code>, <code class="docutils literal notranslate"><span class="pre">GGRS87</span></code>, <code class="docutils literal notranslate"><span class="pre">NAD38</span></code>, <code class="docutils literal notranslate"><span class="pre">NAD27</span></code>, <code class="docutils literal notranslate"><span class="pre">potsdam</span></code>, <code class="docutils literal notranslate"><span class="pre">carthage</span></code>, +<code class="docutils literal notranslate"><span class="pre">hermannskogel</span></code>, <code class="docutils literal notranslate"><span class="pre">ire65</span></code>, <code class="docutils literal notranslate"><span class="pre">nzgd49</span></code>, <code class="docutils literal notranslate"><span class="pre">OSGB336</span></code>.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The <code class="docutils literal notranslate"><span class="pre">+datum</span></code> option is primarily available to support the legacy +use of PROJ.4 strings as CRS descriptors and should in most cases +be avoided.</p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-towgs84"> +<span class="sig-name descname"><span class="pre">+towgs84</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-towgs84" title="Permalink to this definition">¶</a></dt> +<dd><p>A list of three or seven <a class="reference internal" href="../transformations/helmert.html#helmert"><span class="std std-ref">Helmert</span></a> parameters that maps +the input coordinates to the WGS84 datum.</p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="geoc.html" class="btn btn-neutral float-left" title="Geocentric Latitude" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="noop.html" class="btn btn-neutral float-right" title="No operation" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
\ No newline at end of file diff --git a/operations/conversions/noop.html b/operations/conversions/noop.html new file mode 100644 index 00000000..40c602ae --- /dev/null +++ b/operations/conversions/noop.html @@ -0,0 +1,181 @@ +<!DOCTYPE html> +<html class="writer-html5" lang="en" > +<head> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" /> + + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> + <title>No operation — PROJ 9.0.0 documentation</title> + <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" /> + <link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" /> + <link rel="shortcut icon" href="../../_static/favicon.png"/> + <link rel="canonical" href="https://proj.orgoperations/conversions/noop.html"/> + <!--[if lt IE 9]> + <script src="../../_static/js/html5shiv.min.js"></script> + <![endif]--> + + <script data-url_root="../../" id="documentation_options" 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href="../../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="../projections/index.html">Projections</a></li> +<li class="toctree-l2 current"><a class="reference internal" href="index.html">Conversions</a><ul class="current"> +<li class="toctree-l3"><a class="reference internal" href="axisswap.html">Axis swap</a></li> +<li class="toctree-l3"><a class="reference internal" href="cart.html">Geodetic to cartesian conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="geoc.html">Geocentric Latitude</a></li> +<li class="toctree-l3"><a class="reference internal" href="latlon.html">Lat/long (Geodetic alias)</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">No operation</a></li> +<li class="toctree-l3"><a class="reference internal" href="pop.html">Pop coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l3"><a class="reference internal" href="topocentric.html">Geocentric to topocentric conversion</a></li> +<li class="toctree-l3"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Conversions</a> »</li> + <li>No operation</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/conversions/noop.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="latlon.html" class="btn btn-neutral float-left" title="Lat/long (Geodetic alias)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="pop.html" class="btn btn-neutral float-right" title="Pop coordinate value to pipeline stack" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="no-operation"> +<span id="noop"></span><h1>No operation<a class="headerlink" href="#no-operation" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.1.0.</span></p> +</div> +<p>Pass a coordinate through unchanged.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>noop</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<p>The no operation is a dummy operation that returns whatever is passed to it +as seen in this example:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 34 56 78 | cct +proj=noop + 12.0000 34.0000 56.0000 78.0000 +</pre></div> +</div> +<p>The operation has no options and default options will not affect the output.</p> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="latlon.html" class="btn btn-neutral float-left" title="Lat/long (Geodetic alias)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="pop.html" class="btn btn-neutral float-right" title="Pop coordinate value to pipeline stack" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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navigation"> + <a href="noop.html" class="btn btn-neutral float-left" title="No operation" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="push.html" class="btn btn-neutral float-right" title="Push coordinate value to pipeline stack" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="pop-coordinate-value-to-pipeline-stack"> +<span id="pop"></span><h1>Pop coordinate value to pipeline stack<a class="headerlink" href="#pop-coordinate-value-to-pipeline-stack" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>Retrieve components of a coordinate that was saved in a previous pipeline step.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>pop</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<p>This operations makes it possible to retrieve coordinate components that was +saved in previous pipeline steps. A retrieved coordinate component is loaded, +or <em>popped</em>, from a memory stack that is part of a <a class="reference internal" href="../pipeline.html#pipeline"><span class="std std-ref">pipeline</span></a>. +The pipeline coordinate stack is inspired by the stack data structure that is +commonly used in computer science. There’s four stacks available: One four each +coordinate dimension. The dimensions, or coordinate components, are numbered +1–4. It is only possible to move data to and from the stack within the same +coordinate component number. Values can be saved to the stack by using the +<a class="reference internal" href="push.html#push"><span class="std std-ref">push operation</span></a>.</p> +<p>If the pop operation is used by itself, e.g. not in a pipeline, it will +function as a no-operation that passes the coordinate through unchanged. +Similarly, if no coordinate component is available on the stack to be popped +the operation does nothing.</p> +<section id="examples"> +<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2> +<p>A common use of the <a class="reference internal" href="push.html#push"><span class="std std-ref">push</span></a> and pop operations is in 3D +<a class="reference internal" href="../transformations/helmert.html#helmert"><span class="std std-ref">Helmert</span></a> transformations where only the horizontal components +are needed. This is often the case when combining heights from a legacy +vertical reference with a modern geocentric reference. Below is a an example of +such a transformation, where the horizontal part is transformed with a Helmert +operation but the vertical part is kept exactly as the input was.</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 56 12.3 2020 | cct +proj=pipeline \ ++step +proj=push +v_3 \ ++step +proj=cart +ellps=GRS80 \ ++step +proj=helmert +x=3000 +y=1000 +z=2000 \ ++step +proj=cart +ellps=GRS80 +inv \ ++step +proj=pop +v_3 \ + + 12.0056753463 55.9866540552 12.3000 2000.0000 +</pre></div> +</div> +<p>Note that the third coordinate component in the output is the same as the input.</p> +<p>The same transformation without the push and pop operations would look like this:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 56 12.3 2020 | cct +proj=pipeline \ ++step +proj=cart +ellps=GRS80 \ ++step +proj=helmert +x=3000 +y=1000 +z=2000 \ ++step +proj=cart +ellps=GRS80 +inv \ + + 12.0057 55.9867 3427.7404 2000.0000 +</pre></div> +</div> +<p>Here the vertical component is adjusted significantly.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_1"> +<span id="cmdoption-arg-v-1"></span><span class="sig-name descname"><span class="pre">+v_1</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Retrieves the first coordinate component from the pipeline stack</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_2"> +<span id="cmdoption-arg-v-2"></span><span class="sig-name descname"><span class="pre">+v_2</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Retrieves the second coordinate component from the pipeline stack</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_3"> +<span id="cmdoption-arg-v-3"></span><span class="sig-name descname"><span class="pre">+v_3</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_3" title="Permalink to this definition">¶</a></dt> +<dd><p>Retrieves the third coordinate component from the pipeline stack</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_4"> +<span id="cmdoption-arg-v-4"></span><span class="sig-name descname"><span class="pre">+v_4</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_4" title="Permalink to this definition">¶</a></dt> +<dd><p>Retrieves the fourth coordinate component from the pipeline stack</p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Stack_(abstract_data_type)">Stack data structure on Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="noop.html" class="btn btn-neutral float-left" title="No operation" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="push.html" class="btn btn-neutral float-right" title="Push coordinate value to pipeline stack" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="pop.html" class="btn btn-neutral float-left" title="Pop coordinate value to pipeline stack" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="set.html" class="btn btn-neutral float-right" title="Set coordinate value" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="push-coordinate-value-to-pipeline-stack"> +<span id="push"></span><h1>Push coordinate value to pipeline stack<a class="headerlink" href="#push-coordinate-value-to-pipeline-stack" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>Save components of a coordinate from one step of a pipeline and make it +available for retrieving in another pipeline step.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>push</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<p>This operations allows for components of coordinates to be saved for +application in a later step. A saved coordinate component is moved, or +<em>pushed</em>, to a memory stack that is part of a <a class="reference internal" href="../pipeline.html#pipeline"><span class="std std-ref">pipeline</span></a>. The +pipeline coordinate stack is inspired by the stack data structure that is +commonly used in computer science. There’s four stacks available: One four each +coordinate dimension. The dimensions, or coordinate components, are numbered +1–4. It is only possible to move data to and from the stack within the same +coordinate component number. Values can be moved off the stack again by using +the <a class="reference internal" href="pop.html#pop"><span class="std std-ref">pop operation</span></a>.</p> +<p>If the push operation is used by itself, e.g. not in a pipeline, it will +function as a no-operation that passes the coordinate through unchanged.</p> +<section id="examples"> +<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2> +<p>A common use of the push and <a class="reference internal" href="pop.html#pop"><span class="std std-ref">pop</span></a> operations is in 3D +<a class="reference internal" href="../transformations/helmert.html#helmert"><span class="std std-ref">Helmert</span></a> transformations where only the horizontal components +are needed. This is often the case when combining heights from a legacy +vertical reference with a modern geocentric reference. Below is a an example of +such a transformation, where the horizontal part is transformed with a Helmert +operation but the vertical part is kept exactly as the input was.</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 56 12.3 2020 | cct +proj=pipeline \ ++step +proj=push +v_3 \ ++step +proj=cart +ellps=GRS80 \ ++step +proj=helmert +x=3000 +y=1000 +z=2000 \ ++step +proj=cart +ellps=GRS80 +inv \ ++step +proj=pop +v_3 \ + + 12.0056753463 55.9866540552 12.3000 2000.0000 +</pre></div> +</div> +<p>Note that the third coordinate component in the output is the same as the input.</p> +<p>The same transformation without the push and pop operations would look like this:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 56 12.3 2020 | cct +proj=pipeline \ ++step +proj=cart +ellps=GRS80 \ ++step +proj=helmert +x=3000 +y=1000 +z=2000 \ ++step +proj=cart +ellps=GRS80 +inv \ + + 12.0057 55.9867 3427.7404 2000.0000 +</pre></div> +</div> +<p>Here the vertical component is adjusted significantly.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_1"> +<span id="cmdoption-arg-v-1"></span><span class="sig-name descname"><span class="pre">+v_1</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Stores the first coordinate component on the pipeline stack</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_2"> +<span id="cmdoption-arg-v-2"></span><span class="sig-name descname"><span class="pre">+v_2</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Stores the second coordinate component on the pipeline stack</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_3"> +<span id="cmdoption-arg-v-3"></span><span class="sig-name descname"><span class="pre">+v_3</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_3" title="Permalink to this definition">¶</a></dt> +<dd><p>Stores the third coordinate component on the pipeline stack</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_4"> +<span id="cmdoption-arg-v-4"></span><span class="sig-name descname"><span class="pre">+v_4</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-v_4" title="Permalink to this definition">¶</a></dt> +<dd><p>Stores the fourth coordinate component on the pipeline stack</p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Stack_(abstract_data_type)">Stack data structure on Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="pop.html" class="btn btn-neutral float-left" title="Pop coordinate value to pipeline stack" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="set.html" class="btn btn-neutral float-right" title="Set coordinate value" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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stack" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="topocentric.html" class="btn btn-neutral float-right" title="Geocentric to topocentric conversion" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="set-coordinate-value"> +<span id="set"></span><h1>Set coordinate value<a class="headerlink" href="#set-coordinate-value" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 7.0.0.</span></p> +</div> +<p>Set component(s) of a coordinate to a fixed value.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>set</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<p>This operations allows for components of coordinates to be set to a fixed value. +This may be useful in <a class="reference internal" href="../pipeline.html#pipeline"><span class="std std-ref">pipeline</span></a> when a step requires some +component, typically an elevation or a date, to be set to a fixed value.</p> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>In the ETRS89 to Dutch RD with NAP height transformation, the used ellipsoidal +height for the Helmert transformation is not the NAP height, but the height is +set to 0 m. This is an unconventional trick to get the same results as when the +effect of the Helmert transformation is included in the horizontal NTv2 grid. +For the forward transformation from ETRS89 to RD with NAP height, we need to set +the ellipsoidal ETRS89 height for the Helmert transformation to the equivalent +of 0 m NAP. This is 43 m for the centre of the Netherlands and this value can +be used as an approximation elsewhere (the effect of this approximation is +below 1 mm for the horizontal coordinates, in an area up to hundreds of km +outside the Netherlands).</p> +<p>The <code class="docutils literal notranslate"><span class="pre">+proj=set</span> <span class="pre">+v_3=0</span></code> close to the end of the pipeline is to make it usable in +the reverse direction.</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ cct -t 0 -d 4 +proj=pipeline \ + +step +proj=unitconvert +xy_in=deg +xy_out=rad \ + +step +proj=axisswap +order=2,1 \ + +step +proj=vgridshift +grids=nlgeo2018.gtx \ + +step +proj=push +v_3 \ + +step +proj=set +v_3=43 \ + +step +proj=cart +ellps=GRS80 \ + +step +proj=helmert +x=-565.7346 +y=-50.4058 +z=-465.2895 +rx=-0.395023 +ry=0.330776 +rz=-1.876073 +s=-4.07242 +convention=coordinate_frame +exact \ + +step +proj=cart +inv +ellps=bessel \ + +step +proj=hgridshift +inv +grids=rdcorr2018.gsb,null \ + +step +proj=sterea +lat_0=52.156160556 +lon_0=5.387638889 +k=0.9999079 +x_0=155000 +y_0=463000 +ellps=bessel \ + +step +proj=set +v_3=0 \ + +step +proj=pop +v_3 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_1"> +<span id="cmdoption-arg-v-1"></span><span class="sig-name descname"><span class="pre">+v_1</span></span><span class="sig-prename descclassname"><span class="pre">=value</span></span><a class="headerlink" href="#cmdoption-arg-v_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the first coordinate component to the specified value</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_2"> +<span id="cmdoption-arg-v-2"></span><span class="sig-name descname"><span class="pre">+v_2</span></span><span class="sig-prename descclassname"><span class="pre">=value</span></span><a class="headerlink" href="#cmdoption-arg-v_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the second coordinate component to the specified value</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_3"> +<span id="cmdoption-arg-v-3"></span><span class="sig-name descname"><span class="pre">+v_3</span></span><span class="sig-prename descclassname"><span class="pre">=value</span></span><a class="headerlink" href="#cmdoption-arg-v_3" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the third coordinate component to the specified value</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-v_4"> +<span id="cmdoption-arg-v-4"></span><span class="sig-name descname"><span class="pre">+v_4</span></span><span class="sig-prename descclassname"><span class="pre">=value</span></span><a class="headerlink" href="#cmdoption-arg-v_4" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the fourth coordinate component to the specified value</p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="push.html" class="btn btn-neutral float-left" title="Push coordinate value to pipeline stack" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="topocentric.html" class="btn btn-neutral float-right" title="Geocentric to topocentric conversion" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="push.html">Push coordinate value to pipeline stack</a></li> +<li class="toctree-l3"><a class="reference internal" href="set.html">Set coordinate value</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Geocentric to topocentric conversion</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#usage">Usage</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="unitconvert.html">Unit conversion</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" 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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Conversions</a> »</li> + <li>Geocentric to topocentric conversion</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/conversions/topocentric.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="set.html" class="btn btn-neutral float-left" title="Set coordinate value" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="unitconvert.html" class="btn btn-neutral float-right" title="Unit conversion" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="geocentric-to-topocentric-conversion"> +<span id="topocentric"></span><h1>Geocentric to topocentric conversion<a class="headerlink" href="#geocentric-to-topocentric-conversion" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 8.0.0.</span></p> +</div> +<p>Convert geocentric coordinates to topocentric coordinates (in the forward path).</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>topocentric</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geocentric cartesian coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Topocentric cartesian coordinates</p></td> +</tr> +</tbody> +</table> +<p>This operation converts geocentric coordinate values (X, Y, Z) to topocentric +(E/East, N/North, U/Up) values. This is also sometimes known as the ECEF (Earth +Centered Earth Fixed) to ENU conversion.</p> +<p>Topocentric coordinates are expressed in a frame whose East and North axis form +a local tangent plane to the Earth’s ellipsoidal surface fixed to a specific +location (the topocentric origin), and the Up axis points upwards along the +normal to that plane.</p> +<a class="reference internal image-reference" href="../../_images/ECEF_ENU_Longitude_Latitude_relationships.png"><img alt="ENU coordinate frame" class="align-center" src="../../_images/ECEF_ENU_Longitude_Latitude_relationships.png" style="width: 400.0px; height: 379.0px;" /></a> +<p>The topocentric origin is a required parameter of the conversion, and can be +expressed either as geocentric coordinates (<code class="docutils literal notranslate"><span class="pre">X_0</span></code>, <code class="docutils literal notranslate"><span class="pre">Y_0</span></code> and <code class="docutils literal notranslate"><span class="pre">Z_0</span></code>) or +as geographic coordinates (<code class="docutils literal notranslate"><span class="pre">lat_0</span></code>, <code class="docutils literal notranslate"><span class="pre">lon_0</span></code>, <code class="docutils literal notranslate"><span class="pre">h_0</span></code>).</p> +<p>When conversion between geographic and topocentric coordinates is desired, the +topocentric conversion must be preceded by the <a class="reference internal" href="cart.html#cart"><span class="std std-ref">Geodetic to cartesian conversion</span></a> conversion to +perform the initial geographic to geocentric coordinates conversion.</p> +<p>The formulas used come from the “Geocentric/topocentric conversions” paragraph +of <span id="id1">[<a class="reference internal" href="../../zreferences.html#id17" title="IOGP. Geomatics guidance note 7, part 2: coordinate conversions & transformations including formulas. IOGP Publication 373-7-2, International Association For Oil And Gas Producers, 2018. URL: https://www.iogp.org/bookstore/product/coordinate-conversions-and-transformation-including-formulas/.">IOGP2018</a>]</span>. <code class="docutils literal notranslate"><span class="pre">+proj=topocentric</span></code> alone corresponds to the <code class="docutils literal notranslate"><span class="pre">EPSG:9836</span></code> +conversion method, <code class="docutils literal notranslate"><span class="pre">+proj=cart</span></code> followed by <code class="docutils literal notranslate"><span class="pre">+proj=topocentric</span></code> corresponds +to <code class="docutils literal notranslate"><span class="pre">EPSG:9837</span></code>.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Convert geocentric coordinates to topocentric coordinates, with the topocentric +origin specified in geocentric coordinates:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 3771793.968 140253.342 5124304.349 2020 | \ + cct -d 3 +proj=topocentric +ellps=WGS84 +X_0=3652755.3058 +Y_0=319574.6799 +Z_0=5201547.3536 + +-189013.869 -128642.040 -4220.171 2020.0000 +</pre></div> +</div> +<p>Convert geographic coordinates to topocentric coordinates, with the topocentric +origin specified in geographic coordinates:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 2.12955 53.80939444 73 2020 | cct -d 3 +proj=pipeline \ + +step +proj=cart +ellps=WGS84 \ + +step +proj=topocentric +ellps=WGS84 +lon_0=5 +lat_0=55 +h_0=200 + +-189013.869 -128642.040 -4220.171 2020.0000 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<section id="topocentric-origin-described-as-geocentric-coordinates"> +<h3>Topocentric origin described as geocentric coordinates<a class="headerlink" href="#topocentric-origin-described-as-geocentric-coordinates" title="Permalink to this headline">¶</a></h3> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The below options are mutually exclusive with the ones to express the origin as geographic coordinates.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-X_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+X_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-X_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Geocentric X value of the topocentric origin (in metre)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-Y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+Y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-Y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Geocentric Y value of the topocentric origin (in metre)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-Z_0"> +<span id="cmdoption-arg-z-0"></span><span class="sig-name descname"><span class="pre">+Z_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-Z_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Geocentric Z value of the topocentric origin (in metre)</p> +</dd></dl> + +</section> +<section id="topocentric-origin-described-as-geographic-coordinates"> +<h3>Topocentric origin described as geographic coordinates<a class="headerlink" href="#topocentric-origin-described-as-geographic-coordinates" title="Permalink to this headline">¶</a></h3> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The below options are mutually exclusive with the ones to express the origin as geocentric coordinates.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of topocentric origin (in degree)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of topocentric origin (in degree)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-h_0"> +<span id="cmdoption-arg-h-0"></span><span class="sig-name descname"><span class="pre">+h_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-h_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Ellipsoidal height of topocentric origin (in metre)</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="set.html" class="btn btn-neutral float-left" title="Set coordinate value" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="unitconvert.html" class="btn btn-neutral float-right" title="Unit conversion" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> 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fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="topocentric.html" class="btn btn-neutral float-left" title="Geocentric to topocentric conversion" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../transformations/index.html" class="btn btn-neutral float-right" title="Transformations" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="unit-conversion"> +<span id="unitconvert"></span><h1>Unit conversion<a class="headerlink" href="#unit-conversion" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Convert between various distance, angular and time units.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>unitconvert</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D, 3D or 4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<p>There are many examples of coordinate reference systems that are expressed in +other units than the meter. There are also many cases where temporal data +has to be translated to different units. The <cite>unitconvert</cite> operation takes care +of that.</p> +<p>Many North American systems are defined with coordinates in feet. For example +in Vermont:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline ++step +proj=tmerc +lat_0=42.5 +lon_0=-72.5 +k_0=0.999964286 +x_0=500000.00001016 +y_0=0 ++step +proj=unitconvert +xy_in=m +xy_out=us-ft +</pre></div> +</div> +<p>Often when working with GNSS data the timestamps are presented in GPS-weeks, +but when the data transformed with the <cite>helmert</cite> operation timestamps are +expected to be in units of decimalyears. This can be fixed with <cite>unitconvert</cite>:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline ++step +proj=unitconvert +t_in=gps_week +t_out=decimalyear ++step +proj=helmert +epoch=2000.0 +t_obs=2017.5 ... +</pre></div> +</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-xy_in"> +<span id="cmdoption-arg-xy-in"></span><span class="sig-name descname"><span class="pre">+xy_in</span></span><span class="sig-prename descclassname"><span class="pre">=<unit></span> <span class="pre">or</span> <span class="pre"><conversion_factor></span></span><a class="headerlink" href="#cmdoption-arg-xy_in" title="Permalink to this definition">¶</a></dt> +<dd><p>Horizontal input units. See <a class="reference internal" href="#distance-units"><span class="std std-ref">Distance units</span></a> and <a class="reference internal" href="#angular-units"><span class="std std-ref">Angular units</span></a> +for a list of available units. <cite><conversion_factor></cite> is the conversion factor +from the input unit to metre for linear units, or to radian for angular +units.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-xy_out"> +<span id="cmdoption-arg-xy-out"></span><span class="sig-name descname"><span class="pre">+xy_out</span></span><span class="sig-prename descclassname"><span class="pre">=<unit></span> <span class="pre">or</span> <span class="pre"><conversion_factor></span></span><a class="headerlink" href="#cmdoption-arg-xy_out" title="Permalink to this definition">¶</a></dt> +<dd><p>Horizontal output units. See <a class="reference internal" href="#distance-units"><span class="std std-ref">Distance units</span></a> and <a class="reference internal" href="#angular-units"><span class="std std-ref">Angular units</span></a> +for a list of available units. <cite><conversion_factor></cite> is the conversion factor +from the output unit to metre for linear units, or to radian for angular +units.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-z_in"> +<span id="cmdoption-arg-z-in"></span><span class="sig-name descname"><span class="pre">+z_in</span></span><span class="sig-prename descclassname"><span class="pre">=<unit></span> <span class="pre">or</span> <span class="pre"><conversion_factor></span></span><a class="headerlink" href="#cmdoption-arg-z_in" title="Permalink to this definition">¶</a></dt> +<dd><p>Vertical output units. See <a class="reference internal" href="#distance-units"><span class="std std-ref">Distance units</span></a> and <a class="reference internal" href="#angular-units"><span class="std std-ref">Angular units</span></a> +for a list of available units. <cite><conversion_factor></cite> is the conversion factor +from the input unit to metre for linear units, or to radian for angular +units.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-z_out"> +<span id="cmdoption-arg-z-out"></span><span class="sig-name descname"><span class="pre">+z_out</span></span><span class="sig-prename descclassname"><span class="pre">=<unit></span> <span class="pre">or</span> <span class="pre"><conversion_factor></span></span><a class="headerlink" href="#cmdoption-arg-z_out" title="Permalink to this definition">¶</a></dt> +<dd><p>Vertical output units. See <a class="reference internal" href="#distance-units"><span class="std std-ref">Distance units</span></a> and <a class="reference internal" href="#angular-units"><span class="std std-ref">Angular units</span></a> +for a list of available units. <cite><conversion_factor></cite> is the conversion factor +from the output unit to metre for linear units, or to radian for angular +units.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_in"> +<span id="cmdoption-arg-t-in"></span><span class="sig-name descname"><span class="pre">+t_in</span></span><span class="sig-prename descclassname"><span class="pre">=<unit></span></span><a class="headerlink" href="#cmdoption-arg-t_in" title="Permalink to this definition">¶</a></dt> +<dd><p>Temporal input units. See <a class="reference internal" href="#time-units"><span class="std std-ref">Time units</span></a> for a list of available units.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_out"> +<span id="cmdoption-arg-t-out"></span><span class="sig-name descname"><span class="pre">+t_out</span></span><span class="sig-prename descclassname"><span class="pre">=<unit></span></span><a class="headerlink" href="#cmdoption-arg-t_out" title="Permalink to this definition">¶</a></dt> +<dd><p>Temporal output units. See <a class="reference internal" href="#time-units"><span class="std std-ref">Time units</span></a> for a list of available units.</p> +</dd></dl> + +</section> +<section id="distance-units"> +<span id="id1"></span><h2>Distance units<a class="headerlink" href="#distance-units" title="Permalink to this headline">¶</a></h2> +<p>In the table below all distance units supported by PROJ are listed. +The same list can also be produced on the command line with <strong class="program">proj</strong> or +<strong class="program">cs2cs</strong>, by adding the <cite>-lu</cite> flag when calling the utility.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 23%" /> +<col style="width: 77%" /> +</colgroup> +<thead> +<tr class="row-odd"><th class="head"><p>Label</p></th> +<th class="head"><p>Name</p></th> +</tr> +</thead> +<tbody> +<tr class="row-even"><td><p>km</p></td> +<td><p>Kilometer</p></td> +</tr> +<tr class="row-odd"><td><p>m</p></td> +<td><p>Meter</p></td> +</tr> +<tr class="row-even"><td><p>dm</p></td> +<td><p>Decimeter</p></td> +</tr> +<tr class="row-odd"><td><p>cm</p></td> +<td><p>Centimeter</p></td> +</tr> +<tr class="row-even"><td><p>mm</p></td> +<td><p>Millimeter</p></td> +</tr> +<tr class="row-odd"><td><p>kmi</p></td> +<td><p>International Nautical Mile</p></td> +</tr> +<tr class="row-even"><td><p>in</p></td> +<td><p>International Inch</p></td> +</tr> +<tr class="row-odd"><td><p>ft</p></td> +<td><p>International Foot</p></td> +</tr> +<tr class="row-even"><td><p>yd</p></td> +<td><p>International Yard</p></td> +</tr> +<tr class="row-odd"><td><p>mi</p></td> +<td><p>International Statute Mile</p></td> +</tr> +<tr class="row-even"><td><p>fath</p></td> +<td><p>International Fathom</p></td> +</tr> +<tr class="row-odd"><td><p>ch</p></td> +<td><p>International Chain</p></td> +</tr> +<tr class="row-even"><td><p>link</p></td> +<td><p>International Link</p></td> +</tr> +<tr class="row-odd"><td><p>us-in</p></td> +<td><p>U.S. Surveyor’s Inch</p></td> +</tr> +<tr class="row-even"><td><p>us-ft</p></td> +<td><p>U.S. Surveyor’s Foot</p></td> +</tr> +<tr class="row-odd"><td><p>us-yd</p></td> +<td><p>U.S. Surveyor’s Yard</p></td> +</tr> +<tr class="row-even"><td><p>us-ch</p></td> +<td><p>U.S. Surveyor’s Chain</p></td> +</tr> +<tr class="row-odd"><td><p>us-mi</p></td> +<td><p>U.S. Surveyor’s Statute Mile</p></td> +</tr> +<tr class="row-even"><td><p>ind-yd</p></td> +<td><p>Indian Yard</p></td> +</tr> +<tr class="row-odd"><td><p>ind-ft</p></td> +<td><p>Indian Foot</p></td> +</tr> +<tr class="row-even"><td><p>ind-ch</p></td> +<td><p>Indian Chain</p></td> +</tr> +</tbody> +</table> +</section> +<section id="angular-units"> +<span id="id2"></span><h2>Angular units<a class="headerlink" href="#angular-units" title="Permalink to this headline">¶</a></h2> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.2.0.</span></p> +</div> +<p>In the table below all angular units supported by PROJ <cite>unitconvert</cite> are listed.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 23%" /> +<col style="width: 77%" /> +</colgroup> +<thead> +<tr class="row-odd"><th class="head"><p>Label</p></th> +<th class="head"><p>Name</p></th> +</tr> +</thead> +<tbody> +<tr class="row-even"><td><p>deg</p></td> +<td><p>Degree</p></td> +</tr> +<tr class="row-odd"><td><p>grad</p></td> +<td><p>Grad</p></td> +</tr> +<tr class="row-even"><td><p>rad</p></td> +<td><p>Radian</p></td> +</tr> +</tbody> +</table> +</section> +<section id="time-units"> +<span id="id3"></span><h2>Time units<a class="headerlink" href="#time-units" title="Permalink to this headline">¶</a></h2> +<p>In the table below all time units supported by PROJ are listed.</p> +<blockquote> +<div><div class="admonition note"> +<p class="admonition-title">Note</p> +<p>When converting time units from a date-only format (<cite>yyyymmdd</cite>), PROJ +assumes a time value of 00:00 midnight. When converting time units +to a date-only format, PROJ rounds to the <em>nearest</em> date at 00:00 +midnight. That is, any time values less than 12:00 noon will round to +00:00 on the same day. Time values greater than or equal to 12:00 noon +will round to 00:00 on the following day.</p> +</div> +</div></blockquote> +<table class="docutils align-default"> +<colgroup> +<col style="width: 33%" /> +<col style="width: 67%" /> +</colgroup> +<thead> +<tr class="row-odd"><th class="head"><p>Label</p></th> +<th class="head"><p>Name</p></th> +</tr> +</thead> +<tbody> +<tr class="row-even"><td><p>mjd</p></td> +<td><p>Modified Julian date</p></td> +</tr> +<tr class="row-odd"><td><p>decimalyear</p></td> +<td><p>Decimal year</p></td> +</tr> +<tr class="row-even"><td><p>gps_week</p></td> +<td><p>GPS Week</p></td> +</tr> +<tr class="row-odd"><td><p>yyyymmdd</p></td> +<td><p>Date in yyyymmdd format</p></td> +</tr> +</tbody> +</table> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="topocentric.html" class="btn btn-neutral float-left" title="Geocentric to topocentric conversion" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../transformations/index.html" class="btn btn-neutral float-right" title="Transformations" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operations</a><ul> +<li class="toctree-l2"><a class="reference internal" href="projections/index.html">Projections</a></li> +<li class="toctree-l2"><a class="reference internal" href="conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" 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PROJ are divided into three groups: +Projections, conversions and transformations. +Projections are purely cartographic mappings of the sphere onto the plane. +Technically projections are conversions (according to ISO standards), though in +PROJ projections are distinguished from conversions. Conversions are coordinate +operations that do not exert a change in reference frame. Operations that do +exert a change in reference frame are called transformations.</p> +<div class="toctree-wrapper compound"> +<ul> +<li class="toctree-l1"><a class="reference internal" href="projections/index.html">Projections</a></li> +<li class="toctree-l1"><a class="reference internal" href="conversions/index.html">Conversions</a></li> +<li class="toctree-l1"><a class="reference internal" href="transformations/index.html">Transformations</a></li> +<li class="toctree-l1"><a class="reference internal" href="pipeline.html">The pipeline operator</a></li> +<li class="toctree-l1"><a class="reference internal" href="operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</div> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="../apps/projsync.html" class="btn btn-neutral float-left" title="projsync" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="projections/index.html" class="btn btn-neutral float-right" title="Projections" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+<div role="search"> + <form id="rtd-search-form" class="wy-form" action="../search.html" method="get"> + <input type="text" name="q" placeholder="Search docs" /> + <input type="hidden" name="check_keywords" value="yes" /> + <input type="hidden" name="area" value="default" /> + </form> +</div> + </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu"> + <ul class="current"> +<li class="toctree-l1"><a class="reference internal" href="../about.html">About</a></li> +<li class="toctree-l1"><a class="reference internal" href="../news.html">News</a></li> +<li class="toctree-l1"><a class="reference internal" href="../download.html">Download</a></li> +<li class="toctree-l1"><a class="reference internal" href="../install.html">Installation</a></li> +<li class="toctree-l1"><a class="reference internal" href="../usage/index.html">Using PROJ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="projections/index.html">Projections</a></li> +<li class="toctree-l2"><a class="reference internal" href="conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2 current"><a class="current reference internal" href="#">Computation of coordinate operations between two CRS</a><ul> +<li class="toctree-l3"><a class="reference internal" href="#introduction">Introduction</a></li> +<li class="toctree-l3"><a class="reference internal" href="#geographic-crs-to-geographic-crs-with-known-identifiers">Geographic CRS to Geographic CRS, with known identifiers</a></li> +<li class="toctree-l3"><a class="reference internal" href="#filtering-and-sorting-of-coordinate-operations">Filtering and sorting of coordinate operations</a></li> +<li class="toctree-l3"><a class="reference internal" href="#geodetic-geographic-crs-to-geodetic-geographic-crs-without-known-identifiers">Geodetic/geographic CRS to Geodetic/geographic CRS, without known identifiers</a></li> +<li class="toctree-l3"><a class="reference internal" href="#geodetic-geographic-crs-to-geodetic-geographic-crs-without-direct-transformation">Geodetic/geographic CRS to Geodetic/geographic CRS, without direct transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="#projected-crs-to-any-target-crs">Projected CRS to any target CRS</a></li> +<li class="toctree-l3"><a class="reference internal" href="#vertical-crs-to-a-geographic-crs">Vertical CRS to a Geographic CRS</a></li> +<li class="toctree-l3"><a class="reference internal" href="#vertical-crs-to-a-vertical-crs">Vertical CRS to a Vertical CRS</a></li> +<li class="toctree-l3"><a class="reference internal" href="#compound-crs-to-a-geographic-crs">Compound CRS to a Geographic CRS</a></li> +<li class="toctree-l3"><a class="reference internal" href="#compoundcrs-to-compoundcrs">CompoundCRS to CompoundCRS</a></li> +<li class="toctree-l3"><a class="reference internal" href="#when-the-source-or-target-crs-is-a-boundcrs">When the source or target CRS is a BoundCRS</a></li> +</ul> +</li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a 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class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/operations_computation.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="pipeline.html" class="btn btn-neutral float-left" title="The pipeline operator" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../resource_files.html" class="btn btn-neutral float-right" title="Resource files" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="computation-of-coordinate-operations-between-two-crs"> +<span id="operations-computation"></span><h1>Computation of coordinate operations between two CRS<a class="headerlink" href="#computation-of-coordinate-operations-between-two-crs" title="Permalink to this headline">¶</a></h1> +<dl class="field-list simple"> +<dt class="field-odd">Author</dt> +<dd class="field-odd"><p>Even Rouault</p> +</dd> +<dt class="field-even">Last Updated</dt> +<dd class="field-even"><p>2021-02-10</p> +</dd> +</dl> +<section id="introduction"> +<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2> +<p>When using <strong class="command">projinfo -s {crs_def} -t {crs_def}</strong>, +<strong class="command">cs2cs {crs_def} {crs_def}</strong> or the underlying +<a class="reference internal" href="../development/reference/functions.html#c.proj_create_crs_to_crs" title="proj_create_crs_to_crs"><code class="xref c c-func docutils literal notranslate"><span class="pre">proj_create_crs_to_crs()</span></code></a> or <code class="xref cpp cpp-func docutils literal notranslate"><span class="pre">proj_create_operations()</span></code> functions, +PROJ applies an algorithm to compute one or several candidate coordinate operations, +that can be expressed as a PROJ <a class="reference internal" href="pipeline.html#pipeline"><span class="std std-ref">pipeline</span></a> to transform between the source +and the target CRS. This document is about the description of this algorithm that +finds the actual operations to apply to be able later to perform transform coordinates. +So this is mostly about metadata management around coordinate operation methods, +and not about the actual mathematics used to implement those methods. +As a matter of fact with PROJ 6, there are about 60 000 +lines of code dealing with “metadata” management (including conversions between PROJ +strings, all CRS WKT variants), to be compared to 30 000 for the purely computation part.</p> +<p>This document is meant as a plain text explanation of the code for developers, +but also as a in-depth examination of what happens under the hood for curious PROJ +users. It is important to keep in mind that it is not meant to be the ultimate +source of truth of how coordinate operations should be computed. There are clearly +implementation choices and compromises that can be questioned.</p> +<p>Let us start with an example to research operations between the NAD27 and NAD83 +geographic CRS:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s NAD27 -t NAD83 --summary --spatial-test intersects --grid-check none + +Candidate operations found: <span class="m">10</span> +DERIVED_FROM<span class="o">(</span>EPSG<span class="o">)</span>:1312, NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">1</span>.0 m, Canada +DERIVED_FROM<span class="o">(</span>EPSG<span class="o">)</span>:1313, NAD27 to NAD83 <span class="o">(</span><span class="m">4</span><span class="o">)</span>, <span class="m">1</span>.5 m, Canada - NAD27, at least one grid missing +DERIVED_FROM<span class="o">(</span>EPSG<span class="o">)</span>:1241, NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.15 m, USA - CONUS including EEZ +DERIVED_FROM<span class="o">(</span>EPSG<span class="o">)</span>:1243, NAD27 to NAD83 <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">0</span>.5 m, USA - Alaska including EEZ +DERIVED_FROM<span class="o">(</span>EPSG<span class="o">)</span>:1573, NAD27 to NAD83 <span class="o">(</span><span class="m">6</span><span class="o">)</span>, <span class="m">1</span>.5 m, Canada - Quebec, at least one grid missing +EPSG:1462, NAD27 to NAD83 <span class="o">(</span><span class="m">5</span><span class="o">)</span>, <span class="m">1</span>.0 m, Canada - Quebec, at least one grid missing +EPSG:9111, NAD27 to NAD83 <span class="o">(</span><span class="m">9</span><span class="o">)</span>, <span class="m">1</span>.5 m, Canada - Saskatchewan, at least one grid missing +unknown id, Ballpark geographic offset from NAD27 to NAD83, unknown accuracy, World, has ballpark transformation +EPSG:8555, NAD27 to NAD83 <span class="o">(</span><span class="m">7</span><span class="o">)</span>, <span class="m">0</span>.15 m, USA - CONUS and GoM, at least one grid missing +EPSG:8549, NAD27 to NAD83 <span class="o">(</span><span class="m">8</span><span class="o">)</span>, <span class="m">0</span>.5 m, USA - Alaska, at least one grid missing +</pre></div> +</div> +<p>The algorithm involves many cases, so we will progress in the explanation from +the most simple case to more complex ones. We document here the working of this +algorithm as implemented in PROJ 8.0.0. +The results of some examples might also be quite sensitive to the content of the +PROJ database and the PROJ version used.</p> +<p>From a code point of view, the entry point of the algorithm is the C++ +<code class="xref cpp cpp-func docutils literal notranslate"><span class="pre">osgeo::proj::operation::CoordinateOperation::createOperations()</span></code> method.</p> +<p>It combines several strategies:</p> +<blockquote> +<div><ul class="simple"> +<li><p>look up in the PROJ database for available operations</p></li> +<li><p>consider the pair (source CRS, target CRS) to synthetize operations depending +on the nature of the source and target CRS.</p></li> +</ul> +</div></blockquote> +</section> +<section id="geographic-crs-to-geographic-crs-with-known-identifiers"> +<h2>Geographic CRS to Geographic CRS, with known identifiers<a class="headerlink" href="#geographic-crs-to-geographic-crs-with-known-identifiers" title="Permalink to this headline">¶</a></h2> +<p>With the above example of two geographic CRS, that have an identified identifier, +(<strong class="program">projinfo</strong> internally resolves NAD27 to EPSG:4267 and NAD83 to EPSG:4269) +the algorithm will first search +in the coordinate operation related tables of the <code class="file docutils literal notranslate"><span class="pre">proj.db</span></code> if there are records +that list direct transformations between the source and the target CRS. The +transformations typically involve <a class="reference internal" href="transformations/helmert.html#helmert"><span class="std std-ref">Helmert</span></a>-style operations or datum shift based on +grids (more esoteric operations are possible).</p> +<p>A request similar to the following will be emitted:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ sqlite3 proj.db <span class="s2">"SELECT auth_name, code, name, method_name, accuracy FROM \</span> +<span class="s2"> coordinate_operation_view WHERE \</span> +<span class="s2"> source_crs_auth_name = 'EPSG' AND \</span> +<span class="s2"> source_crs_code = '4267' AND \</span> +<span class="s2"> target_crs_auth_name = 'EPSG' AND \</span> +<span class="s2"> target_crs_code = '4269'"</span> + +EPSG<span class="p">|</span><span class="m">1241</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span><span class="p">|</span>NADCON<span class="p">|</span><span class="m">0</span>.15 +EPSG<span class="p">|</span><span class="m">1243</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">2</span><span class="o">)</span><span class="p">|</span>NADCON<span class="p">|</span><span class="m">0</span>.5 +EPSG<span class="p">|</span><span class="m">1312</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span><span class="p">|</span>NTv1<span class="p">|</span><span class="m">1</span>.0 +EPSG<span class="p">|</span><span class="m">1313</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">4</span><span class="o">)</span><span class="p">|</span>NTv2<span class="p">|</span><span class="m">1</span>.5 +EPSG<span class="p">|</span><span class="m">1462</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">5</span><span class="o">)</span><span class="p">|</span>NTv1<span class="p">|</span><span class="m">1</span>.0 +EPSG<span class="p">|</span><span class="m">1573</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">6</span><span class="o">)</span><span class="p">|</span>NTv2<span class="p">|</span><span class="m">1</span>.5 +EPSG<span class="p">|</span><span class="m">8549</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">8</span><span class="o">)</span><span class="p">|</span>NADCON5 <span class="o">(</span>2D<span class="o">)</span><span class="p">|</span><span class="m">0</span>.5 +EPSG<span class="p">|</span><span class="m">8555</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">7</span><span class="o">)</span><span class="p">|</span>NADCON5 <span class="o">(</span>2D<span class="o">)</span><span class="p">|</span><span class="m">0</span>.15 +EPSG<span class="p">|</span><span class="m">9111</span><span class="p">|</span>NAD27 to NAD83 <span class="o">(</span><span class="m">9</span><span class="o">)</span><span class="p">|</span>NTv2<span class="p">|</span><span class="m">1</span>.5 +ESRI<span class="p">|</span><span class="m">108003</span><span class="p">|</span>NAD_1927_To_NAD_1983_PR_VI<span class="p">|</span>NTv2<span class="p">|</span><span class="m">0</span>.05 +</pre></div> +</div> +<p>As we have found direct transformations, we will not attempt any more complicated +research. +One can note in the above result set that a ESRI:108003 operation was found, +but as the source and target CRS are in the EPSG registry, and there are +operations between those CRS in the EPSG registry itself, transformations from +other authorities will be ignored (except if they are in the PROJ authority, +which can be used as an override).</p> +<p>As those results all involve operations that does not have a perfect accuracy and that +does not cover the area of use of the 2 CRSs, a +‘Ballpark geographic offset from NAD27 to NAD83’ operation is synthetized by PROJ +(see <a class="reference internal" href="../glossary.html#term-Ballpark-transformation"><span class="xref std std-term">Ballpark transformation</span></a>)</p> +</section> +<section id="filtering-and-sorting-of-coordinate-operations"> +<h2>Filtering and sorting of coordinate operations<a class="headerlink" href="#filtering-and-sorting-of-coordinate-operations" title="Permalink to this headline">¶</a></h2> +<p>The last step is to filter and sort results in order of relevance.</p> +<p>The filtering takes into account the following criteria to decide which operations +must be retained or discarded:</p> +<ul class="simple"> +<li><p>a minimum accuracy that the user might have expressed,</p></li> +<li><p>an area of use on which the coordinate operation(s) must apply</p></li> +<li><p>if the absence of grids needed by an operation must result in discarding it.</p></li> +</ul> +<p>The sorting algorithm determines the order of relevance of the operations we got. +A comparison function compares pair of operations to determine which of the +two is the most relevant. This is implemented by the <code class="xref cpp cpp-func docutils literal notranslate"><span class="pre">operator</span> <span class="pre">()</span></code> +method of the SortFunction structure. +When comparing two operations, the following criteria are used. The tests are +performed in the order they are listed below:</p> +<ol class="arabic simple"> +<li><p>consider as more relevant an operation that can be expressed as a PROJ operation string +(the database might list operations whose method is not (yet) implemented by PROJ)</p></li> +<li><p>if both operations evaluate identically with respect to the above criterion, +consider as more relevant an operation that does not include a synthetic +ballpark vertical transformation (occurs when there is a geoid model).</p></li> +<li><p>if both operations evaluate identically with respect to the above criterion, +consider as more relevant an operation that does not include a synthetic +ballpark horizontal transformation.</p></li> +<li><p>consider as more relevant an operation that refers to shift grids that are locally available.</p></li> +<li><p>consider as more relevant an operation that refers to grids that are available +in one of the proj-datumgrid packages, but not necessarily locally available</p></li> +<li><p>consider as more relevant an operation that has a known accuracy.</p></li> +<li><p>if two operations have unknown accuracy, consider as more relevant an operation +that uses grid(s) if the other one does not (grid based operations are assumed +to be more precise than operations relying on a few parameters)</p></li> +<li><p>consider as more relevant an operation whose area of use is larger +(note: the computation of the are of use is approximate, based on a bounding box)</p></li> +<li><p>consider as more relevant an operation that has a better accuracy.</p></li> +<li><p>in case of same accuracy, consider as more relevant an operation that does +not use grids (operations that use only parameters will be faster)</p></li> +<li><p>consider as more relevant an operation that involves less transformation steps +(transformation steps considered are the ones listed in the WKT output, not PROJ pipeline steps)</p></li> +<li><p>and for completeness, if two operations are comparable given all the above criteria, +consider as more relevant the one which has the shorter name, and if they +have the same length, consider as more relevant the one whose name comes last in +lexicographic order (e.g. “FOO to BAR (3)” will have higher precedence than +“FOO to BAR (2)”)</p></li> +</ol> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><a class="reference internal" href="../development/reference/functions.html#c.proj_trans" title="proj_trans"><code class="xref c c-func docutils literal notranslate"><span class="pre">proj_trans()</span></code></a>, on the results returned by <a class="reference internal" href="../development/reference/functions.html#c.proj_create_crs_to_crs" title="proj_create_crs_to_crs"><code class="xref c c-func docutils literal notranslate"><span class="pre">proj_create_crs_to_crs()</span></code></a>, +will not necessarily use the operation that +is listed in first position due to the above algorithm. <a class="reference internal" href="../development/reference/functions.html#c.proj_trans" title="proj_trans"><code class="xref c c-func docutils literal notranslate"><span class="pre">proj_trans()</span></code></a> +has more context, since it has the coordinate to transform, so it can compare +this coordinate to the area of use of operations. Typically, the above criteria +will favor an operation that has a larger area of use over another one with a +smaller area, due to it being more generally applicable. But once coordinates are known, +<a class="reference internal" href="../development/reference/functions.html#c.proj_trans" title="proj_trans"><code class="xref c c-func docutils literal notranslate"><span class="pre">proj_trans()</span></code></a> can select an operation with a smaller +area of use that applies to the coordinate to transform.</p> +</div> +</section> +<section id="geodetic-geographic-crs-to-geodetic-geographic-crs-without-known-identifiers"> +<h2>Geodetic/geographic CRS to Geodetic/geographic CRS, without known identifiers<a class="headerlink" href="#geodetic-geographic-crs-to-geodetic-geographic-crs-without-known-identifiers" title="Permalink to this headline">¶</a></h2> +<p>In a number of situations, the source and/or target CRS do not have an identifier +(WKT without identifier, PROJ string, ..) +The first step is to try to find in the <code class="file docutils literal notranslate"><span class="pre">proj.db</span></code> a CRS of the same nature of +the CRS to identify and whose name exactly matches the one provided to the +<code class="xref c c-func docutils literal notranslate"><span class="pre">createOperations()</span></code> method. If there is exactly one match and that the CRS are +“computationally” equivalent, then use the code of the CRS for further computations.</p> +<p>If this search did not succeed, or if the previous case with known CRS identifiers +did not result in matches in the database, the search will be based on the +datums. That is, a list of geographic CRS whose datum matches the datum of the +source and target CRS is searched for in the database (by querying the <cite>geodetic_crs</cite> +database table). If the datum has a known +identifier, we will use it, otherwise we will look for an equivalent datum in the +database based on the datum name.</p> +<p>Let’s consider the case where the datum of the source CRS is EPSG:6171 “Reseau +Geodesique Francais 1993” and the datum of the target CRS is EPSG:6258 “European +Terrestrial Reference System 1989”. +For EPSG:6171, there are 10 matching (non-deprecated) geodetic CRSs:</p> +<ul class="simple"> +<li><p>EPSG:4171, RGF93, geographic 2D</p></li> +<li><p>EPSG:4964, RGF93, geocentric</p></li> +<li><p>EPSG:4965, RGF93, geographic 3D</p></li> +<li><p>EPSG:7042, RGF93 (lon-lat), geographic 3D</p></li> +<li><p>EPSG:7084, RGF93 (lon-lat), geographic 2D</p></li> +<li><p>IGNF:RGF93, RGF93 cartesiennes geocentriques, geocentric</p></li> +<li><p>IGNF:RGF93GDD, RGF93 geographiques (dd),geographic 2D</p></li> +<li><p>IGNF:RGF93GEODD, RGF93 geographiques (dd), geographic 3D</p></li> +<li><p>IGNF:RGF93G, RGF93 geographiques (dms), geographic 2D</p></li> +<li><p>IGNF:RGF93GEO, RGF93 geographiques (dms), geographic 3D</p></li> +</ul> +<p>The first three entries from the EPSG dataset are typical: for each datum, +one can define a geographic 2D CRS (latitude, longitude), a geographic 3D crs +(latitude, longitude, ellipsoidal height) and a geocentric one. For that particular +case, the EPSG dataset has also included two extra definitions corresponding to a +longitude, latitude, [ellipsoidal height] coordinate system, as found in the official +French IGNF registry. This IGNF registry has also definitions for a geographic 2D +CRS (with an extra subtlety with an entry using decimal degree as unit and another +one degree-minute-second), geographic 3D and geocentric.</p> +<p>For EPSG:6258, there are 7 matching (non-deprecated) geodetic CRSs:</p> +<ul class="simple"> +<li><p>EPSG:4258, ETRS89, geographic 2D</p></li> +<li><p>EPSG:4936, ETRS89, geocentric</p></li> +<li><p>EPSG:4937, ETRS89, geographic 3D</p></li> +<li><p>IGNF:ETRS89, ETRS89 cartesiennes geocentriques, geocentric</p></li> +<li><p>IGNF:ETRS89G, ETRS89 geographiques (dms), geographic 2D</p></li> +<li><p>IGNF:ETRS89GEO, ETRS89 geographiques (dms), geographic 3D</p></li> +<li><p>ESRI:104129, GCS_EUREF_FIN, geographic 2D</p></li> +</ul> +<p>So the 3 typical EPSG entries, 3 equivalent (with long, lat ordering for the +geographic CRS) and one from the ESRI registry;</p> +<p>PROJ can now test 10 x 7 different combinations of source x target CRSs, using +the database searching method explained in the previous section. As soon as +one of this combination returns at least one non-ballpark combination, the result +set coming from that combination is used. PROJ will then add before that +transformation a conversion between the source CRS and the first intermediate CRS, +and will add at the end a conversion between the second intermediate CRS and the +target CRS. Those conversions are conversion between geographic 2D and geographic 3D +CRS or geographic 2D/3D and geocentric CRS.</p> +<p>This is done by the <code class="xref c c-func docutils literal notranslate"><span class="pre">createOperationsWithDatumPivot()</span></code> method.</p> +<p>So if transforming between EPSG:7042, RGF93 (lon-lat), geographic 3D and +EPSG:4936, ETRS89, geocentric, one get the following concatenated operation, +chaining an axis order change, the null geocentric translation between +RGF93 and ETRS89 (EPSG:1591), and a conversion between geographic and geocentric +coordinates. This concatenated operation is assumed to have a perfect accuracy +as both the initial and final operations are conversions, and the middle transformation +accounts for the fact that the RGF93 datum is one realization of ETRS89, so they +are equivalent for most purposes.</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s EPSG:7042 -t EPSG:4936 + +Candidate operations found: <span class="m">1</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +unknown id, axis order change <span class="o">(</span>geographic3D horizontal<span class="o">)</span> + RGF93 to ETRS89 <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Conversion from ETRS89 <span class="o">(</span>geog2D<span class="o">)</span> to ETRS89 <span class="o">(</span>geocentric<span class="o">)</span>, <span class="m">0</span> m, France + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad +step +proj<span class="o">=</span>cart +ellps<span class="o">=</span>GRS80 + +WKT2:2019 string: +CONCATENATEDOPERATION<span class="o">[</span><span class="s2">"axis order change (geographic3D horizontal) + RGF93 to ETRS89 (1) + Conversion from ETRS89 (geog2D) to ETRS89 (geocentric)"</span>, + SOURCECRS<span class="o">[</span> + GEOGCRS<span class="o">[</span><span class="s2">"RGF93 (lon-lat)"</span>, + <span class="o">[</span>...<span class="o">]</span> + ID<span class="o">[</span><span class="s2">"EPSG"</span>,7042<span class="o">]]]</span>, + TARGETCRS<span class="o">[</span> + GEODCRS<span class="o">[</span><span class="s2">"ETRS89"</span>, + <span class="o">[</span>...<span class="o">]</span> + ID<span class="o">[</span><span class="s2">"EPSG"</span>,4936<span class="o">]]]</span>, + STEP<span class="o">[</span> + CONVERSION<span class="o">[</span><span class="s2">"axis order change (geographic3D horizontal)"</span>, + METHOD<span class="o">[</span><span class="s2">"Axis Order Reversal (Geographic3D horizontal)"</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,9844<span class="o">]]</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,15499<span class="o">]]]</span>, + STEP<span class="o">[</span> + COORDINATEOPERATION<span class="o">[</span><span class="s2">"RGF93 to ETRS89 (1)"</span>, + <span class="o">[</span>...<span class="o">]</span> + METHOD<span class="o">[</span><span class="s2">"Geocentric translations (geog2D domain)"</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,9603<span class="o">]]</span>, + PARAMETER<span class="o">[</span><span class="s2">"X-axis translation"</span>,0, + LENGTHUNIT<span class="o">[</span><span class="s2">"metre"</span>,1<span class="o">]</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,8605<span class="o">]]</span>, + PARAMETER<span class="o">[</span><span class="s2">"Y-axis translation"</span>,0, + LENGTHUNIT<span class="o">[</span><span class="s2">"metre"</span>,1<span class="o">]</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,8606<span class="o">]]</span>, + PARAMETER<span class="o">[</span><span class="s2">"Z-axis translation"</span>,0, + LENGTHUNIT<span class="o">[</span><span class="s2">"metre"</span>,1<span class="o">]</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,8607<span class="o">]]</span>, + OPERATIONACCURACY<span class="o">[</span><span class="m">0</span>.0<span class="o">]</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,1591<span class="o">]</span>, + REMARK<span class="o">[</span><span class="s2">"May be taken as approximate transformation RGF93 to WGS 84 - see code 1671."</span><span class="o">]]]</span>, + STEP<span class="o">[</span> + CONVERSION<span class="o">[</span><span class="s2">"Conversion from ETRS89 (geog2D) to ETRS89 (geocentric)"</span>, + METHOD<span class="o">[</span><span class="s2">"Geographic/geocentric conversions"</span>, + ID<span class="o">[</span><span class="s2">"EPSG"</span>,9602<span class="o">]]]]</span>, + USAGE<span class="o">[</span> + SCOPE<span class="o">[</span><span class="s2">"unknown"</span><span class="o">]</span>, + AREA<span class="o">[</span><span class="s2">"France"</span><span class="o">]</span>, + BBOX<span class="o">[</span><span class="m">41</span>.15,-9.86,51.56,10.38<span class="o">]]]</span> +</pre></div> +</div> +</section> +<section id="geodetic-geographic-crs-to-geodetic-geographic-crs-without-direct-transformation"> +<h2>Geodetic/geographic CRS to Geodetic/geographic CRS, without direct transformation<a class="headerlink" href="#geodetic-geographic-crs-to-geodetic-geographic-crs-without-direct-transformation" title="Permalink to this headline">¶</a></h2> +<p>Still considering transformations between geodetic/geographic CRS, but let’s +consider that the lookup in the database for a transformation between +the source and target CRS (possibly going through the “equivalent” CRS based on +the same datum as detailed in the previous section) leads to an empty set.</p> +<p>Of course, as most operations are invertible, one first tries to do a lookup switching +the source and target CRS, and inverting the resulting operation(s):</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s NAD83 -t NAD27 --spatial-test intersects --summary + +Candidate operations found: <span class="m">10</span> +INVERSE<span class="o">(</span>DERIVED_FROM<span class="o">(</span>EPSG<span class="o">))</span>:1312, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">2</span>.0 m, Canada +INVERSE<span class="o">(</span>DERIVED_FROM<span class="o">(</span>EPSG<span class="o">))</span>:1313, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">4</span><span class="o">)</span>, <span class="m">1</span>.5 m, Canada - NAD27 +INVERSE<span class="o">(</span>DERIVED_FROM<span class="o">(</span>EPSG<span class="o">))</span>:1241, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.15 m, USA - CONUS including EEZ +INVERSE<span class="o">(</span>DERIVED_FROM<span class="o">(</span>EPSG<span class="o">))</span>:1243, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">0</span>.5 m, USA - Alaska including EEZ +INVERSE<span class="o">(</span>DERIVED_FROM<span class="o">(</span>EPSG<span class="o">))</span>:1573, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">6</span><span class="o">)</span>, <span class="m">1</span>.5 m, Canada - Quebec, at least one grid missing +INVERSE<span class="o">(</span>EPSG<span class="o">)</span>:1462, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">5</span><span class="o">)</span>, <span class="m">2</span>.0 m, Canada - Quebec, at least one grid missing +INVERSE<span class="o">(</span>EPSG<span class="o">)</span>:9111, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">9</span><span class="o">)</span>, <span class="m">1</span>.5 m, Canada - Saskatchewan, at least one grid missing +unknown id, Ballpark geographic offset from NAD83 to NAD27, unknown accuracy, World, has ballpark transformation +INVERSE<span class="o">(</span>EPSG<span class="o">)</span>:8555, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">7</span><span class="o">)</span>, <span class="m">0</span>.15 m, USA - CONUS and GoM, at least one grid missing +INVERSE<span class="o">(</span>EPSG<span class="o">)</span>:8549, Inverse of NAD27 to NAD83 <span class="o">(</span><span class="m">8</span><span class="o">)</span>, <span class="m">0</span>.5 m, USA - Alaska, at least one grid missing +</pre></div> +</div> +<p>That was an easy case. Now let’s consider the transformation between the Australian +CRS AGD84 and GDA2020. There is no direct transformation from AGD84 to GDA2020, or +in the reverse direction, even when considering alternative geodetic CRS based on +the underlying datums. PROJ will then do a cross-join in the coordinate_operation_view +table to find the tuples (op1, op2) of coordinate operations such that:</p> +<ul class="simple"> +<li><p>SOURCE_CRS = op1.source_crs AND op1.target_crs = op2.source_crs AND op2.target_crs = TARGET_CRS or</p></li> +<li><p>SOURCE_CRS = op1.source_crs AND op1.target_crs = op2.target_crs AND op2.source_crs = TARGET_CRS or</p></li> +<li><p>SOURCE_CRS = op1.target_crs AND op1.source_crs = op2.source_crs AND op2.target_crs = TARGET_CRS or</p></li> +<li><p>SOURCE_CRS = op1.target_crs AND op1.source_crs = op2.target_crs AND op2.source_crs = TARGET_CRS</p></li> +</ul> +<p>Depending on which case is selected, op1 and op2 should be reversed, before +being concatenated.</p> +<p>This logic is implement by the <code class="docutils literal notranslate"><span class="pre">findsOpsInRegistryWithIntermediate()</span></code> method.</p> +<p>Assuming that the proj-datumgrid-oceania package is installed, we get the +following results for the AGD84 to GDA2020 coordinate operations lookup:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s AGD84 -t GDA2020 --spatial-test intersects -o PROJ + +Candidate operations found: <span class="m">4</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +unknown id, AGD84 to GDA94 <span class="o">(</span><span class="m">5</span><span class="o">)</span> + GDA94 to GDA2020 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.11 m, Australia - AGD84 + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad <span class="se">\</span> + +step +proj<span class="o">=</span>hgridshift +grids<span class="o">=</span>National_84_02_07_01.gsb <span class="se">\</span> + +step +proj<span class="o">=</span>push +v_3 <span class="se">\</span> + +step +proj<span class="o">=</span>cart +ellps<span class="o">=</span>GRS80 <span class="se">\</span> + +step +proj<span class="o">=</span>helmert +x<span class="o">=</span><span class="m">0</span>.06155 +y<span class="o">=</span>-0.01087 +z<span class="o">=</span>-0.04019 <span class="se">\</span> + +rx<span class="o">=</span>-0.0394924 +ry<span class="o">=</span>-0.0327221 +rz<span class="o">=</span>-0.0328979 <span class="se">\</span> + +s<span class="o">=</span>-0.009994 +convention<span class="o">=</span>coordinate_frame <span class="se">\</span> + +step +inv +proj<span class="o">=</span>cart +ellps<span class="o">=</span>GRS80 <span class="se">\</span> + +step +proj<span class="o">=</span>pop +v_3 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg <span class="se">\</span> + +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 + +------------------------------------- +Operation No. <span class="m">2</span>: + +unknown id, AGD84 to GDA94 <span class="o">(</span><span class="m">2</span><span class="o">)</span> + GDA94 to GDA2020 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">1</span>.01 m, Australia - AGD84 + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad <span class="se">\</span> + +step +proj<span class="o">=</span>push +v_3 <span class="se">\</span> + +step +proj<span class="o">=</span>cart +ellps<span class="o">=</span>aust_SA <span class="se">\</span> + +step +proj<span class="o">=</span>helmert +x<span class="o">=</span>-117.763 +y<span class="o">=</span>-51.51 +z<span class="o">=</span><span class="m">139</span>.061 <span class="se">\</span> + +rx<span class="o">=</span>-0.292 +ry<span class="o">=</span>-0.443 +rz<span class="o">=</span>-0.277 +s<span class="o">=</span>-0.191 <span class="se">\</span> + +convention<span class="o">=</span>coordinate_frame <span class="se">\</span> + +step +proj<span class="o">=</span>helmert +x<span class="o">=</span><span class="m">0</span>.06155 +y<span class="o">=</span>-0.01087 +z<span class="o">=</span>-0.04019 <span class="se">\</span> + +rx<span class="o">=</span>-0.0394924 +ry<span class="o">=</span>-0.0327221 +rz<span class="o">=</span>-0.0328979 <span class="se">\</span> + +s<span class="o">=</span>-0.009994 +convention<span class="o">=</span>coordinate_frame <span class="se">\</span> + +step +inv +proj<span class="o">=</span>cart +ellps<span class="o">=</span>GRS80 <span class="se">\</span> + +step +proj<span class="o">=</span>pop +v_3 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg <span class="se">\</span> + +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 + +------------------------------------- +Operation No. <span class="m">3</span>: + +unknown id, AGD84 to GDA94 <span class="o">(</span><span class="m">5</span><span class="o">)</span> + GDA94 to GDA2020 <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">0</span>.15 m, unknown domain of validity + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad <span class="se">\</span> + +step +proj<span class="o">=</span>hgridshift +grids<span class="o">=</span>National_84_02_07_01.gsb <span class="se">\</span> + +step +proj<span class="o">=</span>hgridshift +grids<span class="o">=</span>GDA94_GDA2020_conformal_and_distortion.gsb <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg <span class="se">\</span> + +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 + +------------------------------------- +Operation No. <span class="m">4</span>: + +unknown id, AGD84 to GDA94 <span class="o">(</span><span class="m">5</span><span class="o">)</span> + GDA94 to GDA2020 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">0</span>.15 m, unknown domain of validity + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad <span class="se">\</span> + +step +proj<span class="o">=</span>hgridshift +grids<span class="o">=</span>National_84_02_07_01.gsb <span class="se">\</span> + +step +proj<span class="o">=</span>hgridshift +grids<span class="o">=</span>GDA94_GDA2020_conformal.gsb <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg <span class="se">\</span> + +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 +</pre></div> +</div> +<p>One can see that the selected intermediate CRS that has been used is GDA94. +This is a completely novel behavior of PROJ 6 as opposed to the logic of PROJ.4 +where datum transformations implied using EPSG:4326 / WGS 84 has the mandatory +datum hub. PROJ 6 no longer hardcodes it as the mandatory datum hub, and relies +on the database to find the appropriate hub(s). +Actually, WGS 84 has been considered during the above lookup, because there are +transformations between AGD84 and WGS 84 and WGS 84 and GDA2020. However those +have been discarded in a step which we did not mention previously: just after +the initial filtering of results and their sorting, there is a final filtering +that is done. In the list of sorted results, given two operations A and B that +have the same area of use, if B has an accuracy lower than A, and A does not use +grids, or all the needed grids are available, then B is discarded.</p> +<p>If one forces the datum hub to be considered to be EPSG:4326, ones gets:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s AGD84 -t GDA2020 --spatial-test intersects --pivot-crs EPSG:4326 -o PROJ + +Candidate operations found: <span class="m">2</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +unknown id, AGD84 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">7</span><span class="o">)</span> + Inverse of GDA2020 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">4</span> m, Australia - AGD84 + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad <span class="se">\</span> + +step +proj<span class="o">=</span>push +v_3 <span class="se">\</span> + +step +proj<span class="o">=</span>cart +ellps<span class="o">=</span>aust_SA <span class="se">\</span> + +step +proj<span class="o">=</span>helmert +x<span class="o">=</span>-117.763 +y<span class="o">=</span>-51.51 +z<span class="o">=</span><span class="m">139</span>.061 <span class="se">\</span> + +rx<span class="o">=</span>-0.292 +ry<span class="o">=</span>-0.443 +rz<span class="o">=</span>-0.277 <span class="se">\</span> + +s<span class="o">=</span>-0.191 +convention<span class="o">=</span>coordinate_frame <span class="se">\</span> + +step +inv +proj<span class="o">=</span>cart +ellps<span class="o">=</span>GRS80 <span class="se">\</span> + +step +proj<span class="o">=</span>pop +v_3 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg <span class="se">\</span> + +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 + +------------------------------------- +Operation No. <span class="m">2</span>: + +unknown id, AGD84 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">9</span><span class="o">)</span> + Inverse of GDA2020 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">4</span> m, Australia - AGD84 + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>deg +xy_out<span class="o">=</span>rad <span class="se">\</span> + +step +proj<span class="o">=</span>hgridshift +grids<span class="o">=</span>National_84_02_07_01.gsb <span class="se">\</span> + +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg <span class="se">\</span> + +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 +</pre></div> +</div> +<p>Those operations are less accurate, since WGS 84 is assumed to be equivalent to +GDA2020 with an accuracy of 4 metre. This is an instance demonstrating that using +WGS 84 as a hub systematically can be sub-optimal.</p> +<p>There are still situations where the attempt to find a hub CRS does not work, +because there is no such hub. This can occur for example when transforming from +GDA94 to the latest realization at time of writing of WGS 84, WGS 84 (G1762). +There are transformations between WGS 84 (G1762). Using the above described +techniques, we would only find one non-ballpark operation taking the route: +1. Conversion from GDA94 (geog2D) to GDA94 (geocentric): synthetized by PROJ +2. Inverse of ITRF2008 to GDA94 (1): from EPSG +3. Inverse of WGS 84 (G1762) to ITRF2008 (1): from EPSG +4. Conversion from WGS 84 (G1762) (geocentric) to WGS 84 (G1762): synthetized by PROJ</p> +<p>This is not bad, but the global validity area of use is “Australia - onshore and EEZ”, +whereas GDA94 has a larger area of use. +There is another road that can be taken by going through GDA2020 instead of ITRF2008. +The GDA94 to GDA2020 transformations operate on the respective geographic CRS, +whereas GDA2020 to WGS 84 (G1762) operate on the geocentric CRS. Consequently, +GDA2020 cannot be identifier as a hub by a “simple” self-join SQL request on +the coordinate operation table. This requires to do the join based on the datum +referenced by the source and target CRS of each operation rather than the +source and target CRS themselves. When there is a match, PROJ inserts the required +conversions between geographic and geocentric CRS to have a consistent concatenated +operation, like the following: +1. GDA94 to GDA2020 (1): from EPSG +2. Conversion from GDA2020 (geog2D) to GDA2020 (geocentric): synthetized by PROJ +3. GDA2020 to WGS 84 (G1762) (1): from EPSG +4. Conversion from WGS 84 (G1762) (geocentric) to WGS 84 (G1762) (geog2D): synthetized by PROJ</p> +</section> +<section id="projected-crs-to-any-target-crs"> +<h2>Projected CRS to any target CRS<a class="headerlink" href="#projected-crs-to-any-target-crs" title="Permalink to this headline">¶</a></h2> +<p>This actually extends to any Derived CRS, whose Projected CRS is a well-known +particular case. Such transformations are done in 2 steps:</p> +<ol class="arabic simple"> +<li><p>Use the inverse conversion of the derived CRS to its base CRS, typically an +inverse map projection.</p></li> +<li><p>Find transformations from this base CRS to the target CRS. If the base CRS +is the target CRS, this step can be skipped.</p></li> +</ol> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s EPSG:32631 -t RGF93 + +Candidate operations found: <span class="m">1</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +unknown id, Inverse of UTM zone 31N + Inverse of RGF93 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">1</span> m, France + +PROJ string: ++proj<span class="o">=</span>pipeline +step +inv +proj<span class="o">=</span>utm +zone<span class="o">=</span><span class="m">31</span> +ellps<span class="o">=</span>WGS84 +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 +</pre></div> +</div> +<p>This is implemented by the <code class="docutils literal notranslate"><span class="pre">createOperationsDerivedTo</span></code> method</p> +<p>For the symmetric case, source CRS to a derived CRS, the above algorithm is applied +by switching the source and target CRS, and then inverting the resulting operation(s). +This is mostly a matter of avoiding to write very similar code twice. This logic +is also applied to all below cases when considering the transformation between 2 different +types of objects.</p> +</section> +<section id="vertical-crs-to-a-geographic-crs"> +<span id="verttogeog"></span><h2>Vertical CRS to a Geographic CRS<a class="headerlink" href="#vertical-crs-to-a-geographic-crs" title="Permalink to this headline">¶</a></h2> +<p>Such transformation is normally not meant as being used as standalone by PROJ +users, but as an internal computation step of a Compound CRS to a target CRS.</p> +<p>In cases where we are lucky, the PROJ database will have a transformation registered +between those:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s <span class="s2">"NAVD88 height"</span> -t <span class="s2">"NAD83(2011)"</span> -o PROJ --spatial-test intersects +Candidate operations found: <span class="m">11</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +INVERSE<span class="o">(</span>DERIVED_FROM<span class="o">(</span>EPSG<span class="o">))</span>:9229, Inverse of NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">0</span>.015 m, USA - CONUS - onshore + +PROJ string: ++proj<span class="o">=</span>vgridshift +grids<span class="o">=</span>g2018u0.gtx +multiplier<span class="o">=</span><span class="m">1</span> +</pre></div> +</div> +<p>But in cases where there is no match, the <code class="docutils literal notranslate"><span class="pre">createOperationsVertToGeog</span></code> method +will be used to synthetize a ballpark vertical transformation, just taking care +of unit changes, and axis reversal in case the vertical CRS was a depth rather than +a height. Of course the results of such an operation are questionable, hence the +ballpark qualifier and a unknown accuracy advertized for such an operation.</p> +</section> +<section id="vertical-crs-to-a-vertical-crs"> +<h2>Vertical CRS to a Vertical CRS<a class="headerlink" href="#vertical-crs-to-a-vertical-crs" title="Permalink to this headline">¶</a></h2> +<p>Overall logic is similar to the above case. There might be direct operations in +the PROJ database, involving grid transformations or simple offsets. The fallback +case is to synthetize a ballpark transformation.</p> +<p>This is implemented by the <code class="docutils literal notranslate"><span class="pre">createOperationsVertToVert</span></code> method</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s <span class="s2">"NGVD29 depth (ftUS)"</span> -t <span class="s2">"NAVD88 height"</span> --spatial-test intersects -o PROJ + +Candidate operations found: <span class="m">3</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +unknown id, Inverse of NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NGVD29 depth <span class="o">(</span>ftUS<span class="o">)</span> + NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NGVD29 height <span class="o">(</span>m<span class="o">)</span> + NGVD29 height <span class="o">(</span>m<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">0</span>.02 m, USA - CONUS east of <span class="m">89</span>°W - onshore + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">1</span>,2,-3 +step +proj<span class="o">=</span>unitconvert +z_in<span class="o">=</span>us-ft +z_out<span class="o">=</span>m +step +proj<span class="o">=</span>vgridshift +grids<span class="o">=</span>vertcone.gtx +multiplier<span class="o">=</span><span class="m">0</span>.001 + +------------------------------------- +Operation No. <span class="m">2</span>: + +unknown id, Inverse of NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NGVD29 depth <span class="o">(</span>ftUS<span class="o">)</span> + NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NGVD29 height <span class="o">(</span>m<span class="o">)</span> + NGVD29 height <span class="o">(</span>m<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">0</span>.02 m, USA - CONUS <span class="m">89</span>°W-107°W - onshore + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">1</span>,2,-3 +step +proj<span class="o">=</span>unitconvert +z_in<span class="o">=</span>us-ft +z_out<span class="o">=</span>m +step +proj<span class="o">=</span>vgridshift +grids<span class="o">=</span>vertconc.gtx +multiplier<span class="o">=</span><span class="m">0</span>.001 + +------------------------------------- +Operation No. <span class="m">3</span>: + +unknown id, Inverse of NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NGVD29 depth <span class="o">(</span>ftUS<span class="o">)</span> + NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NGVD29 height <span class="o">(</span>m<span class="o">)</span> + NGVD29 height <span class="o">(</span>m<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.02 m, USA - CONUS west of <span class="m">107</span>°W - onshore + +PROJ string: ++proj<span class="o">=</span>pipeline +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">1</span>,2,-3 +step +proj<span class="o">=</span>unitconvert +z_in<span class="o">=</span>us-ft +z_out<span class="o">=</span>m +step +proj<span class="o">=</span>vgridshift +grids<span class="o">=</span>vertconw.gtx +multiplier<span class="o">=</span><span class="m">0</span>.001 +</pre></div> +</div> +</section> +<section id="compound-crs-to-a-geographic-crs"> +<h2>Compound CRS to a Geographic CRS<a class="headerlink" href="#compound-crs-to-a-geographic-crs" title="Permalink to this headline">¶</a></h2> +<p>A typical example of a Compound CRS is a CRS made of a geographic or projected CRS +as the horizontal component, and a vertical CRS. E.g. “NAD83 + NAVD88 height”</p> +<p>When the horizontal component of the compound source CRS is a projected CRS, we +first look for the operation from this source CRS to another compound CRS made +of the geographic CRS base of the projected CRS, +like “NAD83 / California zone 1 (ftUS) + NAVD88 height” to “NAD83 + NAVD88 height”, +which ultimately goes to one of the above described case. Then we can consider +the transformation from a compound CRS made of a geographic CRS to another geographic CRS.</p> +<p>It first starts by the vertical transformations from the vertical CRS of the +source compound CRS to the target geographic CRS, using the strategy detailed +in <a class="reference internal" href="#verttogeog"><span class="std std-ref">Vertical CRS to a Geographic CRS</span></a></p> +<p>What we did not mention is that when there is not a transformation registered +between the vertical CRS and the target geographic CRS, PROJ attempts to find +transformations between that vertical CRS and any other geographic CRS. This is +clearly an approximation. +If the research of the vertical CRS to the target geographic CRS resulted in +operations that use grids that are not available, as another approximation, we +research operations from the vertical CRS to the source geographic CRS for the +vertical component.</p> +<p>Once we got those more or less accurate vertical transformations, we must consider +the horizontal transformation(s). The algorithm iterates over all found vertical +transformations and look for their target geographic CRS. This will be used as +the interpolation CRS for horizontal transformations. PROJ will then look for +available transformations from the source geographic CRS to the interpolation CRS +and from the interpolation CRS to the target geographic CRS. There is then a +3-level loop to create the final set of operations chaining together:</p> +<ul class="simple"> +<li><p>the horizontal transformation from the source geographic CRS to the interpolation CRS</p></li> +<li><p>the vertical transformation from the source vertical CRS to the interpolation CRS</p></li> +<li><p>the horizontal transformation from the interpolation CRS to the target geographic CRS.</p></li> +</ul> +<p>This is implemented by the <code class="docutils literal notranslate"><span class="pre">createOperationsCompoundToGeog</span></code> method</p> +<p>Example:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s <span class="s2">"NAD83(NSRS2007) + NAVD88 height"</span> -t <span class="s2">"WGS 84 (G1762)"</span> --spatial-test intersects --summary + +Candidate operations found: <span class="m">21</span> +unknown id, Inverse of NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.05 m, USA - CONUS - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">7</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, <span class="m">95</span>°W to <span class="m">78</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">7</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, <span class="m">95</span>°W to <span class="m">78</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">6</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, <span class="m">112</span>°W to <span class="m">95</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">6</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, <span class="m">112</span>°W to <span class="m">95</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, <span class="m">112</span>°W to <span class="m">95</span>°W +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, <span class="m">112</span>°W to <span class="m">95</span>°W +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, <span class="m">95</span>°W to <span class="m">78</span>°W +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, <span class="m">95</span>°W to <span class="m">78</span>°W +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">5</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, west of <span class="m">112</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">5</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, west of <span class="m">112</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, west of <span class="m">112</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, west of <span class="m">112</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">4</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, east of <span class="m">78</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">4</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS north of <span class="m">41</span>°N, east of <span class="m">78</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">8</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, east of <span class="m">78</span>°W - onshore +unknown id, Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span>HARN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">8</span><span class="o">)</span> + NAD83<span class="o">(</span>HARN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">3</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, <span class="m">3</span>.15 m, USA - CONUS south of <span class="m">41</span>°N, east of <span class="m">78</span>°W - onshore +unknown id, Ballpark geographic offset from NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> to NAD83<span class="o">(</span>FBN<span class="o">)</span> + Inverse of NAD83<span class="o">(</span>FBN<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Ballpark geographic offset from NAD83<span class="o">(</span>FBN<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, unknown accuracy, USA - CONUS - onshore, has ballpark transformation +unknown id, Ballpark geographic offset from NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> to NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + Ballpark geographic offset from NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span>, unknown accuracy, USA - CONUS - onshore, has ballpark transformation +unknown id, Ballpark geographic offset from NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> to NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> + Inverse of NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + Conversion from NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> <span class="o">(</span>geog2D<span class="o">)</span> to NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> <span class="o">(</span>geocentric<span class="o">)</span> + Inverse of ITRF2008 to NAD83<span class="o">(</span><span class="m">2011</span><span class="o">)</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span> to ITRF2008 <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Conversion from WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span> <span class="o">(</span>geocentric<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span> <span class="o">(</span>geog2D<span class="o">)</span>, unknown accuracy, USA - CONUS - onshore, has ballpark transformation +unknown id, NAD83<span class="o">(</span>NSRS2007<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + WGS <span class="m">84</span> to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span> + Transformation from NAVD88 height to WGS <span class="m">84</span> <span class="o">(</span>G1762<span class="o">)</span> <span class="o">(</span>ballpark vertical transformation, without ellipsoid height to vertical height correction<span class="o">)</span>, unknown accuracy, USA - CONUS and Alaska<span class="p">;</span> PRVI, has ballpark transformation +</pre></div> +</div> +</section> +<section id="compoundcrs-to-compoundcrs"> +<h2>CompoundCRS to CompoundCRS<a class="headerlink" href="#compoundcrs-to-compoundcrs" title="Permalink to this headline">¶</a></h2> +<p>There is some similarity with the previous paragraph. We first research the +vertical transformations between the two vertical CRS.</p> +<ol class="arabic"> +<li><p>If there is such a transformation, be it direct, or if both vertical CRS +relate to a common intermediate CRS. +If it has a registered interpolation geographic CRS, then it is used. +Otherwise we fallback to the geographic CRS of the source CRS.</p> +<p>Finally, a 3-level loop to create the final set of operations chaining together:</p> +<ul class="simple"> +<li><p>the horizontal transformation from the source CRS to the interpolation CRS</p></li> +<li><p>the vertical transformation</p></li> +<li><p>the horizontal transformation from the interpolation CRS to the target CRS.</p></li> +</ul> +<blockquote> +<div><p>Example:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s <span class="s2">"NAD27 + NGVD29 height (ftUS)"</span> -t <span class="s2">"NAD83 + NAVD88 height"</span> --spatial-test intersects --summary + +Candidate operations found: <span class="m">20</span> +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.17 m, USA - CONUS east of <span class="m">89</span>°W - onshore +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.17 m, USA - CONUS <span class="m">89</span>°W-107°W - onshore +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">0</span>.17 m, USA - CONUS west of <span class="m">107</span>°W - onshore +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">1</span>.02 m, unknown domain of validity +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">1</span>.02 m, unknown domain of validity +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, <span class="m">1</span>.02 m, unknown domain of validity +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">5</span><span class="o">)</span>, <span class="m">1</span>.02 m, unknown domain of validity, at least one grid missing +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">6</span><span class="o">)</span>, <span class="m">1</span>.52 m, unknown domain of validity, at least one grid missing +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">9</span><span class="o">)</span>, <span class="m">1</span>.52 m, unknown domain of validity, at least one grid missing +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">9</span><span class="o">)</span>, <span class="m">1</span>.52 m, unknown domain of validity, at least one grid missing +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">3</span><span class="o">)</span> + Ballpark geographic offset from NAD27 to NAD83, unknown accuracy, USA - CONUS east of <span class="m">89</span>°W - onshore, has ballpark transformation +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">2</span><span class="o">)</span> + Ballpark geographic offset from NAD27 to NAD83, unknown accuracy, USA - CONUS <span class="m">89</span>°W-107°W - onshore, has ballpark transformation +unknown id, NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Ballpark geographic offset from NAD27 to NAD83, unknown accuracy, USA - CONUS west of <span class="m">107</span>°W - onshore, has ballpark transformation +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">1</span><span class="o">)</span>, unknown accuracy, USA - CONUS including EEZ, has ballpark transformation +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">3</span><span class="o">)</span>, unknown accuracy, Canada, has ballpark transformation +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">4</span><span class="o">)</span>, unknown accuracy, Canada - NAD27, has ballpark transformation +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">5</span><span class="o">)</span>, unknown accuracy, Canada - Quebec, has ballpark transformation, at least one grid missing +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">6</span><span class="o">)</span>, unknown accuracy, Canada - Quebec, has ballpark transformation, at least one grid missing +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + NAD27 to NAD83 <span class="o">(</span><span class="m">9</span><span class="o">)</span>, unknown accuracy, Canada - Saskatchewan, has ballpark transformation, at least one grid missing +unknown id, Transformation from NGVD29 height <span class="o">(</span>ftUS<span class="o">)</span> to NAVD88 height <span class="o">(</span>ballpark vertical transformation<span class="o">)</span> + Ballpark geographic offset from NAD27 to NAD83, unknown accuracy, World, has ballpark transformation +</pre></div> +</div> +</div></blockquote> +</li> +<li><p>Otherwise, when there is no such transformation, we decompose into 3 steps:</p> +<ul class="simple"> +<li><p>transform from the source CRS to the geographic 3D CRS corresponding to it</p></li> +<li><p>transform from the geographic 3D CRS corresponding to the source CRS to the +geographic 3D CRS corresponding to the target CRS</p></li> +<li><p>transform from the geographic 3D CRS corresponding to the target CRS to the +target CRS.</p></li> +</ul> +<blockquote> +<div><p>Example:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s <span class="s2">"WGS 84 + EGM96 height"</span> -t <span class="s2">"ETRS89 + Belfast height"</span> --spatial-test intersects --summary + +Candidate operations found: <span class="m">7</span> +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of ETRS89 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">2</span>.014 m, UK - Northern Ireland - onshore +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Inverse of ETRS89 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">2</span>.03 m, UK - Northern Ireland - onshore, at least one grid missing +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Null geographic offset from WGS <span class="m">84</span> <span class="o">(</span>geog3D<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>geog2D<span class="o">)</span> + Inverse of OSGB <span class="m">1936</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">4</span><span class="o">)</span> + OSGB <span class="m">1936</span> to ETRS89 <span class="o">(</span><span class="m">2</span><span class="o">)</span> + Null geographic offset from ETRS89 <span class="o">(</span>geog2D<span class="o">)</span> to ETRS89 <span class="o">(</span>geog3D<span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">19</span>.044 m, unknown domain of validity +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Null geographic offset from WGS <span class="m">84</span> <span class="o">(</span>geog3D<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>geog2D<span class="o">)</span> + Inverse of OSGB <span class="m">1936</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">2</span><span class="o">)</span> + OSGB <span class="m">1936</span> to ETRS89 <span class="o">(</span><span class="m">2</span><span class="o">)</span> + Null geographic offset from ETRS89 <span class="o">(</span>geog2D<span class="o">)</span> to ETRS89 <span class="o">(</span>geog3D<span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">11</span>.044 m, unknown domain of validity +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Null geographic offset from WGS <span class="m">84</span> <span class="o">(</span>geog3D<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>geog2D<span class="o">)</span> + Inverse of TM75 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">2</span><span class="o">)</span> + TM75 to ETRS89 <span class="o">(</span><span class="m">3</span><span class="o">)</span> + Null geographic offset from ETRS89 <span class="o">(</span>geog2D<span class="o">)</span> to ETRS89 <span class="o">(</span>geog3D<span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">2</span><span class="o">)</span>, <span class="m">2</span>.424 m, UK - Northern Ireland - onshore, at least one grid missing +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Null geographic offset from WGS <span class="m">84</span> <span class="o">(</span>geog3D<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>geog2D<span class="o">)</span> + Inverse of TM75 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">2</span><span class="o">)</span> + TM75 to ETRS89 <span class="o">(</span><span class="m">3</span><span class="o">)</span> + Null geographic offset from ETRS89 <span class="o">(</span>geog2D<span class="o">)</span> to ETRS89 <span class="o">(</span>geog3D<span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">2</span>.44 m, UK - Northern Ireland - onshore, at least one grid missing +unknown id, Inverse of WGS <span class="m">84</span> to EGM96 height <span class="o">(</span><span class="m">1</span><span class="o">)</span> + Null geographic offset from WGS <span class="m">84</span> <span class="o">(</span>geog3D<span class="o">)</span> to WGS <span class="m">84</span> <span class="o">(</span>geog2D<span class="o">)</span> + Inverse of OSGB <span class="m">1936</span> to WGS <span class="m">84</span> <span class="o">(</span><span class="m">4</span><span class="o">)</span> + OSGB <span class="m">1936</span> to ETRS89 <span class="o">(</span><span class="m">2</span><span class="o">)</span> + Null geographic offset from ETRS89 <span class="o">(</span>geog2D<span class="o">)</span> to ETRS89 <span class="o">(</span>geog3D<span class="o">)</span> + ETRS89 to Belfast height <span class="o">(</span><span class="m">1</span><span class="o">)</span>, <span class="m">19</span>.06 m, unknown domain of validity, at least one grid missing +</pre></div> +</div> +</div></blockquote> +</li> +</ol> +<p>This is implemented by the <code class="docutils literal notranslate"><span class="pre">createOperationsCompoundToCompound</span></code> method</p> +</section> +<section id="when-the-source-or-target-crs-is-a-boundcrs"> +<h2>When the source or target CRS is a BoundCRS<a class="headerlink" href="#when-the-source-or-target-crs-is-a-boundcrs" title="Permalink to this headline">¶</a></h2> +<p>The BoundCRS concept is an hybrid concept where a CRS is linked to a transformation +from it to a hub CRS, typically WGS 84. This is a long-time practice in PROJ.4 +strings with the <code class="docutils literal notranslate"><span class="pre">+towgs84</span></code>, <code class="docutils literal notranslate"><span class="pre">+nadgrids</span></code> and <code class="docutils literal notranslate"><span class="pre">+geoidgrids</span></code> keywords, or the +<code class="docutils literal notranslate"><span class="pre">TOWGS84[]</span></code> node of WKT 1. When encountering those attributes when parsing +a CRS string, PROJ will create a BoundCRS object capturing this transformation. +A BoundCRS object can also be provided with a WKT2 string, and in that case with +a hub CRS being potentially different from WGS 84.</p> +<p>Let’s consider the case of a transformation between a BoundCRS +(“+proj=tmerc +lat_0=49 +lon_0=-2 +k=0.9996012717 +x_0=400000 +y_0=-100000 ++ellps=airy +towgs84=446.448,-125.157,542.06,0.15,0.247,0.842,-20.489 +units=m” +which used to be the PROJ.4 definition of “OSGB 1936 / British National Grid”) +and a target Geographic CRS, ETRS89.</p> +<p>We apply the following steps:</p> +<ul class="simple"> +<li><p>transform from the base of the source CRS (that is the CRS wrapped by BoundCRS, +here a ProjectedCRS) to the geographic CRS of this base CRS</p></li> +<li><p>apply the transformation of the BoundCRS to go from the geographic CRS of this base CRS +to the hub CRS of the BoundCRS, in that instance WGS 84.</p></li> +<li><p>apply a transformation from the hub CRS to the target CRS.</p></li> +</ul> +<p>This is implemented by the <code class="docutils literal notranslate"><span class="pre">createOperationsBoundToGeog</span></code> method</p> +<p>Example:</p> +<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ projinfo -s <span class="s2">"+proj=tmerc +lat_0=49 +lon_0=-2 +k=0.9996012717 +x_0=400000 +y_0=-100000 +ellps=airy +towgs84=446.448,-125.157,542.06,0.15,0.247,0.842,-20.489 +units=m +type=crs"</span> -t ETRS89 -o PROJ + +Candidate operations found: <span class="m">1</span> +------------------------------------- +Operation No. <span class="m">1</span>: + +unknown id, Inverse of unknown + Transformation from unknown to WGS84 + Inverse of ETRS89 to WGS <span class="m">84</span> <span class="o">(</span><span class="m">1</span><span class="o">)</span>, unknown accuracy, Europe - ETRS89 + +PROJ string: ++proj<span class="o">=</span>pipeline +step +inv +proj<span class="o">=</span>tmerc +lat_0<span class="o">=</span><span class="m">49</span> +lon_0<span class="o">=</span>-2 +k<span class="o">=</span><span class="m">0</span>.9996012717 +x_0<span class="o">=</span><span class="m">400000</span> +y_0<span class="o">=</span>-100000 +ellps<span class="o">=</span>airy +step +proj<span class="o">=</span>push +v_3 +step +proj<span class="o">=</span>cart +ellps<span class="o">=</span>airy +step +proj<span class="o">=</span>helmert +x<span class="o">=</span><span class="m">446</span>.448 +y<span class="o">=</span>-125.157 +z<span class="o">=</span><span class="m">542</span>.06 +rx<span class="o">=</span><span class="m">0</span>.15 +ry<span class="o">=</span><span class="m">0</span>.247 +rz<span class="o">=</span><span class="m">0</span>.842 +s<span class="o">=</span>-20.489 +convention<span class="o">=</span>position_vector +step +inv +proj<span class="o">=</span>cart +ellps<span class="o">=</span>GRS80 +step +proj<span class="o">=</span>pop +v_3 +step +proj<span class="o">=</span>unitconvert +xy_in<span class="o">=</span>rad +xy_out<span class="o">=</span>deg +step +proj<span class="o">=</span>axisswap +order<span class="o">=</span><span class="m">2</span>,1 +</pre></div> +</div> +<p>There are other situations with BoundCRS, involving vertical transformations, +or transforming to other objects than a geographic CRS, but the curious reader +will have to inspect the code for the actual gory details.</p> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="pipeline.html" class="btn btn-neutral float-left" title="The pipeline operator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../resource_files.html" class="btn btn-neutral float-right" title="Resource files" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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title="Geocentric grid shift" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="operations_computation.html" class="btn btn-neutral float-right" title="Computation of coordinate operations between two CRS" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="the-pipeline-operator"> +<span id="pipeline"></span><h1>The pipeline operator<a class="headerlink" href="#the-pipeline-operator" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Construct complex operations by daisy-chaining operations in a sequential pipeline.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>pipeline</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D, 3D and 4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Any</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Any</p></td> +</tr> +</tbody> +</table> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>See the section on <a class="reference internal" href="../usage/transformation.html#transformation"><span class="std std-ref">Geodetic transformation</span></a> for a more thorough introduction +to the concept of transformation pipelines in PROJ.</p> +</div> +<p>With the pipeline operation it is possible to perform several operations after each +other on the same input data. This feature makes it possible to create transformations +that are made up of more than one operation, e.g. performing a datum shift and then +applying a suitable map projection. Theoretically any transformation between two +coordinate reference systems is possible to perform using the pipeline operation, +provided that the necessary coordinate operations in each step is available in PROJ.</p> +<p>A pipeline is made up of a number of steps, with each step being a coordinate operation +in itself. By connecting these individual steps sequentially we end up with a concatenated +coordinate operation. An example of this is a transformation from geodetic coordinates +on the GRS80 ellipsoid to a projected system where the east-west and north-east axes has +been swapped:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +ellps=GRS80 +step +proj=merc +step +proj=axisswap +order=2,1 +</pre></div> +</div> +<p>Here the first step is applying the <a class="reference internal" href="projections/merc.html#merc"><span class="std std-ref">Mercator</span></a> projection and the second step is +applying the <a class="reference internal" href="conversions/axisswap.html#axisswap"><span class="std std-ref">Axis swap</span></a> conversion. Note that the <cite>+ellps=GRS80</cite> is specified +before the first occurrence of <cite>+step</cite>. This means that the GRS80 ellipsoid is used +in both steps, since any parameter stated before the first occurrence of <cite>+step</cite> is +treated as a global parameter and is transferred to each individual steps.</p> +<section id="rules-for-pipelines"> +<h2>Rules for pipelines<a class="headerlink" href="#rules-for-pipelines" title="Permalink to this headline">¶</a></h2> +<p><strong>1. Pipelines must consist of at least one step.</strong></p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +</pre></div> +</div> +<p>Will result in an error.</p> +<p><strong>2. Pipelines can only be nested if the nested pipeline is defined in an init file.</strong></p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline ++step +proj=pipeline +step +proj=merc +step +proj=axisswap +order=2,1 ++step +proj=unitconvert +xy_in=m +xy_out=us-ft +</pre></div> +</div> +<p>Results in an error, while</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline ++step +init=predefined_pipelines:projectandswap ++step +proj=unitconvert +xy_in=m +xy_out=us-ft +</pre></div> +</div> +<p>does not.</p> +<p><strong>3. Pipelines without a forward path can’t be constructed.</strong></p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +step +inv +proj=urm5 +</pre></div> +</div> +<p>Will result in an error since <a class="reference internal" href="projections/urm5.html#urm5"><span class="std std-ref">Urmaev V</span></a> does not have an inverse operation defined.</p> +<p id="global-pipeline-parameter"><strong>4. Parameters added before the first `+step` are global and will be applied to all steps.</strong></p> +<p>In the following the GRS80 ellipsoid will be applied to all steps.</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +ellps=GRS80 ++step +proj=cart ++step +proj=helmert +x=10 +y=3 +z=1 ++step +proj=cart +inv ++step +proj=merc +</pre></div> +</div> +<p><strong>5. Units of operations must match between steps.</strong></p> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<p>The output units of step <em>n</em> must match the expected input unit of step <em>n+1</em>. E.g., you can’t +pass an operation that outputs projected coordinates to an operation that expects angular units +(degrees). An example of such a unit mismatch is displayed below.</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline ++step +proj=merc # Mercator outputs projected coordinates ++step +proj=robin # The Robinson projection expects angular input +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-step"> +<span class="sig-name descname"><span class="pre">+step</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-step" title="Permalink to this definition">¶</a></dt> +<dd><p>Separate each step in a pipeline.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-inv"> +<span class="sig-name descname"><span class="pre">+inv</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-inv" title="Permalink to this definition">¶</a></dt> +<dd><p>Invert a step in a pipeline.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-omit_fwd"> +<span id="cmdoption-arg-omit-fwd"></span><span class="sig-name descname"><span class="pre">+omit_fwd</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-omit_fwd" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 6.3.0.</span></p> +</div> +<p>Skip a step of the pipeline when it is followed in the forward path.</p> +<p>The following example shows a combined use of <a class="reference internal" href="conversions/push.html#push"><span class="std std-ref">push</span></a> and <a class="reference internal" href="conversions/pop.html#pop"><span class="std std-ref">pop</span></a> operators, +with <code class="docutils literal notranslate"><span class="pre">omit_fwd</span></code> and <code class="docutils literal notranslate"><span class="pre">omit_inv</span></code> options, to implement a vertical adjustment that must +be done in a interpolation CRS that is different from the horizontal CRS +used in input and output. +omit_fwd in the forward path avoid a useless +inverse horizontal transformation and relies on the pop operator to restore +initial horizontal coordinates. +omit_inv serves the similar purpose when +the pipeline is executed in the reverse direction</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline ++step +proj=unitconvert +xy_in=deg +xy_out=rad ++step +proj=push +v_1 +v_2 ++step +proj=hgridshift +grids=nvhpgn.gsb +omit_inv ++step +proj=vgridshift +grids=g1999u05.gtx +multiplier=1 ++step +inv +proj=hgridshift +grids=nvhpgn.gsb +omit_fwd ++step +proj=pop +v_1 +v_2 ++step +proj=unitconvert +xy_in=rad +xy_out=deg +</pre></div> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-omit_inv"> +<span id="cmdoption-arg-omit-inv"></span><span class="sig-name descname"><span class="pre">+omit_inv</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-omit_inv" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 6.3.0.</span></p> +</div> +<p>Skip a step of the pipeline when it is followed in the reverse path.</p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="transformations/xyzgridshift.html" class="btn btn-neutral float-left" title="Geocentric grid shift" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="operations_computation.html" class="btn btn-neutral float-right" title="Computation of coordinate operations between two CRS" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="adams_ws1.html" class="btn btn-neutral float-right" title="Adams World in a Square I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="adams-hemisphere-in-a-square"> +<span id="adams-hemi"></span><h1>Adams Hemisphere in a Square<a class="headerlink" href="#adams-hemisphere-in-a-square" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>adams_hemi</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/adams_hemi.png"><img alt="Adams Hemisphere in a Square" src="../../_images/adams_hemi.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=adams_hemi</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="index.html" class="btn btn-neutral float-left" title="Projections" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="adams_ws1.html" class="btn btn-neutral float-right" title="Adams World in a Square I" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Adams World in a Square I</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/adams_ws1.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="adams_hemi.html" class="btn btn-neutral float-left" title="Adams Hemisphere in a Square" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="adams_ws2.html" class="btn btn-neutral float-right" title="Adams World in a Square II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="adams-world-in-a-square-i"> +<span id="adams-ws1"></span><h1>Adams World in a Square I<a class="headerlink" href="#adams-world-in-a-square-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>adams_ws1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/adams_ws1.png"><img alt="Adams World in a Square I" src="../../_images/adams_ws1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=adams_ws1</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="adams_hemi.html" class="btn btn-neutral float-left" title="Adams Hemisphere in a Square" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="adams_ws2.html" class="btn btn-neutral float-right" title="Adams World in a Square II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Square I" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="aea.html" class="btn btn-neutral float-right" title="Albers Equal Area" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="adams-world-in-a-square-ii"> +<span id="adams-ws2"></span><h1>Adams World in a Square II<a class="headerlink" href="#adams-world-in-a-square-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>adams_ws2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/adams_ws2.png"><img alt="Adams World in a Square II" src="../../_images/adams_ws2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=adams_ws2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="adams_ws1.html" class="btn btn-neutral float-left" title="Adams World in a Square I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="aea.html" class="btn btn-neutral float-right" title="Albers Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Albers Equal Area</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/aea.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="adams_ws2.html" class="btn btn-neutral float-left" title="Adams World in a Square II" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="aeqd.html" class="btn btn-neutral float-right" title="Azimuthal Equidistant" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="albers-equal-area"> +<span id="aea"></span><h1>Albers Equal Area<a class="headerlink" href="#albers-equal-area" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conic</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>aea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/aea.png"><img alt="Albers Equal Area" src="../../_images/aea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=aea</span> <span class="pre">+lat_1=29.5</span> <span class="pre">+lat_2=42.5</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="adams_ws2.html" class="btn btn-neutral float-left" title="Adams World in a Square II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="aeqd.html" class="btn btn-neutral float-right" title="Azimuthal Equidistant" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-label="Sequential page navigation"> + <a href="aea.html" class="btn btn-neutral float-left" title="Albers Equal Area" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="airy.html" class="btn btn-neutral float-right" title="Airy" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="azimuthal-equidistant"> +<span id="aeqd"></span><h1>Azimuthal Equidistant<a class="headerlink" href="#azimuthal-equidistant" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>aeqd</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/aeqd.png"><img alt="Azimuthal Equidistant" src="../../_images/aeqd.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=aeqd</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the Azimuthal Equidistant projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-guam"> +<span class="sig-name descname"><span class="pre">+guam</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-guam" title="Permalink to this definition">¶</a></dt> +<dd><p>Use Guam ellipsoidal formulas. Only accurate near the Island of Guam +(<span class="math notranslate nohighlight">\(\lambda\approx 144.5^{\circ}\)</span>, <span class="math notranslate nohighlight">\(\phi\approx 13.5^{\circ}\)</span>)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="aea.html" class="btn btn-neutral float-left" title="Albers Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="airy.html" class="btn btn-neutral float-right" title="Airy" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Airy</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/airy.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="aeqd.html" class="btn btn-neutral float-left" title="Azimuthal Equidistant" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="aitoff.html" class="btn btn-neutral float-right" title="Aitoff" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="airy"> +<span id="id1"></span><h1>Airy<a class="headerlink" href="#airy" title="Permalink to this headline">¶</a></h1> +<p>The Airy projection is an azimuthal minimum error projection for the region +within the small or great circle defined by an angular distance, +<span class="math notranslate nohighlight">\(\phi_b\)</span>, from the tangency point of the plane <span class="math notranslate nohighlight">\(( \lambda_0, \phi_0 )\)</span>.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>airy</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/airy.png"><img alt="Airy" src="../../_images/airy.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=airy</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_b"> +<span id="cmdoption-arg-lat-b"></span><span class="sig-name descname"><span class="pre">+lat_b</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-lat_b" title="Permalink to this definition">¶</a></dt> +<dd><p>Angular distance from tangency point of the plane <span class="math notranslate nohighlight">\(( \lambda_0, \phi_0 )\)</span> +where the error is kept at minimum.</p> +<p><em>Defaults to 90° (suitable for hemispherical maps).</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-no_cut"> +<span id="cmdoption-arg-no-cut"></span><span class="sig-name descname"><span class="pre">+no_cut</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-no_cut" title="Permalink to this definition">¶</a></dt> +<dd><p>Do not cut at hemisphere limit</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="aeqd.html" class="btn btn-neutral float-left" title="Azimuthal Equidistant" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="aitoff.html" class="btn btn-neutral float-right" title="Aitoff" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Aitoff</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/aitoff.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="airy.html" class="btn btn-neutral float-left" title="Airy" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="alsk.html" class="btn btn-neutral float-right" title="Modified Stereographic of Alaska" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="aitoff"> +<span id="id1"></span><h1>Aitoff<a class="headerlink" href="#aitoff" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>aitoff</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/aitoff.png"><img alt="Aitoff" src="../../_images/aitoff.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=aitoff</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="airy.html" class="btn btn-neutral float-left" title="Airy" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="alsk.html" class="btn btn-neutral float-right" title="Modified Stereographic of Alaska" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="apian.html" class="btn btn-neutral float-right" title="Apian Globular I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="modified-stereographic-of-alaska"> +<span id="alsk"></span><h1>Modified Stereographic of Alaska<a class="headerlink" href="#modified-stereographic-of-alaska" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Modified azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Alaska</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alsk</strong></p></td> +<td><p>alsk</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/alsk.png"><img alt="Modified Stereographic of Alaska" src="../../_images/alsk.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=alsk</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> 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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Apian Globular I</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/apian.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="alsk.html" class="btn btn-neutral float-left" title="Modified Stereographic of Alaska" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="august.html" class="btn btn-neutral float-right" title="August Epicycloidal" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="apian-globular-i"> +<span id="apian"></span><h1>Apian Globular I<a class="headerlink" href="#apian-globular-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>apian</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/apian.png"><img alt="Apian Globular I" src="../../_images/apian.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=apian</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the Apian Globular projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="alsk.html" class="btn btn-neutral float-left" title="Modified Stereographic of Alaska" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="august.html" class="btn btn-neutral float-right" title="August Epicycloidal" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bacon.html" class="btn btn-neutral float-right" title="Bacon Globular" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="august-epicycloidal"> +<span id="august"></span><h1>August Epicycloidal<a class="headerlink" href="#august-epicycloidal" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>august</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/august.png"><img alt="August Epicycloidal" src="../../_images/august.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=august</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the August Epicycloidal projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="apian.html" class="btn btn-neutral float-left" title="Apian Globular I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bacon.html" class="btn btn-neutral float-right" title="Bacon Globular" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Bacon Globular</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/bacon.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="august.html" class="btn btn-neutral float-left" title="August Epicycloidal" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bertin1953.html" class="btn btn-neutral float-right" title="Bertin 1953" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="bacon-globular"> +<span id="bacon"></span><h1>Bacon Globular<a class="headerlink" href="#bacon-globular" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>bacon</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/bacon.png"><img alt="Bacon Globular" src="../../_images/bacon.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=bacon</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Bacon Globular projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="august.html" class="btn btn-neutral float-left" title="August Epicycloidal" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bertin1953.html" class="btn btn-neutral float-right" title="Bertin 1953" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/bertin1953.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="bacon.html" class="btn btn-neutral float-left" title="Bacon Globular" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bipc.html" class="btn btn-neutral float-right" title="Bipolar conic of western hemisphere" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="bertin-1953"> +<span id="bertin1953"></span><h1>Bertin 1953<a class="headerlink" href="#bertin-1953" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 40%" /> +<col style="width: 60%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>bertin1953</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/bertin1953.png"><img alt="Bertin 1953" src="../../_images/bertin1953.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=bertin1953</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>The Bertin 1953 projection is intended for making world maps. Created by Jacques Bertin +in 1953, this projection was the go-to choice of the French cartographic school when they +wished to represent phenomena on a global scale. The projection was formulated in 2017 +by Philippe Rivière for visionscarto.net.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The Bertin 1953 projection has no special options. Its rotation parameters +are fixed. Here is an example of a forward projection with scale 1:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 122 47 | src/proj +proj=bertin1953 +R=1 +0.72 0.73 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p>Philippe Rivière (2017). <cite>Bertin Projection (1953) <https://visionscarto.net/bertin-projection-1953></cite>, Visionscarto.net.</p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="bacon.html" class="btn btn-neutral float-left" title="Bacon Globular" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bipc.html" class="btn btn-neutral float-right" title="Bipolar conic of western hemisphere" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="boggs.html" class="btn btn-neutral float-right" title="Boggs Eumorphic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="bipolar-conic-of-western-hemisphere"> +<span id="bipc"></span><h1>Bipolar conic of western hemisphere<a class="headerlink" href="#bipolar-conic-of-western-hemisphere" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>bipc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/bipc.png"><img alt="Bipolar conic of western hemisphere" src="../../_images/bipc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=bipc</span> <span class="pre">+ns</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the Bipolar Conic projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ns"> +<span class="sig-name descname"><span class="pre">+ns</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-ns" title="Permalink to this definition">¶</a></dt> +<dd><p>Return non-skewed cartesian coordinates.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="bertin1953.html" class="btn btn-neutral float-left" title="Bertin 1953" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="boggs.html" class="btn btn-neutral float-right" title="Boggs Eumorphic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> 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VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" 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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bonne.html" class="btn btn-neutral float-right" title="Bonne (Werner lat_1=90)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="boggs-eumorphic"> +<span id="boggs"></span><h1>Boggs Eumorphic<a class="headerlink" href="#boggs-eumorphic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>boggs</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/boggs.png"><img alt="Boggs Eumorphic" src="../../_images/boggs.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=boggs</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the Boggs Eumorphic projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="bipc.html" class="btn btn-neutral float-left" title="Bipolar conic of western hemisphere" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="bonne.html" class="btn btn-neutral float-right" title="Bonne (Werner lat_1=90)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Bonne (Werner lat_1=90)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/bonne.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="boggs.html" class="btn btn-neutral float-left" title="Boggs Eumorphic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="calcofi.html" class="btn btn-neutral float-right" title="Cal Coop Ocean Fish Invest Lines/Stations" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="bonne-werner-lat-1-90"> +<span id="bonne"></span><h1>Bonne (Werner lat_1=90)<a class="headerlink" href="#bonne-werner-lat-1-90" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>bonne</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/bonne.png"><img alt="Bonne (Werner lat_1=90)" src="../../_images/bonne.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=bonne</span> <span class="pre">+lat_1=10</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="boggs.html" class="btn btn-neutral float-left" title="Boggs Eumorphic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="calcofi.html" class="btn btn-neutral float-right" title="Cal Coop Ocean Fish Invest Lines/Stations" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Lines/Stations</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/calcofi.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="bonne.html" class="btn btn-neutral float-left" title="Bonne (Werner lat_1=90)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cass.html" class="btn btn-neutral float-right" title="Cassini (Cassini-Soldner)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="cal-coop-ocean-fish-invest-lines-stations"> +<span id="calcofi"></span><h1>Cal Coop Ocean Fish Invest Lines/Stations<a class="headerlink" href="#cal-coop-ocean-fish-invest-lines-stations" title="Permalink to this headline">¶</a></h1> +<p>The CalCOFI pseudo-projection is the line and station coordinate system of the +California Cooperative Oceanic Fisheries Investigations program, known as CalCOFI, for sampling offshore of the west coast of the U.S. and Mexico.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Only valid for the west coast of USA and Mexico</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>calcofi</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<a class="reference internal image-reference" href="../../_images/calcofi.png"><img alt="Cal Coop Ocean Fish Invest Lines/Stations" class="align-center" src="../../_images/calcofi.png" style="width: 500px;" /></a> +<p>The coordinate system is based on the Mercator projection with units rotated -30 +degrees from the meridian so that they are oriented with the coastline of the Southern California Bight and Baja California. +Lines increase from Northwest to Southeast. +A unit of line is 12 nautical miles. Stations increase from inshore to offshore. +A unit of station is equal to 4 nautical miles. +The rotation point is located at line 80, station 60, or 34.15 degrees N, -121.15 degrees W, and is depicted by the red dot in the figure. +By convention, the ellipsoid of Clarke 1866 is used to calculate CalCOFI coordinates.</p> +<p>The CalCOFI program is a joint research effort by the U.S. National Oceanic and +Atmospheric Administration, University of California Scripps Oceanographic Institute, and California Department of Fish and Game. +Surveys have been conducted for the CalCOFI program since 1951, creating one of the oldest and most scientifically valuable joint oceanographic and fisheries data sets in the world. +The CalCOFI line and station coordinate system is now used by several other programs including the Investigaciones Mexicanas de la Corriente de California (IMECOCAL) program offshore of Baja California. +The figure depicts some commonly sampled locations from line 40 to line 156.7 and offshore to station 120. Blue numbers indicate line (bottom) or station (left) numbers along the grid. Note that lines spaced at approximate 3-1/3 intervals are commonly sampled, e.g., lines 43.3 and 46.7.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>A typical forward CalCOFI projection would be from lon/lat coordinates on the +Clark 1866 ellipsoid. +For example:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj +proj=calcofi +ellps=clrk66 -E <<EOF +-121.15 34.15 +EOF +</pre></div> +</div> +<p>Output of the above command:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>-121.15 34.15 80.00 60.00 +</pre></div> +</div> +<p>The reverse projection from line/station coordinates to lon/lat would be entered +as:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj +proj=calcofi +ellps=clrk66 -I -E -f "%.2f" <<EOF +80.0 60.0 +EOF +</pre></div> +</div> +<p>Output of the above command:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>80.0 60.0 -121.15 34.15 +</pre></div> +</div> +</section> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the CalCOFI projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The algorithm used to make conversions is described in <span id="id1">[<a class="reference internal" href="../../zreferences.html#id9" title="Eber, L. E. and Hewitt, R. P. Conversion algorithms for the CalCOFI station grid. California Cooperative Oceanic Fisheries Investigations Reports, 20:135–137, 1979. URL: http://www.calcofi.org/publications/calcofireports/v20/Vol_20_Eber___Hewitt.pdf.">EberHewitt1979</a>]</span> with +a few corrections reported in <span id="id2">[<a class="reference internal" href="../../zreferences.html#id42" title="Weber, E. D. and Moore, T. J. Corrected conversion algorithms for the CalCOFI station grid and their implementation in several computer languages. California Cooperative Oceanic Fisheries Investigations Reports, 54:1–10, 2013. URL: http://calcofi.org/publications/calcofireports/v54/Vol_54_Weber.pdf.">WeberMoore2013</a>]</span>.</p> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="http://www.calcofi.org">General information about the CalCOFI program</a></p></li> +<li><p><a class="reference external" href="http://imecocal.cicese.mx">The Investigaciones Mexicanas de la Corriente de California</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="bonne.html" class="btn btn-neutral float-left" title="Bonne (Werner lat_1=90)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cass.html" class="btn btn-neutral float-right" title="Cassini (Cassini-Soldner)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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<li>Cassini (Cassini-Soldner)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/cass.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="calcofi.html" class="btn btn-neutral float-left" title="Cal Coop Ocean Fish Invest Lines/Stations" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cc.html" class="btn btn-neutral float-right" title="Central Cylindrical" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="cassini-cassini-soldner"> +<span id="cass"></span><h1>Cassini (Cassini-Soldner)<a class="headerlink" href="#cassini-cassini-soldner" title="Permalink to this headline">¶</a></h1> +<p>Although the Cassini projection has been largely replaced by the Transverse Mercator, it is still in limited use outside the United States and was one of the major topographic mapping projections until the early 20th century.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 22%" /> +<col style="width: 78%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Transverse and oblique cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, Spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but best used near the central meridian with long, narrow areas</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>cass</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id6"> +<a class="reference internal image-reference" href="../../_images/cass.png"><img alt="Cassini" src="../../_images/cass.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=cass</span></code></span><a class="headerlink" href="#id6" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>There has been little usage of the spherical version of the Cassini, but the ellipsoidal Cassini-Soldner version was adopted by the Ordnance Survey for the official survey of Great Britain during the second half of the 19th century <span id="id1">[<a class="reference internal" href="../../zreferences.html#id38" title="Steers, J. A. An introduction to the study of map projections. University of London Press, 15th edition, 1970.">Steers1970</a>]</span>. +Many of these maps were prepared at a scale of 1:2,500. +The Cassini-Soldner was also used for the detailed mapping of many German states during the same period.</p> +<p>Example using EPSG 30200 (Trinidad 1903, units in clarke’s links):</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 0.17453293 -1.08210414 | proj +proj=cass +lat_0=10.44166666666667 +lon_0=-61.33333333333334 +x_0=86501.46392051999 +y_0=65379.0134283 +a=6378293.645208759 +b=6356617.987679838 +to_meter=0.201166195164 +66644.94 82536.22 +</pre></div> +</div> +<p>Example using EPSG 3068 (Soldner Berlin):</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 13.5 52.4 | proj +proj=cass +lat_0=52.41864827777778 +lon_0=13.62720366666667 +x_0=40000 +y_0=10000 +ellps=bessel +units=m +31343.05 7932.76 +</pre></div> +</div> +</section> +<section id="options"> +<h2>Options<a class="headerlink" href="#options" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All options are optional for the Cassini projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-hyperbolic"> +<span class="sig-name descname"><span class="pre">+hyperbolic</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-hyperbolic" title="Permalink to this definition">¶</a></dt> +<dd><p>Use modified form of the standard Cassini-Soldner projection known as the Hyperbolic Cassini-Soldner. +This is used in particular for the “Vanua Levu Grid” of the island of Vanua Levu, Fiji (EPSG:3139)</p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the Cassini projection are taken from <span id="id2">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>.</p> +<p><span class="math notranslate nohighlight">\(\phi_0\)</span> is the latitude of origin that match the center of the map (default to 0). It can be set with <code class="docutils literal notranslate"><span class="pre">+lat_0</span></code>.</p> +<section id="spherical-form"> +<h3>Spherical form<a class="headerlink" href="#spherical-form" title="Permalink to this headline">¶</a></h3> +<section id="forward-projection"> +<h4>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[x = \arcsin(\cos(\phi) \sin(\lambda))\]</div> +<div class="math notranslate nohighlight"> +\[y = \arctan2(\tan(\phi), \cos(\lambda)) - \phi_0\]</div> +</section> +<section id="inverse-projection"> +<h4>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\phi = \arcsin(\sin(y+\phi_0) \cos(x))\]</div> +<div class="math notranslate nohighlight"> +\[\lambda = \arctan2(\tan(x), \cos(y+\phi_0))\]</div> +</section> +</section> +<section id="ellipsoidal-form"> +<h3>Ellipsoidal form<a class="headerlink" href="#ellipsoidal-form" title="Permalink to this headline">¶</a></h3> +<section id="id3"> +<h4>Forward projection<a class="headerlink" href="#id3" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[N = (1 - e^2 \sin^2(\phi))^{-1/2}\]</div> +<div class="math notranslate nohighlight"> +\[T = \tan^2(\phi)\]</div> +<div class="math notranslate nohighlight"> +\[A = \lambda \cos(\phi)\]</div> +<div class="math notranslate nohighlight"> +\[C = \frac{e^2}{1-e^2} cos^2(\phi)\]</div> +<div class="math notranslate nohighlight"> +\[x = N ( A - T \frac{A^3}{6} - (8-T+8C)T\frac{A^5}{120})\]</div> +<div class="math notranslate nohighlight"> +\[y = M(\phi) - M(\phi_0) + N \tan(\phi)(\frac{A^2}{2} + (5-T+6C)\frac{A^4}{24})\]</div> +<p>and M() is the meridional distance function.</p> +</section> +<section id="id4"> +<h4>Inverse projection<a class="headerlink" href="#id4" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\phi' = M^{-1}(M(\phi_0)+y)\]</div> +<p>if <span class="math notranslate nohighlight">\(\phi' = \frac{\pi}{2}\)</span> then <span class="math notranslate nohighlight">\(\phi=\phi'\)</span> and <span class="math notranslate nohighlight">\(\lambda=0\)</span></p> +<p>otherwise evaluate T and N above using <span class="math notranslate nohighlight">\(\phi'\)</span> and</p> +<div class="math notranslate nohighlight"> +\[R = (1 - e^2)(1 - e^2 sin^2 \phi')^{-3/2}\]</div> +<div class="math notranslate nohighlight"> +\[D = x/N\]</div> +<div class="math notranslate nohighlight"> +\[\phi = \phi' - \tan \phi' \frac{N}{R}(\frac{D^2}{2}-(1+3T)\frac{D^4}{24})\]</div> +<div class="math notranslate nohighlight"> +\[\lambda = \frac{(D - T\frac{D^3}{3} + (1+3T)T\frac{D^5}{15})}{\cos \phi'}\]</div> +</section> +</section> +</section> +<section id="further-reading"> +<span id="id5"></span><h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Equirectangular_projection">Wikipedia</a></p></li> +<li><p><a class="reference external" href="http://www.ihsenergy.com/epsg/guid7.pdf">EPSG, POSC literature pertaining to Coordinate Conversions and Transformations including Formulas</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="calcofi.html" class="btn btn-neutral float-left" title="Cal Coop Ocean Fish Invest Lines/Stations" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cc.html" class="btn btn-neutral float-right" title="Central Cylindrical" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Central Cylindrical</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/cc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="cass.html" class="btn btn-neutral float-left" title="Cassini (Cassini-Soldner)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ccon.html" class="btn btn-neutral float-right" title="Central Conic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="central-cylindrical"> +<span id="cc"></span><h1>Central Cylindrical<a class="headerlink" href="#central-cylindrical" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>cc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/cc.png"><img alt="Central Cylindrical" src="../../_images/cc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=cc</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Central Cylindrical projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="cass.html" class="btn btn-neutral float-left" title="Cassini (Cassini-Soldner)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ccon.html" class="btn btn-neutral float-right" title="Central Conic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li 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class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/ccon.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="cc.html" class="btn btn-neutral float-left" title="Central Cylindrical" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cea.html" class="btn btn-neutral float-right" title="Equal Area Cylindrical" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="central-conic"> +<span id="ccon"></span><h1>Central Conic<a class="headerlink" href="#central-conic" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>This is central (centrographic) projection on cone tangent at :option:<code class="docutils literal notranslate"><span class="pre">lat_1</span></code> +latitude, identical with <code class="docutils literal notranslate"><span class="pre">conic()</span></code> projection from <code class="docutils literal notranslate"><span class="pre">mapproj</span></code> R package.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conic</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but best used near the standard parallel</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>ccon</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id4"> +<a class="reference internal image-reference" href="../../_images/ccon.png"><img alt="Central Conic" src="../../_images/ccon.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=ccon</span> <span class="pre">+lat_1=52</span> <span class="pre">+lon_0=19</span></code></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>This simple projection is rarely used, as it is not equidistant, equal-area, nor +conformal.</p> +<p>An example of usage (and the main reason to implement this projection in proj4) +is the ATPOL geobotanical grid of Poland, developed in Institute of Botany, +Jagiellonian University, Krakow, Poland in 1970s <span id="id1">[<a class="reference internal" href="../../zreferences.html#id43" title="Zajaç, A. Atlas of distribution of vascular plants in Poland (ATPOL). Taxon, 27(5/6):481–484, 1978. doi:10.2307/1219899.">Zajac1978</a>]</span>. The grid was +originally handwritten on paper maps and further copied by hand. The projection +(together with strange Earth radius) was chosen by its creators as the compromise +fit to existing maps during first software development in DOS era. Many years later +it is still de facto standard grid in Polish geobotanical research.</p> +<p>The ATPOL coordinates can be achieved with with the following parameters:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=ccon +lat_1=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 +</pre></div> +</div> +<p>For more information see <span id="id2">[<a class="reference internal" href="../../zreferences.html#id23" title="Komsta, Ł. ATPOL geobotanical grid revisited – a proposal of coordinate conversion algorithms. Annales UMCS Sectio E Agricultura, 71(1):31–37, 2016.">Komsta2016</a>]</span> and <span id="id3">[<a class="reference internal" href="../../zreferences.html#id40" title="Verey, M. Theoretical analysis and practical consequences of adopting a model ATPOL grid as a conical projection defining the conversion of plane coordinates to the WGS 84 ellipsoid. Fragmenta Floristica et Geobotanica Polonica, 24(2):469–488, 2017. URL: http://bomax.botany.pl/pubs-new/#article-4279.">Verey2017</a>]</span>.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Standard parallel of projection.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<section id="forward-projection"> +<h3>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[r = \cot \phi_0 - \tan (\phi - \phi_0)\]</div> +<div class="math notranslate nohighlight"> +\[x = r \sin (\lambda\sin\phi_0)\]</div> +<div class="math notranslate nohighlight"> +\[y = \cot \phi_0 - r \cos (\lambda\sin\phi_0)\]</div> +</section> +<section id="inverse-projection"> +<h3>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[y = \cot \phi_0 - y\]</div> +<div class="math notranslate nohighlight"> +\[\phi = \phi_0 - \tan^{-1} ( \sqrt{x^2+y^2} - \cot \phi_0 )\]</div> +<div class="math notranslate nohighlight"> +\[\lambda = \frac{\tan^{-1} \sqrt{x^2+y^2}}{\sin \phi_0}\]</div> +</section> +</section> +<section id="reference-values"> +<h2>Reference values<a class="headerlink" href="#reference-values" title="Permalink to this headline">¶</a></h2> +<p>For ATPOL to WGS84 test, run the following script:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>#!/bin/bash +cat << EOF | src/cs2cs -v -f "%E" +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 +to +proj=longlat +0 0 +0 700000 +700000 0 +700000 700000 +330000 350000 +EOF +</pre></div> +</div> +<p>It should result with</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1.384023E+01 5.503040E+01 0.000000E+00 +1.451445E+01 4.877385E+01 0.000000E+00 +2.478271E+01 5.500352E+01 0.000000E+00 +2.402761E+01 4.875048E+01 0.000000E+00 +1.900000E+01 5.200000E+01 0.000000E+00 +</pre></div> +</div> +<p>Analogous script can be run for reverse test:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>cat << EOF | src/cs2cs -v -f "%E" +proj=longlat +to +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 +24 55 +15 49 +24 49 +19 52 +EOF +</pre></div> +</div> +<p>and it should give the following results:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>6.500315E+05 4.106162E+03 0.000000E+00 +3.707419E+04 6.768262E+05 0.000000E+00 +6.960534E+05 6.722946E+05 0.000000E+00 +3.300000E+05 3.500000E+05 0.000000E+00 +</pre></div> +</div> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="cc.html" class="btn btn-neutral float-left" title="Central Cylindrical" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="cea.html" class="btn btn-neutral float-right" title="Equal Area Cylindrical" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/cea.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="ccon.html" class="btn btn-neutral float-left" title="Central Conic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="chamb.html" class="btn btn-neutral float-right" title="Chamberlin Trimetric" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="equal-area-cylindrical"> +<span id="cea"></span><h1>Equal Area Cylindrical<a class="headerlink" href="#equal-area-cylindrical" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>cea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/cea.png"><img alt="Equal Area Cylindrical" src="../../_images/cea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=cea</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="named-specializations"> +<h2>Named specializations<a class="headerlink" href="#named-specializations" title="Permalink to this headline">¶</a></h2> +<p>The Equal Area Cylindrical projection is sometimes known under other names when +it is instanciated with particular values of the <code class="docutils literal notranslate"><span class="pre">lat_ts</span></code> parameter:</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 74%" /> +<col style="width: 26%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Name</strong></p></td> +<td><p><strong>lat_ts</strong></p></td> +</tr> +<tr class="row-even"><td><p>Lambert cylindrical equal-area</p></td> +<td><p>0</p></td> +</tr> +<tr class="row-odd"><td><p>Behrmann</p></td> +<td><p>30</p></td> +</tr> +<tr class="row-even"><td><p>Gall-Peters</p></td> +<td><p>45</p></td> +</tr> +</tbody> +</table> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Equal Area Cylindrical projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><code class="docutils literal notranslate"><span class="pre">lat_ts</span></code> and <code class="docutils literal notranslate"><span class="pre">k_0</span></code> are mutually exclusive. If <code class="docutils literal notranslate"><span class="pre">lat_ts</span></code> +is specified, it is equivalent to setting <code class="docutils literal notranslate"><span class="pre">k_0</span></code> to +<span class="math notranslate nohighlight">\(\frac{\cos \phi_{ts}}{\sqrt{1 - e^2 \sin^2 \phi_{ts}}}\)</span></p> +</div> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Lambert_cylindrical_equal-area_projection">Wikipedia: Lambert cylindrical equal-area</a></p></li> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection">Wikipedia: Gall-Peters</a></p></li> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Behrmann_projection">Wikipedia: Behrmann</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="ccon.html" class="btn btn-neutral float-left" title="Central Conic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="chamb.html" class="btn btn-neutral float-right" title="Chamberlin Trimetric" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="collg.html" class="btn btn-neutral float-right" title="Collignon" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="chamberlin-trimetric"> +<span id="chamb"></span><h1>Chamberlin Trimetric<a class="headerlink" href="#chamberlin-trimetric" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>chamb</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/chamb.png"><img alt="Chamberlin Trimetric" src="../../_images/chamb.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=chamb</span> <span class="pre">+lat_1=10</span> <span class="pre">+lon_1=30</span> <span class="pre">+lon_2=40</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>Control points should be oriented clockwise.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of the first control point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_1"> +<span id="cmdoption-arg-lon-1"></span><span class="sig-name descname"><span class="pre">+lon_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of the first control point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of the second control point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_2"> +<span id="cmdoption-arg-lon-2"></span><span class="sig-name descname"><span class="pre">+lon_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of the second control point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_3"> +<span id="cmdoption-arg-lat-3"></span><span class="sig-name descname"><span class="pre">+lat_3</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_3" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of the third control point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_3"> +<span id="cmdoption-arg-lon-3"></span><span class="sig-name descname"><span class="pre">+lon_3</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_3" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of the third control point.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="cea.html" class="btn btn-neutral float-left" title="Equal Area Cylindrical" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="collg.html" class="btn btn-neutral float-right" title="Collignon" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" 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VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Colombia Urban</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/col_urban.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="collg.html" class="btn btn-neutral float-left" title="Collignon" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="comill.html" class="btn btn-neutral float-right" title="Compact Miller" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="colombia-urban"> +<span id="col-urban"></span><h1>Colombia Urban<a class="headerlink" href="#colombia-urban" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 7.2.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse ellipsoidal projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>col_urban</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<p>From <span id="id1">[<a class="reference internal" href="../../zreferences.html#id17" title="IOGP. Geomatics guidance note 7, part 2: coordinate conversions & transformations including formulas. IOGP Publication 373-7-2, International Association For Oil And Gas Producers, 2018. URL: https://www.iogp.org/bookstore/product/coordinate-conversions-and-transformation-including-formulas/.">IOGP2018</a>]</span>:</p> +<blockquote> +<div><blockquote> +<div><p>The capital cites of each department in Colombia use an urban projection for large +scale topographic mapping of the urban areas. It is based on a plane through +the origin at an average height for the area, eliminating the need for corrections +to engineering survey observations.</p> +</div></blockquote> +<p>proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=col_urban</span></code></p> +</div></blockquote> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-h_0"> +<span id="cmdoption-arg-h-0"></span><span class="sig-name descname"><span class="pre">+h_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-h_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Projection plane origin height (in metre)</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="collg.html" class="btn btn-neutral float-left" title="Collignon" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="comill.html" class="btn btn-neutral float-right" title="Compact Miller" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2 current"><a class="reference internal" href="index.html">Projections</a><ul class="current"> +<li class="toctree-l3"><a class="reference internal" href="adams_hemi.html">Adams Hemisphere in a Square</a></li> +<li class="toctree-l3"><a class="reference internal" href="adams_ws1.html">Adams World in a Square I</a></li> +<li class="toctree-l3"><a class="reference internal" href="adams_ws2.html">Adams World in a Square II</a></li> +<li class="toctree-l3"><a class="reference internal" href="aea.html">Albers Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="aeqd.html">Azimuthal Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="airy.html">Airy</a></li> +<li class="toctree-l3"><a class="reference internal" href="aitoff.html">Aitoff</a></li> +<li class="toctree-l3"><a class="reference 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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Collignon</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/collg.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="chamb.html" class="btn btn-neutral float-left" title="Chamberlin Trimetric" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="col_urban.html" class="btn btn-neutral float-right" title="Colombia Urban" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="collignon"> +<span id="collg"></span><h1>Collignon<a class="headerlink" href="#collignon" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>collg</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/collg.png"><img alt="Collignon" src="../../_images/collg.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=collg</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Collignon projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="chamb.html" class="btn btn-neutral float-left" title="Chamberlin Trimetric" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="col_urban.html" class="btn btn-neutral float-right" title="Colombia Urban" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Compact Miller</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/comill.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="col_urban.html" class="btn btn-neutral float-left" title="Colombia Urban" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="crast.html" class="btn btn-neutral float-right" title="Craster Parabolic (Putnins P4)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="compact-miller"> +<span id="comill"></span><h1>Compact Miller<a class="headerlink" href="#compact-miller" title="Permalink to this headline">¶</a></h1> +<p>The Compact Miller projection is a cylindrical map projection with a +height-to-width ratio of 0.6:1.</p> +<p>See <span id="id1">[<a class="reference internal" href="../../zreferences.html#id19" title="Jenny, B., Šavrič, B., and Patterson, T. A compromise aspect-adaptive cylindrical projection for world maps. International Journal of Geographical Information Science, 29(6):935–952, 2015. URL: http://www.cartography.oregonstate.edu/pdf/2015_Jenny_etal_ACompromiseAspect-adaptiveCylindricalProjectionForWorldMaps.pdf, doi:10.1080/13658816.2014.997734.">Jenny2015</a>]</span></p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>comill</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/comill.png"><img alt="Compact Miller" src="../../_images/comill.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=comill</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="col_urban.html" class="btn btn-neutral float-left" title="Colombia Urban" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="crast.html" class="btn btn-neutral float-right" title="Craster Parabolic (Putnins P4)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="denoy.html" class="btn btn-neutral float-right" title="Denoyer Semi-Elliptical" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="craster-parabolic-putnins-p4"> +<span id="crast"></span><h1>Craster Parabolic (Putnins P4)<a class="headerlink" href="#craster-parabolic-putnins-p4" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>crast</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/crast.png"><img alt="Craster Parabolic (Putnins P4)" src="../../_images/crast.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=crast</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Craster Parabolic projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="comill.html" class="btn btn-neutral float-left" title="Compact Miller" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="denoy.html" class="btn btn-neutral float-right" title="Denoyer Semi-Elliptical" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="crast.html" class="btn btn-neutral float-left" title="Craster Parabolic (Putnins P4)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck1.html" class="btn btn-neutral float-right" title="Eckert I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="denoyer-semi-elliptical"> +<span id="denoy"></span><h1>Denoyer Semi-Elliptical<a class="headerlink" href="#denoyer-semi-elliptical" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>denoy</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/denoy.png"><img alt="Denoyer Semi-Elliptical" src="../../_images/denoy.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=denoy</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Denoyer Semi-Elliptical projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="crast.html" class="btn btn-neutral float-left" title="Craster Parabolic (Putnins P4)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck1.html" class="btn btn-neutral float-right" title="Eckert I" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference 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class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" 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Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Eckert I</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/eck1.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="denoy.html" class="btn btn-neutral float-left" title="Denoyer Semi-Elliptical" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck2.html" class="btn btn-neutral float-right" title="Eckert II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="eckert-i"> +<span id="eck1"></span><h1>Eckert I<a class="headerlink" href="#eckert-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eck1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eck1.png"><img alt="Eckert I" src="../../_images/eck1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eck1</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}x &= 2 \sqrt{2/3\pi} \lambda (1- |\phi|/\pi)\\y &= 2 \sqrt{2/3\pi}\phi\end{aligned}\end{align} \]</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Eckert I projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="denoy.html" class="btn btn-neutral float-left" title="Denoyer Semi-Elliptical" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck2.html" class="btn btn-neutral float-right" title="Eckert II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck3.html" class="btn btn-neutral float-right" title="Eckert III" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="eckert-ii"> +<span id="eck2"></span><h1>Eckert II<a class="headerlink" href="#eckert-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eck2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eck2.png"><img alt="Eckert II" src="../../_images/eck2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eck2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Eckert II projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eck1.html" class="btn btn-neutral float-left" title="Eckert I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck3.html" class="btn btn-neutral float-right" title="Eckert III" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Eckert III</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/eck3.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="eck2.html" class="btn btn-neutral float-left" title="Eckert II" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck4.html" class="btn btn-neutral float-right" title="Eckert IV" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="eckert-iii"> +<span id="eck3"></span><h1>Eckert III<a class="headerlink" href="#eckert-iii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eck3</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eck3.png"><img alt="Eckert III" src="../../_images/eck3.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eck3</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Eckert III projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eck2.html" class="btn btn-neutral float-left" title="Eckert II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck4.html" class="btn btn-neutral float-right" title="Eckert IV" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="btn btn-neutral float-left" title="Eckert III" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck5.html" class="btn btn-neutral float-right" title="Eckert V" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="eckert-iv"> +<span id="eck4"></span><h1>Eckert IV<a class="headerlink" href="#eckert-iv" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eck4</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eck4.png"><img alt="Eckert IV" src="../../_images/eck4.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eck4</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="math notranslate nohighlight"> +\[x = \lambda(1+cos\phi) / \sqrt{ 2 + \pi }\]</div> +<div class="math notranslate nohighlight"> +\[y = 2 \phi / \sqrt { 2 + \pi }\]</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Eckert IV projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eck3.html" class="btn btn-neutral float-left" title="Eckert III" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck5.html" class="btn btn-neutral float-right" title="Eckert V" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Eckert V</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/eck5.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="eck4.html" class="btn btn-neutral float-left" title="Eckert IV" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck6.html" class="btn btn-neutral float-right" title="Eckert VI" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="eckert-v"> +<span id="eck5"></span><h1>Eckert V<a class="headerlink" href="#eckert-v" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eck5</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eck5.png"><img alt="Eckert V" src="../../_images/eck5.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eck5</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Eckert V projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eck4.html" class="btn btn-neutral float-left" title="Eckert IV" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eck6.html" class="btn btn-neutral float-right" title="Eckert VI" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Eckert VI</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/eck6.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="eck5.html" class="btn btn-neutral float-left" title="Eckert V" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eqc.html" class="btn btn-neutral float-right" title="Equidistant Cylindrical (Plate Carrée)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="eckert-vi"> +<span id="eck6"></span><h1>Eckert VI<a class="headerlink" href="#eckert-vi" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eck6</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eck6.png"><img alt="Eckert VI" src="../../_images/eck6.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eck6</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Eckert VI projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eck5.html" class="btn btn-neutral float-left" title="Eckert V" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eqc.html" class="btn btn-neutral float-right" title="Equidistant Cylindrical (Plate Carrée)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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<li>Equidistant Cylindrical (Plate Carrée)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/eqc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="eck6.html" class="btn btn-neutral float-left" title="Eckert VI" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eqdc.html" class="btn btn-neutral float-right" title="Equidistant Conic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="equidistant-cylindrical-plate-carree"> +<span id="eqc"></span><h1>Equidistant Cylindrical (Plate Carrée)<a class="headerlink" href="#equidistant-cylindrical-plate-carree" title="Permalink to this headline">¶</a></h1> +<p>The simplest of all projections. Standard parallels (0° when omitted) may be specified that determine latitude of true scale (k=h=1).</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but best used near the equator</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eqc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/eqc.png"><img alt="Equidistant Cylindrical (Plate Carrée)" src="../../_images/eqc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eqc</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. +In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.</p> +<p>The following table gives special cases of the cylindrical equidistant projection.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 69%" /> +<col style="width: 31%" /> +</colgroup> +<thead> +<tr class="row-odd"><th class="head"><p>Projection Name</p></th> +<th class="head"><p>(lat ts=) <span class="math notranslate nohighlight">\(\phi_0\)</span></p></th> +</tr> +</thead> +<tbody> +<tr class="row-even"><td><p>Plain/Plane Chart</p></td> +<td><p>0°</p></td> +</tr> +<tr class="row-odd"><td><p>Simple Cylindrical</p></td> +<td><p>0°</p></td> +</tr> +<tr class="row-even"><td><p>Plate Carrée</p></td> +<td><p>0°</p></td> +</tr> +<tr class="row-odd"><td><p>Ronald Miller—minimum overall scale distortion</p></td> +<td><p>37°30′</p></td> +</tr> +<tr class="row-even"><td><p>E.Grafarend and A.Niermann</p></td> +<td><p>42°</p></td> +</tr> +<tr class="row-odd"><td><p>Ronald Miller—minimum continental scale distortion</p></td> +<td><p>43°30′</p></td> +</tr> +<tr class="row-even"><td><p>Gall Isographic</p></td> +<td><p>45°</p></td> +</tr> +<tr class="row-odd"><td><p>Ronald Miller Equirectangular</p></td> +<td><p>50°30′</p></td> +</tr> +<tr class="row-even"><td><p>E.Grafarend and A.Niermann minimum linear distortion</p></td> +<td><p>61°7′</p></td> +</tr> +</tbody> +</table> +<p>Example using EPSG 32662 (WGS84 Plate Carrée):</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 2 47 | proj +proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +units=m +222638.98 5232016.07 +</pre></div> +</div> +<p>Example using Plate Carrée projection with true scale at latitude 30° and central meridian 90°W:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo -88 30 | proj +proj=eqc +lat_ts=30 +lon_0=90w +192811.01 3339584.72 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the Equidistant Cylindrical projection are all taken from <span id="id1">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>.</p> +<p><span class="math notranslate nohighlight">\(\phi_{ts}\)</span> is the latitude of true scale, that mean the standard parallels where the scale of the projection is true. It can be set with <code class="docutils literal notranslate"><span class="pre">+lat_ts</span></code>.</p> +<p><span class="math notranslate nohighlight">\(\phi_0\)</span> is the latitude of origin that match the center of the map. It can be set with <code class="docutils literal notranslate"><span class="pre">+lat_0</span></code>.</p> +<section id="forward-projection"> +<h3>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[x = \lambda \cos \phi_{ts}\]</div> +<div class="math notranslate nohighlight"> +\[y = \phi - \phi_0\]</div> +</section> +<section id="inverse-projection"> +<h3>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[\lambda = x / cos \phi_{ts}\]</div> +<div class="math notranslate nohighlight"> +\[\phi = y + \phi_0\]</div> +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Equirectangular_projection">Wikipedia</a></p></li> +<li><p><a class="reference external" href="http://mathworld.wolfram.com/CylindricalEquidistantProjection.html">Wolfram Mathworld</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eck6.html" class="btn btn-neutral float-left" title="Eckert VI" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eqdc.html" class="btn btn-neutral float-right" title="Equidistant Conic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Equidistant Conic</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li 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class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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href="eqc.html" class="btn btn-neutral float-left" title="Equidistant Cylindrical (Plate Carrée)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eqearth.html" class="btn btn-neutral float-right" title="Equal Earth" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="equidistant-conic"> +<span id="eqdc"></span><h1>Equidistant Conic<a class="headerlink" href="#equidistant-conic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conic</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eqdc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/eqdc.png"><img alt="Equidistant Conic" src="../../_images/eqdc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eqdc</span> <span class="pre">+lat_1=55</span> <span class="pre">+lat_2=60</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eqc.html" class="btn btn-neutral float-left" title="Equidistant Cylindrical (Plate Carrée)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="eqearth.html" class="btn btn-neutral float-right" title="Equal Earth" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/eqearth.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="eqdc.html" class="btn btn-neutral float-left" title="Equidistant Conic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="euler.html" class="btn btn-neutral float-right" title="Euler" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="equal-earth"> +<span id="eqearth"></span><h1>Equal Earth<a class="headerlink" href="#equal-earth" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.2.0.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 26%" /> +<col style="width: 74%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudo cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>eqearth</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/eqearth.png"><img alt="Equal Earth" src="../../_images/eqearth.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=eqearth</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>The Equal Earth projection is intended for making world maps. Equal Earth is a +projection inspired by the Robinson projection, but unlike +the Robinson projection retains the relative size of areas. The projection +was designed in 2018 by Bojan Savric, Tom Patterson and Bernhard Jenny <span id="id1">[<a class="reference internal" href="../../zreferences.html#id32" title="Šavrič, B., Patterson, T., and Jenny, B. The Equal Earth map projection. International Journal of Geographical Information Science, 33(3):454–465, 2018. URL: https://www.researchgate.net/publication/326879978_The_Equal_Earth_map_projection, doi:10.1080/13658816.2018.1504949.">Savric2018</a>]</span>.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The Equal Earth projection has no special options. Here is +an example of an forward projection on a sphere with a radius of 1 m:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 122 47 | src/proj +proj=eqearth +R=1 +1.55 0.89 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p>Bojan Savric, Tom Patterson & Bernhard Jenny (2018). <a class="reference external" href="https://www.researchgate.net/profile/Bojan_Savric2/publication/326879978_The_Equal_Earth_map_projection/links/5b69d0ae299bf14c6d951b77/The-Equal-Earth-map-projection.pdf">The Equal Earth map projection</a>, International Journal of Geographical Information Science</p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eqdc.html" class="btn btn-neutral float-left" title="Equidistant Conic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="euler.html" class="btn btn-neutral float-right" title="Euler" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Euler</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/euler.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="eqearth.html" class="btn btn-neutral float-left" title="Equal Earth" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="fahey.html" class="btn btn-neutral float-right" title="Fahey" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="euler"> +<span id="id1"></span><h1>Euler<a class="headerlink" href="#euler" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>euler</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/euler.png"><img alt="Euler" src="../../_images/euler.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=euler</span> <span class="pre">+lat_1=67</span> <span class="pre">+lat_2=75</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="eqearth.html" class="btn btn-neutral float-left" title="Equal Earth" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="fahey.html" class="btn btn-neutral float-right" title="Fahey" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Fahey</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/fahey.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="euler.html" class="btn btn-neutral float-left" title="Euler" accesskey="p"><span class="fa 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class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>fahey</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/fahey.png"><img alt="Fahey" src="../../_images/fahey.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=fahey</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Fahey projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="euler.html" class="btn btn-neutral float-left" title="Euler" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="fouc.html" class="btn btn-neutral float-right" title="Foucaut" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Foucaut</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/fouc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="fahey.html" class="btn btn-neutral float-left" title="Fahey" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="fouc_s.html" class="btn btn-neutral float-right" title="Foucaut Sinusoidal" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="foucaut"> +<span id="fouc"></span><h1>Foucaut<a class="headerlink" href="#foucaut" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>fouc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/fouc.png"><img alt="Foucaut" src="../../_images/fouc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=fouc</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Foucaut projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="fahey.html" class="btn btn-neutral float-left" title="Fahey" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="fouc_s.html" class="btn btn-neutral float-right" title="Foucaut Sinusoidal" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-label="Sequential page navigation"> + <a href="fouc.html" class="btn btn-neutral float-left" title="Foucaut" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gall.html" class="btn btn-neutral float-right" title="Gall (Gall Stereographic)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="foucaut-sinusoidal"> +<span id="fouc-s"></span><h1>Foucaut Sinusoidal<a class="headerlink" href="#foucaut-sinusoidal" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>fouc_s</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/fouc_s.png"><img alt="Foucaut Sinusoidal" src="../../_images/fouc_s.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=fouc_s</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>The <cite>y</cite>-axis is based upon a weighted mean of the cylindrical equal-area and +the sinusoidal projections. Parameter <span class="math notranslate nohighlight">\(n=n\)</span> is the weighting factor where +<span class="math notranslate nohighlight">\(0 <= n <= 1\)</span>.</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi)\\y &= n \phi + (1 - n) \sin \phi\end{aligned}\end{align} \]</div> +<p>For the inverse, the Newton-Raphson method can be used to determine +<span class="math notranslate nohighlight">\(\phi\)</span> from the equation for <span class="math notranslate nohighlight">\(y\)</span> above. As <span class="math notranslate nohighlight">\(n \rightarrow 0\)</span> and +<span class="math notranslate nohighlight">\(\phi \rightarrow \pi/2\)</span>, convergence is slow but for <span class="math notranslate nohighlight">\(n = 0\)</span>, <span class="math notranslate nohighlight">\(\phi = +\sin^1y\)</span></p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Foucaut Sinusoidal projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-n"> +<span class="sig-name descname"><span class="pre">+n</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-n" title="Permalink to this definition">¶</a></dt> +<dd><p>Weighting factor. Value should be in the interval 0-1.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="fouc.html" class="btn btn-neutral float-left" title="Foucaut" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gall.html" class="btn btn-neutral float-right" title="Gall (Gall Stereographic)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" 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class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference 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class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" 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class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a 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<li>Gall (Gall Stereographic)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/gall.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="fouc_s.html" class="btn btn-neutral float-left" title="Foucaut Sinusoidal" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="geos.html" class="btn btn-neutral float-right" title="Geostationary Satellite View" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="gall-gall-stereographic"> +<span id="gall"></span><h1>Gall (Gall Stereographic)<a class="headerlink" href="#gall-gall-stereographic" title="Permalink to this headline">¶</a></h1> +<p>The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. +It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Transverse and oblique cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, Spherical</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gall</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/gall.png"><img alt="Gall (Gall Stereographic)" src="../../_images/gall.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gall</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The need for a world map which avoids some of the scale exaggeration of the Mercator projection has led to some commonly used cylindrical modifications, as well as to other modifications which are not cylindrical. +The earliest common cylindrical example was developed by James Gall of Edinburgh about 1855 (Gall, 1885, p. 119-123). +His meridians are equally spaced, but the parallels are spaced at increasing intervals away from the Equator. +The parallels of latitude are actually projected onto a cylinder wrapped about the sphere, but cutting it at lats. 45° N. and S., the point of perspective being a point on the Equator opposite the meridian being projected. +It is used in several British atlases, but seldom in the United States. +The Gall projection is neither conformal nor equal-area, but has a blend of various features. +Unlike the Mercator, the Gall shows the poles as lines running across the top and bottom of the map.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The Gall projection must not be confused with the Gall-Peters one, the later +being a specialization of <a class="reference internal" href="cea.html#cea"><span class="std std-ref">Equal Area Cylindrical</span></a>.</p> +</div> +<p>Example using Gall Stereographic</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 9 51 | proj +proj=gall +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +units=m +708432.90 5193386.36 +</pre></div> +</div> +<p>Example using Gall Stereographic (Central meridian 90°W)</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 9 51 | proj +proj=gall +lon_0=90w +x_0=0 +y_0=0 +ellps=WGS84 +units=m +7792761.91 5193386.36 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the Gall Stereographic are all taken from <span id="id1">[<a class="reference internal" href="../../zreferences.html#id35" title="Snyder, J. P. Flattening the Earth. University of Chicago Press, 1993.">Snyder1993</a>]</span>.</p> +<section id="spherical-form"> +<h3>Spherical form<a class="headerlink" href="#spherical-form" title="Permalink to this headline">¶</a></h3> +<section id="forward-projection"> +<h4>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[x = \frac{\lambda}{\sqrt{2}}\]</div> +<div class="math notranslate nohighlight"> +\[y = (1+\frac{\sqrt{2}}{2}) \tan(\phi/2)\]</div> +</section> +<section id="inverse-projection"> +<h4>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\phi = 2 \arctan( \frac{y}{1+\frac{\sqrt{2}}{2}} )\]</div> +<div class="math notranslate nohighlight"> +\[\lambda = \sqrt{2} x\]</div> +</section> +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Gall_stereographic_projection">Wikipedia</a></p></li> +<li><p><a class="reference external" href="http://sites.lsa.umich.edu/zhukov/wp-content/uploads/sites/140/2014/08/projection-procedures.pdf">Cartographic Projection Procedures for the UNIX Environment-A User’s Manual</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="fouc_s.html" class="btn btn-neutral float-left" title="Foucaut Sinusoidal" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="geos.html" class="btn btn-neutral float-right" title="Geostationary Satellite View" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li 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</ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="gall.html" class="btn btn-neutral float-left" title="Gall (Gall Stereographic)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gins8.html" class="btn btn-neutral float-right" title="Ginsburg VIII (TsNIIGAiK)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="geostationary-satellite-view"> +<span id="geos"></span><h1>Geostationary Satellite View<a class="headerlink" href="#geostationary-satellite-view" title="Permalink to this headline">¶</a></h1> +<p>The geos projection pictures how a geostationary satellite scans the earth at regular +scanning angle intervals.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>geos</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/geos.png"><img alt="Geostationary Satellite View" src="../../_images/geos.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=geos</span> <span class="pre">+h=35785831.0</span> <span class="pre">+lon_0=-60</span> <span class="pre">+sweep=y</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>In order to project using the geos projection you can do the following:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj +proj=geos +h=35785831.0 +</pre></div> +</div> +<p>The required argument <code class="docutils literal notranslate"><span class="pre">h</span></code> is the viewing point (satellite position) height above +the earth.</p> +<p>The projection coordinate relate to the scanning angle by the following simple +relation:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>scanning_angle (radians) = projection_coordinate / h +</pre></div> +</div> +<section id="note-on-sweep-angle"> +<h3>Note on sweep angle<a class="headerlink" href="#note-on-sweep-angle" title="Permalink to this headline">¶</a></h3> +<p>The viewing instrument on-board geostationary satellites described by this +projection have a two-axis gimbal viewing geometry. This means that the different +scanning positions are obtained by rotating the gimbal along a N/S axis (or <code class="docutils literal notranslate"><span class="pre">y</span></code>) +and a E/W axis (or <code class="docutils literal notranslate"><span class="pre">x</span></code>).</p> +<a class="reference internal image-reference" href="../../_images/geos_sweep.png"><img alt="Gimbal geometry" class="align-center" src="../../_images/geos_sweep.png" style="width: 500px;" /></a> +<p>In the image above, the outer-gimbal axis, or sweep-angle axis, is the N/S axis (<code class="docutils literal notranslate"><span class="pre">y</span></code>) +while the inner-gimbal axis, or fixed-angle axis, is the E/W axis (<code class="docutils literal notranslate"><span class="pre">x</span></code>).</p> +<p>This example represents the scanning geometry of the Meteosat series satellite. +However, the GOES satellite series use the opposite scanning geometry, with the +E/W axis (<code class="docutils literal notranslate"><span class="pre">x</span></code>) as the sweep-angle axis, and the N/S (<code class="docutils literal notranslate"><span class="pre">y</span></code>) as the fixed-angle axis.</p> +<p>The sweep argument is used to tell PROJ which on which axis the outer-gimbal +is rotating. The possible values are x or y, y being the default. Thus, the +scanning geometry of the Meteosat series satellite should take sweep as y, and +GOES should take sweep as x.</p> +</section> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-h"> +<span class="sig-name descname"><span class="pre">+h</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-h" title="Permalink to this definition">¶</a></dt> +<dd><p>Height of the view point above the Earth and must be in the same units as +the radius of the sphere or semimajor axis of the ellipsoid.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-sweep"> +<span class="sig-name descname"><span class="pre">+sweep</span></span><span class="sig-prename descclassname"><span class="pre">=<axis></span></span><a class="headerlink" href="#cmdoption-arg-sweep" title="Permalink to this definition">¶</a></dt> +<dd><p>Sweep angle axis of the viewing instrument. Valid options are <em>“x”</em> and <em>“y</em>”.</p> +<p><em>Defaults to “y”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gall.html" class="btn btn-neutral float-left" title="Gall (Gall Stereographic)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gins8.html" class="btn btn-neutral float-right" title="Ginsburg VIII (TsNIIGAiK)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="geos.html" class="btn btn-neutral float-left" title="Geostationary Satellite View" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gn_sinu.html" class="btn btn-neutral float-right" title="General Sinusoidal Series" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="ginsburg-viii-tsniigaik"> +<span id="gins8"></span><h1>Ginsburg VIII (TsNIIGAiK)<a class="headerlink" href="#ginsburg-viii-tsniigaik" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gins8</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/gins8.png"><img alt="Ginsburg VIII (TsNIIGAiK)" src="../../_images/gins8.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gins8</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Ginsburg VIII projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="geos.html" class="btn btn-neutral float-left" title="Geostationary Satellite View" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gn_sinu.html" class="btn btn-neutral float-right" title="General Sinusoidal Series" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="gins8.html" class="btn btn-neutral float-left" title="Ginsburg VIII (TsNIIGAiK)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gnom.html" class="btn btn-neutral float-right" title="Gnomonic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="general-sinusoidal-series"> +<span id="gn-sinu"></span><h1>General Sinusoidal Series<a class="headerlink" href="#general-sinusoidal-series" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gn_sinu</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/gn_sinu.png"><img alt="General Sinusoidal Series" src="../../_images/gn_sinu.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gn_sinu</span> <span class="pre">+m=2</span> <span class="pre">+n=3</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the General Sinusoidal Series +projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gins8.html" class="btn btn-neutral float-left" title="Ginsburg VIII (TsNIIGAiK)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gnom.html" class="btn btn-neutral float-right" title="Gnomonic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Gnomonic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/gnom.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="gn_sinu.html" class="btn btn-neutral float-left" title="General Sinusoidal Series" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="goode.html" class="btn btn-neutral float-right" title="Goode Homolosine" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="gnomonic"> +<span id="gnom"></span><h1>Gnomonic<a class="headerlink" href="#gnomonic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gnom</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/gnom.png"><img alt="Gnomonic" src="../../_images/gnom.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gnom</span> <span class="pre">+lat_0=90</span> <span class="pre">+lon_0=-50</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Gnomonic projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gn_sinu.html" class="btn btn-neutral float-left" title="General Sinusoidal Series" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="goode.html" class="btn btn-neutral float-right" title="Goode Homolosine" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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href="gnom.html" class="btn btn-neutral float-left" title="Gnomonic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gs48.html" class="btn btn-neutral float-right" title="Modified Stereographic of 48 U.S." accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="goode-homolosine"> +<span id="goode"></span><h1>Goode Homolosine<a class="headerlink" href="#goode-homolosine" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>goode</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/goode.png"><img alt="Goode Homolosine" src="../../_images/goode.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=goode</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Goode Homolosine projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gnom.html" class="btn btn-neutral float-left" title="Gnomonic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gs48.html" class="btn btn-neutral float-right" title="Modified Stereographic of 48 U.S." accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" 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+ <a href="goode.html" class="btn btn-neutral float-left" title="Goode Homolosine" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gs50.html" class="btn btn-neutral float-right" title="Modified Stereographic of 50 U.S." accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="modified-stereographic-of-48-u-s"> +<span id="gs48"></span><h1>Modified Stereographic of 48 U.S.<a class="headerlink" href="#modified-stereographic-of-48-u-s" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>The lower 48 states of the U.S.</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gs48</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/gs48.png"><img alt="Modified Stereographic of 48 U.S." src="../../_images/gs48.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gs48</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="goode.html" class="btn btn-neutral float-left" title="Goode Homolosine" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gs50.html" class="btn btn-neutral float-right" title="Modified Stereographic of 50 U.S." accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a 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+ <a href="gs48.html" class="btn btn-neutral float-left" title="Modified Stereographic of 48 U.S." accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="guyou.html" class="btn btn-neutral float-right" title="Guyou" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="modified-stereographic-of-50-u-s"> +<span id="gs50"></span><h1>Modified Stereographic of 50 U.S.<a class="headerlink" href="#modified-stereographic-of-50-u-s" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>All 50 states of the U.S.</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gs50</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/gs50.png"><img alt="Modified Stereographic of 50 U.S." src="../../_images/gs50.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gs50</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gs48.html" class="btn btn-neutral float-left" title="Modified Stereographic of 48 U.S." accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="guyou.html" class="btn btn-neutral float-right" title="Guyou" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a 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class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/gstmerc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="sterea.html" class="btn btn-neutral float-left" title="Oblique Stereographic Alternative" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tcc.html" class="btn btn-neutral float-right" title="Transverse Central Cylindrical" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="gauss-schreiber-transverse-mercator-aka-gauss-laborde-reunion"> +<span id="gstmerc"></span><h1>Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)<a class="headerlink" href="#gauss-schreiber-transverse-mercator-aka-gauss-laborde-reunion" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>gstmerc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/gstmerc.png"><img alt="Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)" src="../../_images/gstmerc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=gstmerc</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="sterea.html" class="btn btn-neutral float-left" title="Oblique Stereographic Alternative" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tcc.html" class="btn btn-neutral float-right" title="Transverse Central Cylindrical" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Guyou</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/guyou.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="gs50.html" class="btn btn-neutral float-left" title="Modified Stereographic of 50 U.S." accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="hammer.html" class="btn btn-neutral float-right" title="Hammer & Eckert-Greifendorff" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="guyou"> +<span id="id1"></span><h1>Guyou<a class="headerlink" href="#guyou" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>guyou</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/guyou.png"><img alt="Guyou" src="../../_images/guyou.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=guyou</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gs50.html" class="btn btn-neutral float-left" title="Modified Stereographic of 50 U.S." accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="hammer.html" class="btn btn-neutral float-right" title="Hammer & Eckert-Greifendorff" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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<a href="guyou.html" class="btn btn-neutral float-left" title="Guyou" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="hatano.html" class="btn btn-neutral float-right" title="Hatano Asymmetrical Equal Area" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="hammer-eckert-greifendorff"> +<span id="hammer"></span><h1>Hammer & Eckert-Greifendorff<a class="headerlink" href="#hammer-eckert-greifendorff" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>hammer</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/hammer.png"><img alt="Hammer & Eckert-Greifendorff" src="../../_images/hammer.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=hammer</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-W"> +<span id="cmdoption-arg-w"></span><span class="sig-name descname"><span class="pre">+W</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-W" title="Permalink to this definition">¶</a></dt> +<dd><p>Set to 0.5 for the Hammer projection and 0.25 for the Eckert-Greifendorff +projection. <a class="reference internal" href="lagrng.html#cmdoption-arg-W"><code class="xref std std-option docutils literal notranslate"><span class="pre">+W</span></code></a> has to be larger than zero.</p> +<p><em>Defaults to 0.5.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-M"> +<span id="cmdoption-arg-m"></span><span class="sig-name descname"><span class="pre">+M</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-M" title="Permalink to this definition">¶</a></dt> +<dd><p><a class="reference internal" href="#cmdoption-arg-M"><code class="xref std std-option docutils literal notranslate"><span class="pre">+M</span></code></a> has to be larger than zero.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="guyou.html" class="btn btn-neutral float-left" title="Guyou" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="hatano.html" class="btn btn-neutral float-right" title="Hatano Asymmetrical Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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role="navigation" aria-label="Sequential page navigation"> + <a href="hammer.html" class="btn btn-neutral float-left" title="Hammer & Eckert-Greifendorff" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="healpix.html" class="btn btn-neutral float-right" title="HEALPix" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="hatano-asymmetrical-equal-area"> +<span id="hatano"></span><h1>Hatano Asymmetrical Equal Area<a class="headerlink" href="#hatano-asymmetrical-equal-area" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p><a class="reference internal" href="../../glossary.html#term-Pseudocylindrical-Projection"><span class="xref std std-term">Pseudocylindrical Projection</span></a></p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>hatano</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/hatano.png"><img alt="Hatano Asymmetrical Equal Area" src="../../_images/hatano.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=hatano</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<section id="mathematical-definition"> +<h3>Mathematical Definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h3> +<section id="forward"> +<h4>Forward<a class="headerlink" href="#forward" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}x &= 0.85\lambda \cos \theta\\y &= C_y \sin \theta\\P(\theta) &= 2\theta + \sin 2\theta - C_p \sin \phi\\P'(\theta) &= 2(1 + \cos 2\theta)\\\theta_0 &= 2\phi\end{aligned}\end{align} \]</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 49%" /> +<col style="width: 25%" /> +<col style="width: 26%" /> +</colgroup> +<thead> +<tr class="row-odd"><th class="head"><p>Condition</p></th> +<th class="head"><p><span class="math notranslate nohighlight">\(C_y\)</span></p></th> +<th class="head"><p><span class="math notranslate nohighlight">\(C_p\)</span></p></th> +</tr> +</thead> +<tbody> +<tr class="row-even"><td><p>For <span class="math notranslate nohighlight">\(\phi > 0\)</span></p></td> +<td><p>1.75859</p></td> +<td><p>2.67595</p></td> +</tr> +<tr class="row-odd"><td><p>For <span class="math notranslate nohighlight">\(\phi < 0\)</span></p></td> +<td><p>1.93052</p></td> +<td><p>2.43763</p></td> +</tr> +</tbody> +</table> +<p>For <span class="math notranslate nohighlight">\(\phi = 0\)</span>, <span class="math notranslate nohighlight">\(y \leftarrow 0\)</span>, and <span class="math notranslate nohighlight">\(x \leftarrow 0.85\lambda\)</span>.</p> +</section> +</section> +<section id="further-reading"> +<h3>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h3> +<ol class="arabic simple"> +<li><p><a class="reference external" href="http://map-projections.net/single-view/hatano">Compare Map Projections</a></p></li> +<li><p><a class="reference external" href="http://www.mathworks.com/help/map/hatano.html">Mathworks</a></p></li> +</ol> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="hammer.html" class="btn btn-neutral float-left" title="Hammer & Eckert-Greifendorff" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="healpix.html" class="btn btn-neutral float-right" title="HEALPix" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/healpix.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="hatano.html" class="btn btn-neutral float-left" title="Hatano Asymmetrical Equal Area" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="rhealpix.html" class="btn btn-neutral float-right" title="rHEALPix" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="healpix"> +<span id="id1"></span><h1>HEALPix<a class="headerlink" href="#healpix" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>healpix</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<a class="reference internal image-reference" href="../../_images/healpix.png"><img alt="HEALPix" src="../../_images/healpix.png" style="width: 613.5px; height: 325.5px;" /></a> +<p>The HEALPix projection is area preserving and can be used with a spherical and +ellipsoidal model. It was initially developed for mapping cosmic background +microwave radiation. The image below is the graphical representation of the +mapping and consists of eight isomorphic triangular interrupted map graticules. +The north and south contains four in which straight meridians converge polewards +to a point and unequally spaced horizontal parallels. HEALPix provides a mapping +in which points of equal latitude and equally spaced longitude are mapped to points +of equal latitude and equally spaced longitude with the module of the polar +interruptions.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>To run a forward HEALPix projection on a unit sphere model, use the following command:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj +proj=healpix +lon_0=0 +a=1 -E <<EOF +0 0 +EOF +# output +0 0 0.00 0.00 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-rot_xy"> +<span id="cmdoption-arg-rot-xy"></span><span class="sig-name descname"><span class="pre">+rot_xy</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-rot_xy" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 6.3.0.</span></p> +</div> +<p>Rotation of the HEALPix map in degrees. A positive value results in a clockwise +rotation around (x_0, y_0) in the cartesian / projected coordinate space.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="http://healpix.jpl.nasa.gov/">NASA</a></p></li> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/HEALPix">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="hatano.html" class="btn btn-neutral float-left" title="Hatano Asymmetrical Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="rhealpix.html" class="btn btn-neutral float-right" title="rHEALPix" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="rhealpix.html" class="btn btn-neutral float-left" title="rHEALPix" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="igh_o.html" class="btn btn-neutral float-right" title="Interrupted Goode Homolosine (Oceanic View)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="interrupted-goode-homolosine"> +<span id="igh"></span><h1>Interrupted Goode Homolosine<a class="headerlink" href="#interrupted-goode-homolosine" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>igh</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/igh.png"><img alt="Interrupted Goode Homolosine" src="../../_images/igh.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=igh</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="rhealpix.html" class="btn btn-neutral float-left" title="rHEALPix" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="igh_o.html" class="btn btn-neutral float-right" title="Interrupted Goode Homolosine (Oceanic View)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="igh.html" class="btn btn-neutral float-left" title="Interrupted Goode Homolosine" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="imw_p.html" class="btn btn-neutral float-right" title="International Map of the World Polyconic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="interrupted-goode-homolosine-oceanic-view"> +<span id="igh-o"></span><h1>Interrupted Goode Homolosine (Oceanic View)<a class="headerlink" href="#interrupted-goode-homolosine-oceanic-view" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>igh_o</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/igh_o.png"><img alt="Interrupted Goode Homolosine" src="../../_images/igh_o.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=igh_o</span> <span class="pre">+lon_0=-160</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection. A value of +lon_0=-160 is recommended.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="igh.html" class="btn btn-neutral float-left" title="Interrupted Goode Homolosine" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="imw_p.html" class="btn btn-neutral float-right" title="International Map of the World Polyconic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="igh_o.html" class="btn btn-neutral float-left" title="Interrupted Goode Homolosine (Oceanic View)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="isea.html" class="btn btn-neutral float-right" title="Icosahedral Snyder Equal Area" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="international-map-of-the-world-polyconic"> +<span id="imw-p"></span><h1>International Map of the World Polyconic<a class="headerlink" href="#international-map-of-the-world-polyconic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudoconical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>imw_p</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/imw_p.png"><img alt="International Map of the World Polyconic" src="../../_images/imw_p.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=imw_p</span> <span class="pre">+lat_1=30</span> <span class="pre">+lat_2=-40</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="igh_o.html" class="btn btn-neutral float-left" title="Interrupted Goode Homolosine (Oceanic View)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="isea.html" class="btn btn-neutral float-right" title="Icosahedral Snyder Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li 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class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a 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class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li>Projections</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/index.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="../index.html" class="btn btn-neutral float-left" title="Coordinate operations" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="adams_hemi.html" class="btn btn-neutral float-right" title="Adams Hemisphere in a Square" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="projections"> +<span id="id1"></span><h1>Projections<a class="headerlink" href="#projections" title="Permalink to this headline">¶</a></h1> +<p>Projections are coordinate operations that are technically conversions but since +projections are so fundamental to PROJ we differentiate them from conversions.</p> +<p>Projections map the spherical 3D space to a flat 2D space.</p> +<div class="toctree-wrapper compound"> +<ul> +<li class="toctree-l1"><a class="reference internal" href="adams_hemi.html">Adams Hemisphere in a Square</a></li> +<li class="toctree-l1"><a class="reference internal" href="adams_ws1.html">Adams World in a Square I</a></li> +<li class="toctree-l1"><a class="reference internal" href="adams_ws2.html">Adams World in a Square II</a></li> +<li class="toctree-l1"><a class="reference internal" href="aea.html">Albers Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="aeqd.html">Azimuthal Equidistant</a></li> +<li class="toctree-l1"><a class="reference internal" href="airy.html">Airy</a></li> +<li class="toctree-l1"><a class="reference internal" href="aitoff.html">Aitoff</a></li> +<li class="toctree-l1"><a class="reference internal" href="alsk.html">Modified Stereographic of Alaska</a></li> +<li class="toctree-l1"><a class="reference internal" href="apian.html">Apian Globular I</a></li> +<li class="toctree-l1"><a class="reference internal" href="august.html">August Epicycloidal</a></li> +<li class="toctree-l1"><a class="reference internal" href="bacon.html">Bacon Globular</a></li> +<li class="toctree-l1"><a class="reference internal" href="bertin1953.html">Bertin 1953</a></li> +<li class="toctree-l1"><a class="reference internal" href="bipc.html">Bipolar conic of western hemisphere</a></li> +<li class="toctree-l1"><a class="reference internal" href="boggs.html">Boggs Eumorphic</a></li> +<li class="toctree-l1"><a class="reference internal" href="bonne.html">Bonne (Werner lat_1=90)</a></li> +<li class="toctree-l1"><a class="reference internal" href="calcofi.html">Cal Coop Ocean Fish Invest Lines/Stations</a></li> +<li class="toctree-l1"><a class="reference internal" href="cass.html">Cassini (Cassini-Soldner)</a></li> +<li class="toctree-l1"><a class="reference internal" href="cc.html">Central Cylindrical</a></li> +<li class="toctree-l1"><a class="reference internal" href="ccon.html">Central Conic</a></li> +<li class="toctree-l1"><a class="reference internal" href="cea.html">Equal Area Cylindrical</a></li> +<li class="toctree-l1"><a class="reference internal" href="chamb.html">Chamberlin Trimetric</a></li> +<li class="toctree-l1"><a class="reference internal" href="collg.html">Collignon</a></li> +<li class="toctree-l1"><a class="reference internal" href="col_urban.html">Colombia Urban</a></li> +<li class="toctree-l1"><a class="reference internal" href="comill.html">Compact Miller</a></li> +<li class="toctree-l1"><a class="reference internal" href="crast.html">Craster Parabolic (Putnins P4)</a></li> +<li class="toctree-l1"><a class="reference internal" href="denoy.html">Denoyer Semi-Elliptical</a></li> +<li class="toctree-l1"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l1"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l1"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l1"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l1"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l1"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l1"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l1"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l1"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l1"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l1"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l1"><a class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l1"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l1"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l1"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l1"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l1"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l1"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l1"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l1"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l1"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l1"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l1"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l1"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l1"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l1"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l1"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l1"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l1"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l1"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l1"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l1"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l1"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l1"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l1"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l1"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l1"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l1"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l1"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l1"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l1"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l1"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l1"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l1"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l1"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l1"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l1"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l1"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l1"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l1"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l1"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l1"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l1"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l1"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l1"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l1"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l1"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l1"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l1"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l1"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l1"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l1"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l1"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l1"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l1"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l1"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l1"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l1"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l1"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l1"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l1"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l1"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l1"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l1"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l1"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l1"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l1"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l1"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l1"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l1"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l1"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l1"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l1"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l1"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l1"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l1"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l1"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l1"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l1"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l1"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l1"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l1"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l1"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l1"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l1"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l1"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l1"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l1"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l1"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l1"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l1"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l1"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l1"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l1"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l1"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</div> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" 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class="toctree-l3"><a class="reference internal" href="cass.html">Cassini (Cassini-Soldner)</a></li> +<li class="toctree-l3"><a class="reference internal" href="cc.html">Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="ccon.html">Central Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="cea.html">Equal Area Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="chamb.html">Chamberlin Trimetric</a></li> +<li class="toctree-l3"><a class="reference internal" href="collg.html">Collignon</a></li> +<li class="toctree-l3"><a class="reference internal" href="col_urban.html">Colombia Urban</a></li> +<li class="toctree-l3"><a class="reference internal" href="comill.html">Compact Miller</a></li> +<li class="toctree-l3"><a class="reference internal" href="crast.html">Craster Parabolic (Putnins P4)</a></li> +<li class="toctree-l3"><a class="reference internal" href="denoy.html">Denoyer Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a 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class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Icosahedral Snyder Equal Area</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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href="imw_p.html" class="btn btn-neutral float-left" title="International Map of the World Polyconic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="kav5.html" class="btn btn-neutral float-right" title="Kavrayskiy V" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="icosahedral-snyder-equal-area"> +<span id="isea"></span><h1>Icosahedral Snyder Equal Area<a class="headerlink" href="#icosahedral-snyder-equal-area" title="Permalink to this headline">¶</a></h1> +<p>Snyder’s Icosahedral Equal Area map projections on polyhedral globes for the +dodecahedron and truncated icosahedron offer relatively low scale and +angular distortion. The equations involved are relatively straight-forward, +and for certain instructional tools and databases, the projections are useful +for world maps. The interruptions remain a disadvantage, as with any low-error +projection system applied to the entire globe <span id="id1">[<a class="reference internal" href="../../zreferences.html#id34" title="Snyder, J. P. An equal-area map projection for polyhedral globes. Cartographica, 29(1):10–21, 1992. doi:10.3138/27H7-8K88-4882-1752.">Snyder1992</a>]</span>.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Polyhedral, equal area</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward, spherical</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>isea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id3"> +<a class="reference internal image-reference" href="../../_images/isea.png"><img alt="Icosahedral Snyder Equal Area" src="../../_images/isea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=isea</span></code></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-orient"> +<span class="sig-name descname"><span class="pre">+orient</span></span><span class="sig-prename descclassname"><span class="pre">=<string></span></span><a class="headerlink" href="#cmdoption-arg-orient" title="Permalink to this definition">¶</a></dt> +<dd><p>Can be set to either <code class="docutils literal notranslate"><span class="pre">isea</span></code> or <code class="docutils literal notranslate"><span class="pre">pole</span></code>. See Snyder’s Figure 12 for pole orientation <span id="id2">[<a class="reference internal" href="../../zreferences.html#id34" title="Snyder, J. P. An equal-area map projection for polyhedral globes. Cartographica, 29(1):10–21, 1992. doi:10.3138/27H7-8K88-4882-1752.">Snyder1992</a>]</span>.</p> +<p><em>Defaults to isea</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-azi"> +<span class="sig-name descname"><span class="pre">+azi</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-azi" title="Permalink to this definition">¶</a></dt> +<dd><p>Azimuth.</p> +<p><em>Defaults to 0.0</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-aperture"> +<span class="sig-name descname"><span class="pre">+aperture</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-aperture" title="Permalink to this definition">¶</a></dt> +<dd><p><em>Defaults to 3.0</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-resolution"> +<span class="sig-name descname"><span class="pre">+resolution</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-resolution" title="Permalink to this definition">¶</a></dt> +<dd><p><em>Defaults to 4.0</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-mode"> +<span class="sig-name descname"><span class="pre">+mode</span></span><span class="sig-prename descclassname"><span class="pre">=<string></span></span><a class="headerlink" href="#cmdoption-arg-mode" title="Permalink to this definition">¶</a></dt> +<dd><p>Can be either <code class="docutils literal notranslate"><span class="pre">plane</span></code>, <code class="docutils literal notranslate"><span class="pre">di</span></code>, <code class="docutils literal notranslate"><span class="pre">dd</span></code> or <code class="docutils literal notranslate"><span class="pre">hex</span></code>.</p> +<p><em>Defaults to plane</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="imw_p.html" class="btn btn-neutral float-left" title="International Map of the World Polyconic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="kav5.html" class="btn btn-neutral float-right" title="Kavrayskiy V" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="btn btn-neutral float-left" title="Icosahedral Snyder Equal Area" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="kav7.html" class="btn btn-neutral float-right" title="Kavrayskiy VII" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="kavrayskiy-v"> +<span id="kav5"></span><h1>Kavrayskiy V<a class="headerlink" href="#kavrayskiy-v" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>kav5</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/kav5.png"><img alt="Kavrayskiy V" src="../../_images/kav5.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=kav5</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>This projection name may also be transliterated as Kavraisky V.</p> +</div> +<p>Created by Soviet cartographer Vladimir V. Kavrayskiy in 1933 <span id="id1">[<a class="reference internal" href="../../zreferences.html#id35" title="Snyder, J. P. Flattening the Earth. University of Chicago Press, 1993.">Snyder1993</a>]</span>.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Kavrayskiy V projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="isea.html" class="btn btn-neutral float-left" title="Icosahedral Snyder Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="kav7.html" class="btn btn-neutral float-right" title="Kavrayskiy VII" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="krovak.html" class="btn btn-neutral float-right" title="Krovak" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="kavrayskiy-vii"> +<span id="kav7"></span><h1>Kavrayskiy VII<a class="headerlink" href="#kavrayskiy-vii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>kav7</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/kav7.png"><img alt="Kavrayskiy VII" src="../../_images/kav7.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=kav7</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>This projection name may also be transliterated as Kavraisky VII.</p> +</div> +<p>Created by Soviet cartographer Vladimir V. Kavrayskiy in 1939 <span id="id1">[<a class="reference internal" href="../../zreferences.html#id35" title="Snyder, J. P. Flattening the Earth. University of Chicago Press, 1993.">Snyder1993</a>]</span>.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Kavrayskiy VII projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="kav5.html" class="btn btn-neutral float-left" title="Kavrayskiy V" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="krovak.html" class="btn btn-neutral float-right" title="Krovak" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l3"><a 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class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Krovak</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference 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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li 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class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" 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aria-hidden="true"></span> Previous</a> + <a href="labrd.html" class="btn btn-neutral float-right" title="Laborde" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="krovak"> +<span id="id1"></span><h1>Krovak<a class="headerlink" href="#krovak" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but more accurate around Czechoslovakia</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>krovak</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/krovak.png"><img alt="Krovak" src="../../_images/krovak.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=krovak</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Krovak projection.</p> +<p>The latitude of pseudo standard parallel is hardcoded to 78.5° and +the ellipsoid to Bessel.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-czech"> +<span class="sig-name descname"><span class="pre">+czech</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-czech" title="Permalink to this definition">¶</a></dt> +<dd><p>Reverse the sign of the output coordinates, as is tradition in the +Czech Republic.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 24°50’ (24.8333333333333)</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 49.5</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 0.9999</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="kav7.html" class="btn btn-neutral float-left" title="Kavrayskiy VII" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="labrd.html" class="btn btn-neutral float-right" title="Laborde" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="laea.html" class="btn btn-neutral float-right" title="Lambert Azimuthal Equal Area" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="laborde"> +<span id="labrd"></span><h1>Laborde<a class="headerlink" href="#laborde" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but more accurate around Madagascar</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>labrd</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/labrd.png"><img alt="Laborde" src="../../_images/labrd.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=labrd</span> <span class="pre">+lon_0=40</span> <span class="pre">+lat_0=-10</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center. Must not be zero.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-azi"> +<span class="sig-name descname"><span class="pre">+azi</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-azi" title="Permalink to this definition">¶</a></dt> +<dd><p>Azimuth of the central line.</p> +<p><em>Defaults to 0.0</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="krovak.html" class="btn btn-neutral float-left" title="Krovak" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="laea.html" class="btn btn-neutral float-right" title="Lambert Azimuthal Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="labrd.html" class="btn btn-neutral float-left" title="Laborde" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lagrng.html" class="btn btn-neutral float-right" title="Lagrange" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="lambert-azimuthal-equal-area"> +<span id="laea"></span><h1>Lambert Azimuthal Equal Area<a class="headerlink" href="#lambert-azimuthal-equal-area" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>laea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/laea.png"><img alt="Lambert Azimuthal Equal Area" src="../../_images/laea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=laea</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="labrd.html" class="btn btn-neutral float-left" title="Laborde" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lagrng.html" class="btn btn-neutral float-right" title="Lagrange" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="larr.html" class="btn btn-neutral float-right" title="Larrivee" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="lagrange"> +<span id="lagrng"></span><h1>Lagrange<a class="headerlink" href="#lagrange" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>lagrng</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/lagrng.png"><img alt="Lagrange" src="../../_images/lagrng.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=lagrng</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-W"> +<span id="cmdoption-arg-w"></span><span class="sig-name descname"><span class="pre">+W</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-W" title="Permalink to this definition">¶</a></dt> +<dd><p>The factor <a class="reference internal" href="#cmdoption-arg-W"><code class="xref std std-option docutils literal notranslate"><span class="pre">+W</span></code></a> is the ratio of the difference in longitude from the +central meridian to the a circular meridian to 90. <a class="reference internal" href="#cmdoption-arg-W"><code class="xref std std-option docutils literal notranslate"><span class="pre">+W</span></code></a> must be a +positive value.</p> +<p><em>Defaults to 2.0</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="laea.html" class="btn btn-neutral float-left" title="Lambert Azimuthal Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="larr.html" class="btn btn-neutral float-right" title="Larrivee" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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(I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" 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aria-hidden="true"></span> Previous</a> + <a href="lask.html" class="btn btn-neutral float-right" title="Laskowski" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="larrivee"> +<span id="larr"></span><h1>Larrivee<a class="headerlink" href="#larrivee" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>larr</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/larr.png"><img alt="Larrivee" src="../../_images/larr.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=larr</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Larrivee projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="lagrng.html" class="btn btn-neutral float-left" title="Lagrange" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lask.html" class="btn btn-neutral float-right" title="Laskowski" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="lcc.html" class="btn btn-neutral float-right" title="Lambert Conformal Conic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="laskowski"> +<span id="lask"></span><h1>Laskowski<a class="headerlink" href="#laskowski" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>lask</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/lask.png"><img alt="Laskowski" src="../../_images/lask.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=lask</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="larr.html" class="btn btn-neutral float-left" title="Larrivee" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lcc.html" class="btn btn-neutral float-right" title="Lambert Conformal Conic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Lambert Conformal Conic</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +<li class="toctree-l4"><a class="reference internal" href="#further-reading">Further reading</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" 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Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" 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many national and regional mapping systems. It is one of +seven projections introduced by Johann Heinrich Lambert in 1772.</p> +<p>It has several different forms: with one and two standard parallels +(referred to as 1SP and 2SP in EPSG guidance notes). Additionally we +provide “2SP Michigan” form which is very similar to normal 2SP, but +with a scaling factor on the ellipsoid (given as <cite>k_0</cite> parameter). +It is implemented as per EPSG Guidance Note 7-2 (version 54, August +2018, page 25). It is used in a few systems in the EPSG database which +justifies adding this otherwise non-standard projection.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal conic</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal . +One or two standard parallels (1SP and 2SP). +“LCC 2SP Michigan” form can be used by setting +<code class="docutils literal notranslate"><span class="pre">+k_0</span></code> parameter to specify ellipsoid scale.</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Best for regions predominantly east–west in extent and +located in the middle north or south latitudes.</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>lcc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/lcc.png"><img alt="Lambert Conformal Conic" src="../../_images/lcc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=lcc</span> <span class="pre">+lon_0=-90</span> <span class="pre">+lat_1=33</span> <span class="pre">+lat_2=45</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>This parameter can represent two different values depending on the +form of the projection. In LCC 1SP it determines the scale factor +at natural origin. In LCC 2SP Michigan it determines the ellipsoid +scale factor.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Lambert_conformal_conic_projection">Wikipedia</a></p></li> +<li><p><a class="reference external" href="http://mathworld.wolfram.com/LambertConformalConicProjection.html">Wolfram Mathworld</a></p></li> +<li><p><a class="reference external" href="https://pubs.er.usgs.gov/publication/pp1395">John P. Snyder “Map projections: A working manual” (pp. 104-110)</a></p></li> +<li><p><a class="reference external" href="http://desktop.arcgis.com/en/arcmap/10.3/guide-books/map-projections/lambert-conformal-conic.htm">ArcGIS documentation on “Lambert Conformal Conic”</a></p></li> +<li><p><a class="reference external" href="http://www.epsg.org/Guidancenotes.aspx">EPSG Guidance Note 7-2 (version 54, August 2018, page 25)</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="lask.html" class="btn btn-neutral float-left" title="Laskowski" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lcca.html" class="btn btn-neutral float-right" title="Lambert Conformal Conic Alternative" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="lcc.html" class="btn btn-neutral float-left" title="Lambert Conformal Conic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="leac.html" class="btn btn-neutral float-right" title="Lambert Equal Area Conic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="lambert-conformal-conic-alternative"> +<span id="lcca"></span><h1>Lambert Conformal Conic Alternative<a class="headerlink" href="#lambert-conformal-conic-alternative" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>lcca</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/lcca.png"><img alt="Lambert Conformal Conic Alternative" src="../../_images/lcca.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=lcca</span> <span class="pre">+lat_0=35</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="lcc.html" class="btn btn-neutral float-left" title="Lambert Conformal Conic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="leac.html" class="btn btn-neutral float-right" title="Lambert Equal Area Conic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="lcca.html" class="btn btn-neutral float-left" title="Lambert Conformal Conic Alternative" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lee_os.html" class="btn btn-neutral float-right" title="Lee Oblated Stereographic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="lambert-equal-area-conic"> +<span id="leac"></span><h1>Lambert Equal Area Conic<a class="headerlink" href="#lambert-equal-area-conic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>leac</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/leac.png"><img alt="Lambert Equal Area Conic" src="../../_images/leac.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=leac</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Lambert Equal Area Conic +projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-south"> +<span class="sig-name descname"><span class="pre">+south</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-south" title="Permalink to this definition">¶</a></dt> +<dd><p>Sets the second standard parallel to 90°S. When the flag is off the second +standard parallel is set to 90°N.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="lcca.html" class="btn btn-neutral float-left" title="Lambert Conformal Conic Alternative" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lee_os.html" class="btn btn-neutral float-right" title="Lee Oblated Stereographic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="leac.html" class="btn btn-neutral float-left" title="Lambert Equal Area Conic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="loxim.html" class="btn btn-neutral float-right" title="Loximuthal" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="lee-oblated-stereographic"> +<span id="lee-os"></span><h1>Lee Oblated Stereographic<a class="headerlink" href="#lee-oblated-stereographic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>lee_os</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/lee_os.png"><img alt="Lee Oblated Stereographic" src="../../_images/lee_os.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=lee_os</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="leac.html" class="btn btn-neutral float-left" title="Lambert Equal Area Conic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="loxim.html" class="btn btn-neutral float-right" title="Loximuthal" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + 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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Loximuthal</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/loxim.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="lee_os.html" class="btn btn-neutral float-left" title="Lee Oblated Stereographic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lsat.html" class="btn btn-neutral float-right" title="Space oblique for LANDSAT" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="loximuthal"> +<span id="loxim"></span><h1>Loximuthal<a class="headerlink" href="#loximuthal" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>loxim</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/loxim.png"><img alt="Loximuthal" src="../../_images/loxim.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=loxim</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Loximuthal projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="lee_os.html" class="btn btn-neutral float-left" title="Lee Oblated Stereographic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="lsat.html" class="btn btn-neutral float-right" title="Space oblique for LANDSAT" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Space oblique for LANDSAT</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/lsat.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="loxim.html" class="btn btn-neutral float-left" title="Loximuthal" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbt_s.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Polar Sine (No. 1)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="space-oblique-for-landsat"> +<span id="lsat"></span><h1>Space oblique for LANDSAT<a class="headerlink" href="#space-oblique-for-landsat" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>lsat</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/lsat.png"><img alt="Space oblique for LANDSAT" src="../../_images/lsat.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=lsat</span> <span class="pre">+ellps=GRS80</span> <span class="pre">+lat_1=-60</span> <span class="pre">+lat_2=60</span> <span class="pre">+lsat=2</span> <span class="pre">+path=2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lsat"> +<span class="sig-name descname"><span class="pre">+lsat</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lsat" title="Permalink to this definition">¶</a></dt> +<dd><p>Landsat satellite used for the projection. Value between 1 and 5.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-path"> +<span class="sig-name descname"><span class="pre">+path</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-path" title="Permalink to this definition">¶</a></dt> +<dd><p>Selected path of satellite. Value between 1 and 253 when <a class="reference internal" href="#cmdoption-arg-lsat"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lsat</span></code></a> is +set to 1,2 or 3, otherwise valid input is between 1 and 233.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="loxim.html" class="btn btn-neutral float-left" title="Loximuthal" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbt_s.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Polar Sine (No. 1)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-label="Sequential page navigation"> + <a href="mbt_s.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Polar Sine (No. 1)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbtfpp.html" class="btn btn-neutral float-right" title="McBride-Thomas Flat-Polar Parabolic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mcbryde-thomas-flat-pole-sine-no-2"> +<span id="mbt-fps"></span><h1>McBryde-Thomas Flat-Pole Sine (No. 2)<a class="headerlink" href="#mcbryde-thomas-flat-pole-sine-no-2" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mbt_fps</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/mbt_fps.png"><img alt="McBryde-Thomas Flat-Pole Sine (No. 2)" src="../../_images/mbt_fps.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mbt_fps</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mbt_s.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Polar Sine (No. 1)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbtfpp.html" class="btn btn-neutral float-right" title="McBride-Thomas Flat-Polar Parabolic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="lsat.html" class="btn btn-neutral float-left" title="Space oblique for LANDSAT" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbt_fps.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Pole Sine (No. 2)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mcbryde-thomas-flat-polar-sine-no-1"> +<span id="mbt-s"></span><h1>McBryde-Thomas Flat-Polar Sine (No. 1)<a class="headerlink" href="#mcbryde-thomas-flat-polar-sine-no-1" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mbt_s</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/mbt_s.png"><img alt="McBryde-Thomas Flat-Polar Sine (No. 1)" src="../../_images/mbt_s.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mbt_s</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the McBryde-Thomas Flat-Polar Sine +projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="lsat.html" class="btn btn-neutral float-left" title="Space oblique for LANDSAT" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbt_fps.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Pole Sine (No. 2)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="mbt_fps.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Pole Sine (No. 2)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbtfpq.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Polar Quartic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mcbride-thomas-flat-polar-parabolic"> +<span id="mbtfpp"></span><h1>McBride-Thomas Flat-Polar Parabolic<a class="headerlink" href="#mcbride-thomas-flat-polar-parabolic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mbtfpp</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/mbtfpp.png"><img alt="McBride-Thomas Flat-Polar Parabolic" src="../../_images/mbtfpp.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mbtfpp</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mbt_fps.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Pole Sine (No. 2)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbtfpq.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Polar Quartic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">McBryde-Thomas Flat-Polar Quartic</a><ul> +<li class="toctree-l4"><a class="reference 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navigation"> + <a href="mbtfpp.html" class="btn btn-neutral float-left" title="McBride-Thomas Flat-Polar Parabolic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbtfps.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Polar Sinusoidal" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mcbryde-thomas-flat-polar-quartic"> +<span id="mbtfpq"></span><h1>McBryde-Thomas Flat-Polar Quartic<a class="headerlink" href="#mcbryde-thomas-flat-polar-quartic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mbtfpq</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/mbtfpq.png"><img alt="McBryde-Thomas Flat-Polar Quartic" src="../../_images/mbtfpq.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mbtfpq</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mbtfpp.html" class="btn btn-neutral float-left" title="McBride-Thomas Flat-Polar Parabolic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mbtfps.html" class="btn btn-neutral float-right" title="McBryde-Thomas Flat-Polar Sinusoidal" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3 current"><a class="current 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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navigation"> + <a href="mbtfpq.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Polar Quartic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="merc.html" class="btn btn-neutral float-right" title="Mercator" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mcbryde-thomas-flat-polar-sinusoidal"> +<span id="mbtfps"></span><h1>McBryde-Thomas Flat-Polar Sinusoidal<a class="headerlink" href="#mcbryde-thomas-flat-polar-sinusoidal" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mbtfps</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/mbtfps.png"><img alt="McBryde-Thomas Flat-Polar Sinusoidal" src="../../_images/mbtfps.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mbtfps</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the McBryde-Thomas Flat-Polar +Sinusoidal projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mbtfpq.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Polar Quartic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="merc.html" class="btn btn-neutral float-right" title="Mercator" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a 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<li>Mercator</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/merc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="mbtfps.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Polar Sinusoidal" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mil_os.html" class="btn btn-neutral float-right" title="Miller Oblated Stereographic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mercator"> +<span id="merc"></span><h1>Mercator<a class="headerlink" href="#mercator" title="Permalink to this headline">¶</a></h1> +<p>The Mercator projection is a cylindrical map projection that origins +from the 16th century. It is widely recognized as the first regularly +used map projection. It is a conformal projection in which the equator +projects to a straight line at constant scale. The projection has the +property that a rhumb line, a course of constant heading, projects to a +straight line. This makes it suitable for navigational purposes.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but best used near the equator</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>merc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id5"> +<a class="reference internal image-reference" href="../../_images/merc.png"><img alt="Mercator" src="../../_images/merc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=merc</span></code></span><a class="headerlink" href="#id5" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Applications should be limited to equatorial regions, but is frequently +used for navigational charts with latitude of true scale (<a class="reference internal" href="wink2.html#cmdoption-arg-lat_ts"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_ts</span></code></a>) specified within +or near chart’s boundaries. +It is considered to be inappropriate for world maps because of the gross +distortions in area; for example the projected area of Greenland is +larger than that of South America, despite the fact that Greenland’s +area is <span class="math notranslate nohighlight">\(\frac18\)</span> that of South America <span id="id1">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>.</p> +<p>Example using latitude of true scale:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 56.35 12.32 | proj +proj=merc +lat_ts=56.5 +3470306.37 759599.90 +</pre></div> +</div> +<p>Example using scaling factor:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 56.35 12.32 | proj +proj=merc +k_0=2 +12545706.61 2746073.80 +</pre></div> +</div> +<p>Note that <a class="reference internal" href="wink2.html#cmdoption-arg-lat_ts"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_ts</span></code></a> and <a class="reference internal" href="tobmerc.html#cmdoption-arg-k_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+k_0</span></code></a> are mutually exclusive. +If used together, <a class="reference internal" href="wink2.html#cmdoption-arg-lat_ts"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_ts</span></code></a> takes precedence over <a class="reference internal" href="tobmerc.html#cmdoption-arg-k_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+k_0</span></code></a>.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<section id="spherical-form"> +<h3>Spherical form<a class="headerlink" href="#spherical-form" title="Permalink to this headline">¶</a></h3> +<p>For the spherical form of the projection we introduce the scaling factor:</p> +<div class="math notranslate nohighlight"> +\[k_0 = \cos \phi_{ts}\]</div> +<section id="forward-projection"> +<h4>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[x = k_0R \lambda; \qquad y = k_0R \psi\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\psi &= \ln \tan \biggl(\frac{\pi}{4} + \frac{\phi}{2} \biggr)\\ + &= \sinh^{-1}\tan\phi\end{split}\]</div> +<p>The quantity <span class="math notranslate nohighlight">\(\psi\)</span> is the isometric latitude.</p> +</section> +<section id="inverse-projection"> +<h4>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\lambda = \frac{x}{k_0R}; \qquad \psi = \frac{y}{k_0R}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\phi &= \frac{\pi}{2} - 2 \tan^{-1} \exp(-\psi)\\ + &= \tan^{-1}\sinh\psi\end{split}\]</div> +</section> +</section> +<section id="ellipsoidal-form"> +<h3>Ellipsoidal form<a class="headerlink" href="#ellipsoidal-form" title="Permalink to this headline">¶</a></h3> +<p>For the ellipsoidal form of the projection we introduce the scaling factor:</p> +<div class="math notranslate nohighlight"> +\[k_0 = m( \phi_{ts} )\]</div> +<p>where</p> +<div class="math notranslate nohighlight"> +\[m(\phi) = \frac{\cos\phi}{\sqrt{1 - e^2\sin^2\phi}}\]</div> +<p><span class="math notranslate nohighlight">\(a\,m(\phi)\)</span> is the radius of the circle of latitude <span class="math notranslate nohighlight">\(\phi\)</span>.</p> +<section id="id2"> +<h4>Forward projection<a class="headerlink" href="#id2" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[x = k_0 a \lambda; \qquad y = k_0 a \psi\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\psi &= \ln\tan\biggl(\frac\pi4 + \frac{\phi}2\biggr) + -\frac12 e + \ln \biggl(\frac{1 + e \sin\phi}{1 - e \sin\phi}\biggr)\\ + &= \sinh^{-1}\tan\phi - e \tanh^{-1}(e \sin\phi)\end{split}\]</div> +</section> +<section id="id3"> +<h4>Inverse projection<a class="headerlink" href="#id3" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\lambda = \frac{x}{k_0 a}; \quad \psi = \frac{y}{k_0 a}\]</div> +<p>The latitude <span class="math notranslate nohighlight">\(\phi\)</span> is found by inverting the equation for +<span class="math notranslate nohighlight">\(\psi\)</span>. This follows the method given by <span id="id4">[<a class="reference internal" href="../../zreferences.html#id21" title="Karney, C. F. F. Transverse Mercator with an accuracy of a few nanometers. J. Geod., 85(8):475-485, August 2011. arXiv:1002.1417, doi:10.1007/s00190-011-0445-3.">Karney2011tm</a>]</span>. +Start by introducing the conformal latitude</p> +<div class="math notranslate nohighlight"> +\[\chi = \tan^{-1}\sinh\psi\]</div> +<p>The tangents of the latitudes <span class="math notranslate nohighlight">\(\tau = \tan\phi\)</span> and <span class="math notranslate nohighlight">\(\tau' = +\tan\chi = \sinh\psi\)</span> are related by</p> +<div class="math notranslate nohighlight"> +\[\tau' = \tau \sqrt{1 + \sigma^2} - \sigma \sqrt{1 + \tau^2}\]</div> +<p>where</p> +<div class="math notranslate nohighlight"> +\[\sigma = \sinh\bigl(e \tanh^{-1}(e \tau/\sqrt{1 + \tau^2}) \bigr)\]</div> +<p>This is obtained by taking the <span class="math notranslate nohighlight">\(\sinh\)</span> of the equation for +<span class="math notranslate nohighlight">\(\psi\)</span> and using the multiple argument formula. The equation for +<span class="math notranslate nohighlight">\(\tau'\)</span> can be solved to give <span class="math notranslate nohighlight">\(\tau\)</span> using Newton’s method +using <span class="math notranslate nohighlight">\(\tau = \tau'/(1 - e^2)\)</span> as an initial guess and with the +needed derivative given by</p> +<div class="math notranslate nohighlight"> +\[\frac{d\tau'}{d\tau} = \frac{1 - e^2}{1 + (1 - e^2)\tau^2} +\sqrt{1 + \tau'^2} \sqrt{1 + \tau^2}\]</div> +<p>This converges after no more than 2 iterations. Finally set +<span class="math notranslate nohighlight">\(\phi=\tan^{-1}\tau\)</span>.</p> +</section> +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Mercator_projection">Wikipedia</a></p></li> +<li><p><a class="reference external" href="http://mathworld.wolfram.com/MercatorProjection.html">Wolfram Mathworld</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mbtfps.html" class="btn btn-neutral float-left" title="McBryde-Thomas Flat-Polar Sinusoidal" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mil_os.html" class="btn btn-neutral float-right" title="Miller Oblated Stereographic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="aitoff.html">Aitoff</a></li> +<li class="toctree-l3"><a class="reference internal" href="alsk.html">Modified Stereographic of Alaska</a></li> +<li class="toctree-l3"><a class="reference internal" href="apian.html">Apian Globular I</a></li> +<li class="toctree-l3"><a class="reference internal" href="august.html">August Epicycloidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="bacon.html">Bacon Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="bertin1953.html">Bertin 1953</a></li> +<li class="toctree-l3"><a class="reference internal" href="bipc.html">Bipolar conic of western hemisphere</a></li> +<li class="toctree-l3"><a class="reference internal" href="boggs.html">Boggs Eumorphic</a></li> +<li class="toctree-l3"><a class="reference internal" href="bonne.html">Bonne (Werner lat_1=90)</a></li> +<li class="toctree-l3"><a class="reference internal" href="calcofi.html">Cal Coop Ocean Fish Invest Lines/Stations</a></li> +<li class="toctree-l3"><a class="reference internal" href="cass.html">Cassini (Cassini-Soldner)</a></li> +<li class="toctree-l3"><a class="reference internal" href="cc.html">Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="ccon.html">Central Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="cea.html">Equal Area Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="chamb.html">Chamberlin Trimetric</a></li> +<li class="toctree-l3"><a class="reference internal" href="collg.html">Collignon</a></li> +<li class="toctree-l3"><a class="reference internal" href="col_urban.html">Colombia Urban</a></li> +<li class="toctree-l3"><a class="reference internal" href="comill.html">Compact Miller</a></li> +<li class="toctree-l3"><a class="reference internal" href="crast.html">Craster Parabolic (Putnins P4)</a></li> +<li class="toctree-l3"><a class="reference internal" href="denoy.html">Denoyer Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Miller Oblated Stereographic</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Miller Oblated Stereographic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/mil_os.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="merc.html" class="btn btn-neutral float-left" title="Mercator" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mill.html" class="btn btn-neutral float-right" title="Miller Cylindrical" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="miller-oblated-stereographic"> +<span id="mil-os"></span><h1>Miller Oblated Stereographic<a class="headerlink" href="#miller-oblated-stereographic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mil_os</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/mil_os.png"><img alt="Miller Oblated Stereographic" src="../../_images/mil_os.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mil_os</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="merc.html" class="btn btn-neutral float-left" title="Mercator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="mill.html" class="btn btn-neutral float-right" title="Miller Cylindrical" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the 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<li>Miller Cylindrical</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/mill.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="mil_os.html" class="btn btn-neutral float-left" title="Miller Oblated Stereographic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="misrsom.html" class="btn btn-neutral float-right" title="Space oblique for MISR" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="miller-cylindrical"> +<span id="mill"></span><h1>Miller Cylindrical<a class="headerlink" href="#miller-cylindrical" title="Permalink to this headline">¶</a></h1> +<p>The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. +The latitude is scaled by a factor of <span class="math notranslate nohighlight">\(\frac{4}{5}\)</span>, projected according to Mercator, and then the result is multiplied by <span class="math notranslate nohighlight">\(\frac{5}{4}\)</span> to retain scale along the equator.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Neither conformal nor equal area cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse spherical</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but best used near the equator</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>mill</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id3"> +<a class="reference internal image-reference" href="../../_images/mill.png"><img alt="Miller Cylindrical" src="../../_images/mill.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=mill</span></code></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The Miller Cylindrical projection is used for world maps and in several atlases, +including the National Atlas of the United States (USGS, 1970, p. 330-331) <span id="id1">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>.</p> +<p>Example using Central meridian 90°W:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo -100 35 | proj +proj=mill +lon_0=90w +-1113194.91 4061217.24 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the Miller projection are all taken from <span id="id2">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>.</p> +<section id="forward-projection"> +<h3>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[x = \lambda\]</div> +<div class="math notranslate nohighlight"> +\[y = 1.25 * \ln \left[ \tan \left(\frac{\pi}{4} + 0.4 * \phi \right) \right]\]</div> +</section> +<section id="inverse-projection"> +<h3>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[\lambda = x\]</div> +<div class="math notranslate nohighlight"> +\[\phi = 2.5 * ( \arctan \left[ e^{0.8 * y} \right] - \frac{\pi}{4} )\]</div> +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Miller_cylindrical_projection">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mil_os.html" class="btn btn-neutral float-left" title="Miller Oblated Stereographic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="misrsom.html" class="btn btn-neutral float-right" title="Space oblique for MISR" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference 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class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" 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Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Space oblique for MISR</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/misrsom.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="mill.html" class="btn btn-neutral float-left" title="Miller Cylindrical" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="moll.html" class="btn btn-neutral float-right" title="Mollweide" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="space-oblique-for-misr"> +<span id="misrsom"></span><h1>Space oblique for MISR<a class="headerlink" href="#space-oblique-for-misr" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>misrsom</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/misrsom.png"><img alt="Space oblique for MISR" src="../../_images/misrsom.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=misrsom</span> <span class="pre">+path=1</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-path"> +<span class="sig-name descname"><span class="pre">+path</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-path" title="Permalink to this definition">¶</a></dt> +<dd><p>Selected path of satellite. Value between 1 and 233.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="mill.html" class="btn btn-neutral float-left" title="Miller Cylindrical" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="moll.html" class="btn btn-neutral float-right" title="Mollweide" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Mollweide</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/moll.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="misrsom.html" class="btn btn-neutral float-left" title="Space oblique for MISR" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="murd1.html" class="btn btn-neutral float-right" title="Murdoch I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="mollweide"> +<span id="moll"></span><h1>Mollweide<a class="headerlink" href="#mollweide" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>moll</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/moll.png"><img alt="Mollweide" src="../../_images/moll.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=moll</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="misrsom.html" class="btn btn-neutral float-left" title="Space oblique for MISR" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="murd1.html" class="btn btn-neutral float-right" title="Murdoch I" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" 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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li 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class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Murdoch I</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/murd1.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="moll.html" class="btn btn-neutral float-left" title="Mollweide" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="murd2.html" class="btn btn-neutral float-right" title="Murdoch II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="murdoch-i"> +<span id="murd1"></span><h1>Murdoch I<a class="headerlink" href="#murdoch-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>murd1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/murd1.png"><img alt="Murdoch I" src="../../_images/murd1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=murd1</span> <span class="pre">+lat_1=30</span> <span class="pre">+lat_2=50</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="moll.html" class="btn btn-neutral float-left" title="Mollweide" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="murd2.html" class="btn btn-neutral float-right" title="Murdoch II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Murdoch II</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" 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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Murdoch II</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/murd2.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="murd1.html" class="btn btn-neutral float-left" title="Murdoch I" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="murd3.html" class="btn btn-neutral float-right" title="Murdoch III" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="murdoch-ii"> +<span id="murd2"></span><h1>Murdoch II<a class="headerlink" href="#murdoch-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>murd2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/murd2.png"><img alt="Murdoch II" src="../../_images/murd2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=murd2</span> <span class="pre">+lat_1=30</span> <span class="pre">+lat_2=50</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="murd1.html" class="btn btn-neutral float-left" title="Murdoch I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="murd3.html" class="btn btn-neutral float-right" title="Murdoch III" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="natearth.html" class="btn btn-neutral float-right" title="Natural Earth" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="murdoch-iii"> +<span id="murd3"></span><h1>Murdoch III<a class="headerlink" href="#murdoch-iii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>murd3</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/murd3.png"><img alt="Murdoch III" src="../../_images/murd3.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=murd3</span> <span class="pre">+lat_1=30</span> <span class="pre">+lat_2=50</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="murd2.html" class="btn btn-neutral float-left" title="Murdoch II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="natearth.html" class="btn btn-neutral float-right" title="Natural Earth" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li 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href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/natearth.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="murd3.html" class="btn btn-neutral float-left" title="Murdoch III" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="natearth2.html" class="btn btn-neutral float-right" title="Natural Earth II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="natural-earth"> +<span id="natearth"></span><h1>Natural Earth<a class="headerlink" href="#natural-earth" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudo cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>natearth</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/natearth.png"><img alt="Natural Earth" src="../../_images/natearth.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=natearth</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>The Natural Earth projection is intended for making world maps. A distinguishing trait +is its slightly rounded corners fashioned to emulate the spherical shape of Earth. +The meridians (except for the central meridian) bend acutely inward as they approach +the pole lines, giving the projection a hint of three-dimensionality. This bending +also suggests that the meridians converge at the poles instead of truncating at the +top and bottom edges. The distortion characteristics of the Natural Earth projection +compare favorably to other world map projections.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The Natural Earth projection has no special options so usage is simple. Here is +an example of an inverse projection on a sphere with a radius of 7500 m:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 3500 -8000 | proj -I +proj=natearth +a=7500 +37d54'6.091"E 61d23'4.582"S +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Natural_Earth_projection">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="murd3.html" class="btn btn-neutral float-left" title="Murdoch III" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="natearth2.html" class="btn btn-neutral float-right" title="Natural Earth II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Natural Earth II</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/natearth2.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="natearth.html" class="btn btn-neutral float-left" title="Natural Earth" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nell.html" class="btn btn-neutral float-right" title="Nell" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="natural-earth-ii"> +<span id="natearth2"></span><h1>Natural Earth II<a class="headerlink" href="#natural-earth-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudo cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>natearth2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/natearth2.png"><img alt="Natural Earth II" src="../../_images/natearth2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=natearth2</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>The Natural Earth II projection is intended for making world maps. At high +latitudes, meridians bend steeply toward short pole lines resulting in a map +with highly rounded corners that resembles an elongated globe.</p> +<p>See <span id="id1">[<a class="reference internal" href="../../zreferences.html#id33" title="Šavrič, B., Patterson, T., and Jenny, B. The Natural Earth II world map projection. International Journal of Cartography, 1(2):123–133, 2015. URL: https://www.researchgate.net/publication/290447301_The_Natural_Earth_II_world_map_projection, doi:10.1080/23729333.2015.1093312.">Savric2015</a>]</span></p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="natearth.html" class="btn btn-neutral float-left" title="Natural Earth" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nell.html" class="btn btn-neutral float-right" title="Nell" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Nell</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Nell</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/nell.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="natearth2.html" class="btn btn-neutral float-left" title="Natural Earth II" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nell_h.html" class="btn btn-neutral float-right" title="Nell-Hammer" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="nell"> +<span id="id1"></span><h1>Nell<a class="headerlink" href="#nell" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>nell</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/nell.png"><img alt="Nell" src="../../_images/nell.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=nell</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="natearth2.html" class="btn btn-neutral float-left" title="Natural Earth II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nell_h.html" class="btn btn-neutral float-right" title="Nell-Hammer" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="nell.html" class="btn btn-neutral float-left" title="Nell" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nicol.html" class="btn btn-neutral float-right" title="Nicolosi Globular" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="nell-hammer"> +<span id="nell-h"></span><h1>Nell-Hammer<a class="headerlink" href="#nell-hammer" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>nell_h</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/nell_h.png"><img alt="Nell-Hammer" src="../../_images/nell_h.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=nell_h</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="nell.html" class="btn btn-neutral float-left" title="Nell" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nicol.html" class="btn btn-neutral float-right" title="Nicolosi Globular" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Nicolosi Globular</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/nicol.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="nell_h.html" class="btn btn-neutral float-left" title="Nell-Hammer" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nsper.html" class="btn btn-neutral float-right" title="Near-sided perspective" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="nicolosi-globular"> +<span id="nicol"></span><h1>Nicolosi Globular<a class="headerlink" href="#nicolosi-globular" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudoconical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>nicol</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/nicol.png"><img alt="Nicolosi Globular" src="../../_images/nicol.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=nicol</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="nell_h.html" class="btn btn-neutral float-left" title="Nell-Hammer" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nsper.html" class="btn btn-neutral float-right" title="Near-sided perspective" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li 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Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li 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class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a 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class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Near-sided perspective</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/nsper.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="nicol.html" class="btn btn-neutral float-left" title="Nicolosi Globular" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nzmg.html" class="btn btn-neutral float-right" title="New Zealand Map Grid" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="near-sided-perspective"> +<span id="nsper"></span><h1>Near-sided perspective<a class="headerlink" href="#near-sided-perspective" title="Permalink to this headline">¶</a></h1> +<p>The near-sided perspective projection simulates a view from a height +<span class="math notranslate nohighlight">\(h\)</span> similar to how a satellite in orbit would see it.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal. Neither conformal nor equal area.</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, although for one hemisphere at a time.</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>nsper</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/nsper.png"><img alt="Near-sided perspective" src="../../_images/nsper.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=nsper</span> <span class="pre">+h=3000000</span> <span class="pre">+lat_0=-20</span> <span class="pre">+lon_0=145</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-h"> +<span class="sig-name descname"><span class="pre">+h</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-h" title="Permalink to this definition">¶</a></dt> +<dd><p>Height of the view point above the Earth and must be in the same units as +the radius of the sphere or semimajor axis of the ellipsoid.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="nicol.html" class="btn btn-neutral float-left" title="Nicolosi Globular" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="nzmg.html" class="btn btn-neutral float-right" title="New Zealand Map Grid" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal 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Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>New Zealand Map Grid</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/nzmg.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="nsper.html" class="btn btn-neutral float-left" title="Near-sided perspective" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ob_tran.html" class="btn btn-neutral float-right" title="General Oblique Transformation" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="new-zealand-map-grid"> +<span id="nzmg"></span><h1>New Zealand Map Grid<a class="headerlink" href="#new-zealand-map-grid" title="Permalink to this headline">¶</a></h1> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/nzmg.png"><img alt="New Zealand Map Grid" src="../../_images/nzmg.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=nzmg</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All standard projection parameters are hard-coded for this projection</p> +</div> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="nsper.html" class="btn btn-neutral float-left" title="Near-sided perspective" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ob_tran.html" class="btn btn-neutral float-right" title="General Oblique Transformation" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div 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Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev 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+</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>ob_tran</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/ob_tran.png"><img alt="General Oblique Transformation" src="../../_images/ob_tran.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=ob_tran</span> <span class="pre">+o_proj=mill</span> <span class="pre">+o_lon_p=40</span> <span class="pre">+o_lat_p=50</span> <span class="pre">+lon_0=60</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>All of the projections of spherical library can be used as an +oblique projection by means of the General Oblique Transformation. The user +performs the oblique transformation by selecting the oblique projection +<code class="docutils literal notranslate"><span class="pre">+proj=ob_tran</span></code>, specifying the translation factors, <a class="reference internal" href="#cmdoption-arg-o_lat_p"><code class="xref std std-option docutils literal notranslate"><span class="pre">+o_lat_p</span></code></a>, and +<a class="reference internal" href="#cmdoption-arg-o_lon_p"><code class="xref std std-option docutils literal notranslate"><span class="pre">+o_lon_p</span></code></a>, and the projection to be used, <a class="reference internal" href="#cmdoption-arg-o_proj"><code class="xref std std-option docutils literal notranslate"><span class="pre">+o_proj</span></code></a>. In the +example of the Fairgrieve projection, the latitude and longitude of the North pole +of the unrotated geographic CRS, <span class="math notranslate nohighlight">\(\alpha\)</span> and <span class="math notranslate nohighlight">\(\beta\)</span> respectively, +expressed in the rotated geographic CRS, are to be placed +at 45°N and 90°W and the <a class="reference internal" href="moll.html#moll"><span class="std std-ref">Mollweide</span></a> projection is used. Because the central meridian +of the translated coordinates will follow the <span class="math notranslate nohighlight">\(\beta\)</span> meridian it is +necessary to translate the translated system so that the Greenwich meridian +will pass through the center of the projection by offsetting the central meridian.</p> +<p>The final control for this projection is:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=ob_tran +o_proj=moll +o_lat_p=45 +o_lon_p=-90 +lon_0=-90 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_proj"> +<span id="cmdoption-arg-o-proj"></span><span class="sig-name descname"><span class="pre">+o_proj</span></span><span class="sig-prename descclassname"><span class="pre">=<projection></span></span><a class="headerlink" href="#cmdoption-arg-o_proj" title="Permalink to this definition">¶</a></dt> +<dd><p>Oblique projection.</p> +</dd></dl> + +<p>In addition to specifying an oblique projection, <em>how</em> to rotate the projection +should be specified. This is done in one of three ways: Define a new pole, +rotate the projection about a given point or define a new “equator” spanned by +two points on the sphere. See the details below.</p> +<section id="new-pole"> +<h4>New pole<a class="headerlink" href="#new-pole" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lat_p"> +<span id="cmdoption-arg-o-lat-p"></span><span class="sig-name descname"><span class="pre">+o_lat_p</span></span><span class="sig-prename descclassname"><span class="pre">=<latitude></span></span><a class="headerlink" href="#cmdoption-arg-o_lat_p" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of the North pole of the unrotated source CRS, expressed in the rotated geographic CRS.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lon_p"> +<span id="cmdoption-arg-o-lon-p"></span><span class="sig-name descname"><span class="pre">+o_lon_p</span></span><span class="sig-prename descclassname"><span class="pre">=<longitude></span></span><a class="headerlink" href="#cmdoption-arg-o_lon_p" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of the North pole of the unrotated source CRS, expressed in the rotated geographic CRS.</p> +</dd></dl> + +</section> +<section id="rotate-about-point"> +<h4>Rotate about point<a class="headerlink" href="#rotate-about-point" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_alpha"> +<span id="cmdoption-arg-o-alpha"></span><span class="sig-name descname"><span class="pre">+o_alpha</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_alpha" title="Permalink to this definition">¶</a></dt> +<dd><p>Angle to rotate the projection with.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lon_c"> +<span id="cmdoption-arg-o-lon-c"></span><span class="sig-name descname"><span class="pre">+o_lon_c</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_lon_c" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of the point the projection will be rotated about.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lat_c"> +<span id="cmdoption-arg-o-lat-c"></span><span class="sig-name descname"><span class="pre">+o_lat_c</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_lat_c" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of the point the projection will be rotated about.</p> +</dd></dl> + +</section> +<section id="new-equator-points"> +<h4>New “equator” points<a class="headerlink" href="#new-equator-points" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lon_1"> +<span id="cmdoption-arg-o-lon-1"></span><span class="sig-name descname"><span class="pre">+o_lon_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_lon_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lat_1"> +<span id="cmdoption-arg-o-lat-1"></span><span class="sig-name descname"><span class="pre">+o_lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lon_2"> +<span id="cmdoption-arg-o-lon-2"></span><span class="sig-name descname"><span class="pre">+o_lon_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_lon_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of second point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-o_lat_2"> +<span id="cmdoption-arg-o-lat-2"></span><span class="sig-name descname"><span class="pre">+o_lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-o_lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of second point.</p> +</dd></dl> + +</section> +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="nzmg.html" class="btn btn-neutral float-left" title="New Zealand Map Grid" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ocea.html" class="btn btn-neutral float-right" title="Oblique Cylindrical Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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<a href="ob_tran.html" class="btn btn-neutral float-left" title="General Oblique Transformation" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="oea.html" class="btn btn-neutral float-right" title="Oblated Equal Area" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="oblique-cylindrical-equal-area"> +<span id="ocea"></span><h1>Oblique Cylindrical Equal Area<a class="headerlink" href="#oblique-cylindrical-equal-area" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>ocea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/ocea.png"><img alt="Oblique Cylindrical Equal Area" src="../../_images/ocea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=ocea</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<p>For the Oblique Cylindrical Equal Area projection a pole of rotation is needed. +The pole can be defined in two ways: By a point and azimuth or by providing to +points that make up the pole.</p> +<section id="point-azimuth"> +<h4>Point & azimuth<a class="headerlink" href="#point-azimuth" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lonc"> +<span class="sig-name descname"><span class="pre">+lonc</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lonc" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of rotational pole point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-alpha"> +<span class="sig-name descname"><span class="pre">+alpha</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-alpha" title="Permalink to this definition">¶</a></dt> +<dd><p>Angle of rotational pole.</p> +</dd></dl> + +</section> +<section id="two-points"> +<h4>Two points<a class="headerlink" href="#two-points" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_1"> +<span id="cmdoption-arg-lon-1"></span><span class="sig-name descname"><span class="pre">+lon_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_2"> +<span id="cmdoption-arg-lon-2"></span><span class="sig-name descname"><span class="pre">+lon_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of second point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of second point.</p> +</dd></dl> + +</section> +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="ob_tran.html" class="btn btn-neutral float-left" title="General Oblique Transformation" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="oea.html" class="btn btn-neutral float-right" title="Oblated Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="ocea.html" class="btn btn-neutral float-left" title="Oblique Cylindrical Equal Area" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="omerc.html" class="btn btn-neutral float-right" title="Oblique Mercator" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="oblated-equal-area"> +<span id="oea"></span><h1>Oblated Equal Area<a class="headerlink" href="#oblated-equal-area" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>oea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/oea.png"><img alt="Oblated Equal Area" src="../../_images/oea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=oea</span> <span class="pre">+m=1</span> <span class="pre">+n=2</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>Described in <span id="id1">[<a class="reference internal" href="../../zreferences.html#id36" title="Snyder, J. P. New equal-area map projections for noncircular regions. The American Cartographer, 15(4):341–356, 1988. doi:10.1559/152304088783886784.">Snyder1988</a>]</span>.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-m"> +<span class="sig-name descname"><span class="pre">+m</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-m" title="Permalink to this definition">¶</a></dt> +<dd></dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-n"> +<span class="sig-name descname"><span class="pre">+n</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-n" title="Permalink to this definition">¶</a></dt> +<dd></dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-theta"> +<span class="sig-name descname"><span class="pre">+theta</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-theta" title="Permalink to this definition">¶</a></dt> +<dd></dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="ocea.html" class="btn btn-neutral float-left" title="Oblique Cylindrical Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="omerc.html" class="btn btn-neutral float-right" title="Oblique Mercator" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="#usage">Usage</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Oblique Mercator</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/omerc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="oea.html" class="btn btn-neutral float-left" title="Oblated Equal Area" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ortel.html" class="btn btn-neutral float-right" title="Ortelius Oval" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="oblique-mercator"> +<span id="omerc"></span><h1>Oblique Mercator<a class="headerlink" href="#oblique-mercator" title="Permalink to this headline">¶</a></h1> +<p>The Oblique Mercator projection is a cylindrical map projection that closes the +gap between the Mercator and the Transverse Mercator projections.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conformal cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, but reasonably accurate only within 15 degrees +of the oblique central line</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>omerc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id3"> +<a class="reference internal image-reference" href="../../_images/omerc.png"><img alt="Oblique Mercator" src="../../_images/omerc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=omerc</span> <span class="pre">+lat_1=45</span> <span class="pre">+lat_2=55</span></code></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>Figuratively, the cylinder used for developing the Mercator projection touches +the planet along the Equator, while that of the Transverse Mercator touches the +planet along a meridian, i.e. along a line perpendicular to the Equator.</p> +<p>The cylinder for the Oblique Mercator, however, touches the planet along a line +at an arbitrary angle with the Equator. Hence, the Oblique Mercator projection +is useful for mapping areas having their greatest extent along a direction that +is neither north-south, nor east-west.</p> +<p>The Mercator and the Transverse Mercator projections are both limiting forms of +the Oblique Mercator: The Mercator projection is equivalent to an Oblique Mercator +with central line along the Equator, while the Transverse Mercator is equivalent +to an Oblique Mercator with central line along a meridian.</p> +<p>For the sphere, the construction of the Oblique Mercator projection can be +imagined as “tilting the cylinder of a plain Mercator projection”, +so the cylinder, instead of touching the equator, touches an arbitrary great circle +on the sphere. The great circle is defined by the tilt angle of the central line, +hence putting land masses along that great circle near the centre of the map, +where the Equator would go in the plain Mercator case.</p> +<p>The ellipsoidal case, developed by Hotine, and refined by Snyder <span id="id1">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span> +is more complex, involving initial steps projecting from the ellipsoid to another +curved surface, the “aposphere”, then projection from the aposphere to the skew +uv-plane, before finally rectifying the skew uv-plane onto the map XY plane.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The tilt angle (azimuth) of the central line can be given in two different ways. +In the first case, the azimuth is given directly, using the option <a class="reference internal" href="urm5.html#cmdoption-arg-alpha"><code class="xref std std-option docutils literal notranslate"><span class="pre">+alpha</span></code></a> +and defining the centre of projection using the options <a class="reference internal" href="#cmdoption-arg-lonc"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lonc</span></code></a> and +<a class="reference internal" href="tpers.html#cmdoption-arg-lat_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_0</span></code></a>. +In the second case, the azimuth is given indirectly by specifying two points on +the central line, using the options +<a class="reference internal" href="wintri.html#cmdoption-arg-lat_1"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_1</span></code></a>, <a class="reference internal" href="tpeqd.html#cmdoption-arg-lon_1"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lon_1</span></code></a>, <a class="reference internal" href="vitk1.html#cmdoption-arg-lat_2"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_2</span></code></a>, and <a class="reference internal" href="tpeqd.html#cmdoption-arg-lon_2"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lon_2</span></code></a>.</p> +<p>Example: Verify that the Mercator projection is a limiting form of the Oblique +Mercator</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 55 | proj +proj=merc +ellps=GRS80 +1335833.89 7326837.71 + +$ echo 12 55 | proj +proj=omerc +lonc=0 +alpha=90 +ellps=GRS80 +1335833.89 7326837.71 +</pre></div> +</div> +<p>Example: Second case - indirectly given azimuth</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 55 | proj +proj=omerc +lon_1=-1 +lat_1=1 +lon_2=0 +lat_2=0 +ellps=GRS80 + 349567.57 6839490.50 +</pre></div> +</div> +<p>Example: An approximation of the Danish “System 34” from <span id="id2">[<a class="reference internal" href="../../zreferences.html#id30" title="Rittri, M. New omerc approximations of Denmark System 34. e-mail, 2012. URL: https://lists.osgeo.org/pipermail/proj/2012-June/005926.html.">Rittri2012</a>]</span></p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 10.536498003 56.229892362 | proj +proj=omerc +axis=wnu +lonc=9.46 +lat_0=56.13333333 +x_0=-266906.229 +y_0=189617.957 +k=0.9999537 +alpha=-0.76324 +gamma=0 +ellps=GRS80 +200000.13 199999.89 +</pre></div> +</div> +<p>The input coordinate represents the System 34 datum point “Agri Bavnehoj”, with coordinates +(200000, 200000) by definition. So at the datum point, the approximation is off by about 17 cm. +This use case represents a datum shift from a cylinder projection on an old, slightly +misaligned datum, to a similar projection on a modern datum.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="central-point-and-azimuth-method"> +<h3>Central point and azimuth method<a class="headerlink" href="#central-point-and-azimuth-method" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-alpha"> +<span class="sig-name descname"><span class="pre">+alpha</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-alpha" title="Permalink to this definition">¶</a></dt> +<dd><p>Azimuth of centerline clockwise from north at the center point of the line. +If <a class="reference internal" href="#cmdoption-arg-gamma"><code class="xref std std-option docutils literal notranslate"><span class="pre">+gamma</span></code></a> is not given then <a class="reference internal" href="urm5.html#cmdoption-arg-alpha"><code class="xref std std-option docutils literal notranslate"><span class="pre">+alpha</span></code></a> determines the value of +<a class="reference internal" href="#cmdoption-arg-gamma"><code class="xref std std-option docutils literal notranslate"><span class="pre">+gamma</span></code></a>.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-gamma"> +<span class="sig-name descname"><span class="pre">+gamma</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-gamma" title="Permalink to this definition">¶</a></dt> +<dd><p>Azimuth of centerline clockwise from north of the rectified +bearing of centre line. If <a class="reference internal" href="urm5.html#cmdoption-arg-alpha"><code class="xref std std-option docutils literal notranslate"><span class="pre">+alpha</span></code></a> is not given, then +<a class="reference internal" href="#cmdoption-arg-gamma"><code class="xref std std-option docutils literal notranslate"><span class="pre">+gamma</span></code></a> is used to determine <a class="reference internal" href="urm5.html#cmdoption-arg-alpha"><code class="xref std std-option docutils literal notranslate"><span class="pre">+alpha</span></code></a>.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lonc"> +<span class="sig-name descname"><span class="pre">+lonc</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lonc" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of the central point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of the central point.</p> +</dd></dl> + +</section> +<section id="two-point-method"> +<h3>Two point method<a class="headerlink" href="#two-point-method" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_1"> +<span id="cmdoption-arg-lon-1"></span><span class="sig-name descname"><span class="pre">+lon_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_2"> +<span id="cmdoption-arg-lon-2"></span><span class="sig-name descname"><span class="pre">+lon_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of second point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of second point.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-no_rot"> +<span id="cmdoption-arg-no-rot"></span><span class="sig-name descname"><span class="pre">+no_rot</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-no_rot" title="Permalink to this definition">¶</a></dt> +<dd><p>No rectification (not “no rotation” as one may well assume). +Do not take the last step from the skew uv-plane to the map +XY plane.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>This option is probably only marginally useful, but remains for (mostly) historical reasons.</p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-no_off"> +<span id="cmdoption-arg-no-off"></span><span class="sig-name descname"><span class="pre">+no_off</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-no_off" title="Permalink to this definition">¶</a></dt> +<dd><p>Do not offset origin to center of projection.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="oea.html" class="btn btn-neutral float-left" title="Oblated Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ortel.html" class="btn btn-neutral float-right" title="Ortelius Oval" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Ortelius Oval</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/ortel.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="omerc.html" class="btn btn-neutral float-left" title="Oblique Mercator" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ortho.html" class="btn btn-neutral float-right" title="Orthographic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="ortelius-oval"> +<span id="ortel"></span><h1>Ortelius Oval<a class="headerlink" href="#ortelius-oval" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>ortel</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/ortel.png"><img alt="Ortelius Oval" src="../../_images/ortel.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=ortel</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="omerc.html" class="btn btn-neutral float-left" title="Oblique Mercator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ortho.html" class="btn btn-neutral float-right" title="Orthographic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" 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VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Orthographic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/ortho.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="ortel.html" class="btn btn-neutral float-left" title="Ortelius Oval" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="patterson.html" class="btn btn-neutral float-right" title="Patterson" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="orthographic"> +<span id="ortho"></span><h1>Orthographic<a class="headerlink" href="#orthographic" title="Permalink to this headline">¶</a></h1> +<p>The orthographic projection is a perspective azimuthal projection centered +around a given latitude and longitude.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, although only one hemisphere can be seen at a +time</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>ortho</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/ortho.png"><img alt="Orthographic" src="../../_images/ortho.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=ortho</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>Before PROJ 7.2, only the spherical formulation was implemented. If +wanting to replicate PROJ < 7.2 results with newer versions, the +ellipsoid must be forced to a sphere, for example by adding a <code class="docutils literal notranslate"><span class="pre">+f=0</span></code> +parameter.</p> +</div> +<p>This projection method corresponds to <code class="docutils literal notranslate"><span class="pre">EPSG:9840</span></code>.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="ortel.html" class="btn btn-neutral float-left" title="Ortelius Oval" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="patterson.html" class="btn btn-neutral float-right" title="Patterson" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference 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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Patterson</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" 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Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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href="ortho.html" class="btn btn-neutral float-left" title="Orthographic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="pconic.html" class="btn btn-neutral float-right" title="Perspective Conic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="patterson"> +<span id="id1"></span><h1>Patterson<a class="headerlink" href="#patterson" title="Permalink to this headline">¶</a></h1> +<p>The Patterson projection is a cylindrical map projection designed for +general-purpose mapmaking.</p> +<p>See <span id="id2">[<a class="reference internal" href="../../zreferences.html#id28" title="Patterson, T., Šavrič, B., and Jenny, B. Introducing the Patterson cylindrical projection. Cartographic Perspectives, 2014. doi:10.14714/CP78.1270.">Patterson2014</a>]</span></p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>patterson</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id3"> +<a class="reference internal image-reference" href="../../_images/patterson.png"><img alt="Patterson" src="../../_images/patterson.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=patterson</span></code></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="ortho.html" class="btn btn-neutral float-left" title="Orthographic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="pconic.html" class="btn btn-neutral float-right" title="Perspective Conic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Perspective Conic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/pconic.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="patterson.html" class="btn btn-neutral float-left" title="Patterson" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="peirce_q.html" class="btn btn-neutral float-right" title="Peirce Quincuncial" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="perspective-conic"> +<span id="pconic"></span><h1>Perspective Conic<a class="headerlink" href="#perspective-conic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>pconic</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/pconic.png"><img alt="Perspective Conic" src="../../_images/pconic.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=pconic</span> <span class="pre">+lat_1=25</span> <span class="pre">+lat_2=75</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="patterson.html" class="btn btn-neutral float-left" title="Patterson" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="peirce_q.html" class="btn btn-neutral float-right" title="Peirce Quincuncial" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Peirce Quincuncial</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/peirce_q.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="pconic.html" class="btn btn-neutral float-left" title="Perspective Conic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="poly.html" class="btn btn-neutral float-right" title="Polyconic (American)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="peirce-quincuncial"> +<span id="peirce-q"></span><h1>Peirce Quincuncial<a class="headerlink" href="#peirce-quincuncial" title="Permalink to this headline">¶</a></h1> +<p>The Peirce Quincuncial projection is a conformal map projection +that transforms the circle of the northern hemisphere into a square, +and the southern hemisphere split into four triangles arranged +around the square to form a quincunx. The resulting projection +is a regular diamond shape or can be rotated to form a square. +The resulting tile can be infinitely tessellated. Though this implementation +defaults to a central meridian of 0, it is more common to use a central +meridian of around 25 to optimise the distortions. Peirce’s original +published map from 1879 used a central meridian of approx -70. +The diamond and square versions can be produced using the +<code class="docutils literal notranslate"><span class="pre">+shape=diamond</span></code> and <code class="docutils literal notranslate"><span class="pre">+shape=square</span></code> options respectively. +This implementation includes an alternative lateral projection +which places hemispheres side-by-side (<code class="docutils literal notranslate"><span class="pre">+shape=horizontal</span></code> or +<code class="docutils literal notranslate"><span class="pre">+shape=vertical</span></code>). Combined with a general oblique transformation, +this can be used to produced a Grieger Triptychial projection +(see example below).</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>peirce_q</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/peirce_q_square.png"><img alt="Peirce Quincuncial (Square)" src="../../_images/peirce_q_square.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=peirce_q</span> <span class="pre">+lon_0=25</span> <span class="pre">+shape=square</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/peirce_q_diamond.png"><img alt="Peirce Quincuncial (Diamond)" src="../../_images/peirce_q_diamond.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=peirce_q</span> <span class="pre">+lon_0=25</span> <span class="pre">+shape=diamond</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<figure class="align-center" id="id3"> +<a class="reference internal image-reference" href="../../_images/peirce_q_horizontal.png"><img alt="Peirce Quincuncial (Horizontal)" src="../../_images/peirce_q_horizontal.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=peirce_q</span> <span class="pre">+lon_0=25</span> <span class="pre">+shape=horizontal</span></code></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<figure class="align-center" id="id4"> +<a class="reference internal image-reference" href="../../_images/grieger_triptychial.png"><img alt="Grieger Triptychial" src="../../_images/grieger_triptychial.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=pipeline</span> <span class="pre">+step</span> <span class="pre">+proj=ob_tran</span> <span class="pre">+o_proj=peirce_q</span> <span class="pre">+o_lat_p=-45</span> <span class="pre">+o_lon_p=45</span> <span class="pre">+o_type=horizontal</span> <span class="pre">+o_scrollx=-0.25</span> <span class="pre">+step</span> <span class="pre">+proj=affine</span> <span class="pre">+s11=-1</span> <span class="pre">+s12=0</span> <span class="pre">+s21=0</span> <span class="pre">+s22=-1</span></code></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-shape"> +<span class="sig-name descname"><span class="pre">+shape</span></span><span class="sig-prename descclassname"><span class="pre">=square/diamond/horizontal/vertical/nhemisphere/shemisphere</span></span><a class="headerlink" href="#cmdoption-arg-shape" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 9.0.</span></p> +</div> +<p><em>Defaults to diamond.</em></p> +<div class="admonition warning"> +<p class="admonition-title">Warning</p> +<p>This option was wrongly introduced introduced in 8.2.1 with the +<code class="docutils literal notranslate"><span class="pre">type</span></code> name, which was inappropriate as it conflicted with +the <code class="docutils literal notranslate"><span class="pre">+type=crs</span></code> general hint.</p> +</div> +<p>Indicates the shape of transformation applied to the southern hemisphere: +<code class="docutils literal notranslate"><span class="pre">square</span></code> and <code class="docutils literal notranslate"><span class="pre">diamond</span></code> represent the traditional quincuncial form suggested +by Peirce with the southern hemisphere divided into 4 triangles and reflected +outward from the northern hemisphere. The <code class="docutils literal notranslate"><span class="pre">square</span></code> shape is rotated by 45 +degrees to produce the conventional square presentation. The origin lies at +the centre of the square or diamond.</p> +<p>By contrast, the <code class="docutils literal notranslate"><span class="pre">horizontal</span></code> and <code class="docutils literal notranslate"><span class="pre">vertical</span></code> forms reflect the southern +hemisphere laterally across the x or y axis respectively to produce a rectangular +form. The origin lies at the centre of the rectangle.</p> +<p>The other two types, <code class="docutils literal notranslate"><span class="pre">nhemisphere</span></code> and <code class="docutils literal notranslate"><span class="pre">shemisphere</span></code>, discard latitudes of less +than 0 or more than 0, respectively, to allow single hemispheres to be selected. +The origin lies at the centre of the square or diamond.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-scrollx"> +<span class="sig-name descname"><span class="pre">+scrollx</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-scrollx" title="Permalink to this definition">¶</a></dt> +<dd><p>For <code class="docutils literal notranslate"><span class="pre">horizontal</span></code> shape allows a scalar circular scroll of resulting x coordinates +to shift sections of the projection to the other horizontal side of the map.</p> +<p><em>Defaults to 0.0. Must be a scale between -1.0 and 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-scrolly"> +<span class="sig-name descname"><span class="pre">+scrolly</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-scrolly" title="Permalink to this definition">¶</a></dt> +<dd><p>For <code class="docutils literal notranslate"><span class="pre">vertical</span></code> shape allows a scalar circular scroll of resulting y coordinates +to shift sections of the projection to the other vertical side of the map.</p> +<p><em>Defaults to 0.0. Must be a scale between -1.0 and 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="pconic.html" class="btn btn-neutral float-left" title="Perspective Conic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="poly.html" class="btn btn-neutral float-right" title="Polyconic (American)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Polyconic (American)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/poly.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="peirce_q.html" class="btn btn-neutral float-left" title="Peirce Quincuncial" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp1.html" class="btn btn-neutral float-right" title="Putnins P1" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="polyconic-american"> +<span id="poly"></span><h1>Polyconic (American)<a class="headerlink" href="#polyconic-american" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudoconical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>poly</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/poly.png"><img alt="Polyconic (American)" src="../../_images/poly.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=poly</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="peirce_q.html" class="btn btn-neutral float-left" title="Peirce Quincuncial" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp1.html" class="btn btn-neutral float-right" title="Putnins P1" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" 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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Putnins P1</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/putp1.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="poly.html" class="btn btn-neutral float-left" title="Polyconic (American)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp2.html" class="btn btn-neutral float-right" title="Putnins P2" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p1"> +<span id="putp1"></span><h1>Putnins P1<a class="headerlink" href="#putnins-p1" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp1.png"><img alt="Putnins P1" src="../../_images/putp1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp1</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Putnins P1 projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="poly.html" class="btn btn-neutral float-left" title="Polyconic (American)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp2.html" class="btn btn-neutral float-right" title="Putnins P2" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" 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VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" 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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Putnins P2</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/putp2.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="putp1.html" class="btn btn-neutral float-left" title="Putnins P1" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp3.html" class="btn btn-neutral float-right" title="Putnins P3" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p2"> +<span id="putp2"></span><h1>Putnins P2<a class="headerlink" href="#putnins-p2" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp2.png"><img alt="Putnins P2" src="../../_images/putp2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp1.html" class="btn btn-neutral float-left" title="Putnins P1" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp3.html" class="btn btn-neutral float-right" title="Putnins P3" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Putnins P3</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/putp3.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="putp2.html" class="btn btn-neutral float-left" title="Putnins P2" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp3p.html" class="btn btn-neutral float-right" title="Putnins P3’" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p3"> +<span id="putp3"></span><h1>Putnins P3<a class="headerlink" href="#putnins-p3" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp3</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp3.png"><img alt="Putnins P3" src="../../_images/putp3.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp3</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp2.html" class="btn btn-neutral float-left" title="Putnins P2" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp3p.html" class="btn btn-neutral float-right" title="Putnins P3’" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="putp3.html" class="btn btn-neutral float-left" title="Putnins P3" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp4p.html" class="btn btn-neutral float-right" title="Putnins P4’" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p3"> +<span id="putp3p"></span><h1>Putnins P3’<a class="headerlink" href="#putnins-p3" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp3p</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp3p.png"><img alt="Putnins P3'" src="../../_images/putp3p.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp3p</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp3.html" class="btn btn-neutral float-left" title="Putnins P3" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp4p.html" class="btn btn-neutral float-right" title="Putnins P4’" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="putp3p.html" class="btn btn-neutral float-left" title="Putnins P3’" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp5.html" class="btn btn-neutral float-right" title="Putnins P5" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p4"> +<span id="putp4p"></span><h1>Putnins P4’<a class="headerlink" href="#putnins-p4" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp4p</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp4p.png"><img alt="Putnins P4'" src="../../_images/putp4p.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp4p</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp3p.html" class="btn btn-neutral float-left" title="Putnins P3’" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp5.html" class="btn btn-neutral float-right" title="Putnins P5" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" 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class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Putnins P5</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/putp5.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="putp4p.html" class="btn btn-neutral float-left" title="Putnins P4’" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp5p.html" class="btn btn-neutral float-right" title="Putnins P5’" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p5"> +<span id="putp5"></span><h1>Putnins P5<a class="headerlink" href="#putnins-p5" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp5</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp5.png"><img alt="Putnins P5" src="../../_images/putp5.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp5</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp4p.html" class="btn btn-neutral float-left" title="Putnins P4’" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp5p.html" class="btn btn-neutral float-right" title="Putnins P5’" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="toctree-l3"><a class="reference internal" href="cass.html">Cassini (Cassini-Soldner)</a></li> +<li class="toctree-l3"><a class="reference internal" href="cc.html">Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="ccon.html">Central Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="cea.html">Equal Area Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="chamb.html">Chamberlin Trimetric</a></li> +<li class="toctree-l3"><a class="reference internal" href="collg.html">Collignon</a></li> +<li class="toctree-l3"><a class="reference internal" href="col_urban.html">Colombia Urban</a></li> +<li class="toctree-l3"><a class="reference internal" href="comill.html">Compact Miller</a></li> +<li class="toctree-l3"><a class="reference internal" href="crast.html">Craster Parabolic (Putnins P4)</a></li> +<li class="toctree-l3"><a class="reference internal" href="denoy.html">Denoyer Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Putnins P5’</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Putnins P5’</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/putp5p.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="putp5.html" class="btn btn-neutral float-left" title="Putnins P5" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp6.html" class="btn btn-neutral float-right" title="Putnins P6" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p5"> +<span id="putp5p"></span><h1>Putnins P5’<a class="headerlink" href="#putnins-p5" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp5p</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp5p.png"><img alt="Putnins P5'" src="../../_images/putp5p.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp5p</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp5.html" class="btn btn-neutral float-left" title="Putnins P5" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp6.html" class="btn btn-neutral float-right" title="Putnins P6" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="putp6p.html" class="btn btn-neutral float-right" title="Putnins P6’" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p6"> +<span id="putp6"></span><h1>Putnins P6<a class="headerlink" href="#putnins-p6" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp6</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp6.png"><img alt="Putnins P6" src="../../_images/putp6.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp6</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp5p.html" class="btn btn-neutral float-left" title="Putnins P5’" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="putp6p.html" class="btn btn-neutral float-right" title="Putnins P6’" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Putnins P6’</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Putnins P6’</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/putp6p.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="putp6.html" class="btn btn-neutral float-left" title="Putnins P6" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="qua_aut.html" class="btn btn-neutral float-right" title="Quartic Authalic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="putnins-p6"> +<span id="putp6p"></span><h1>Putnins P6’<a class="headerlink" href="#putnins-p6" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>putp6p</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/putp6p.png"><img alt="Putnins P6'" src="../../_images/putp6p.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=putp6p</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp6.html" class="btn btn-neutral float-left" title="Putnins P6" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="qua_aut.html" class="btn btn-neutral float-right" title="Quartic Authalic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/qsc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="qua_aut.html" class="btn btn-neutral float-left" title="Quartic Authalic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="robin.html" class="btn btn-neutral float-right" title="Robinson" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="quadrilateralized-spherical-cube"> +<span id="qsc"></span><h1>Quadrilateralized Spherical Cube<a class="headerlink" href="#quadrilateralized-spherical-cube" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>qsc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<p>The purpose of the Quadrilateralized Spherical Cube (QSC) projection is to project +a sphere surface onto the six sides of a cube:</p> +<a class="reference internal image-reference" href="../../_images/qsc_concept.jpg"><img alt="Quadrilateralized Spherical Cube" class="align-center" src="../../_images/qsc_concept.jpg" style="width: 500px;" /></a> +<p>For this purpose, other alternatives can be used, notably <a class="reference internal" href="gnom.html#gnom"><span class="std std-ref">Gnomonic</span></a> or +<a class="reference internal" href="healpix.html#healpix"><span class="std std-ref">HEALPix</span></a>. However, QSC projection has the following favorable properties:</p> +<p>It is an equal-area projection, and at the same time introduces only limited angular +distortions. It treats all cube sides equally, i.e. it does not use different +projections for polar areas and equatorial areas. These properties make QSC +projection a good choice for planetary-scale terrain rendering. Map data can be +organized in quadtree structures for each cube side. See <span id="id1">[<a class="reference internal" href="../../zreferences.html#id25" title="Lambers, M. and Kolb, A. Ellipsoidal cube maps for accurate rendering of planetary-scale terrain data. In Bregler, C., Sander, P., and Wimmer, M., editors, Pacific Graphics Short Papers. The Eurographics Association, 2012. doi:10.2312/PE/PG/PG2012short/005-010.">LambersKolb2012</a>]</span> for an example.</p> +<p>The QSC projection was introduced by <span id="id2">[<a class="reference internal" href="../../zreferences.html#id27" title="O'Neill, E. M. and Laubscher, R. E. Extended studies of a quadrilateralized spherical cube earth data base. Tech. Rep. EPRF 3-76 (CSC), Computer Sciences Corporation, System Sciences Division, Silver Spring, Md, 1976. URL: https://archive.org/details/DTIC_ADA026294.">ONeilLaubscher1976</a>]</span>, +building on previous work by <span id="id3">[<a class="reference internal" href="../../zreferences.html#id6" title="Chan, F. K. and O'Neill, E. M. Feasibility study of a quadrilateralized spherical cube earth data base. Tech. Rep. EPRF 2-75 (CSC), Computer Sciences Corporation, System Sciences Division, Silver Spring, Md, 1975. URL: https://archive.org/details/ADA010232.">ChanONeil1975</a>]</span>. For clarity: The +earlier QSC variant described in <span id="id4">[<a class="reference internal" href="../../zreferences.html#id6" title="Chan, F. K. and O'Neill, E. M. Feasibility study of a quadrilateralized spherical cube earth data base. Tech. Rep. EPRF 2-75 (CSC), Computer Sciences Corporation, System Sciences Division, Silver Spring, Md, 1975. URL: https://archive.org/details/ADA010232.">ChanONeil1975</a>]</span> became known as the COBE QSC since it +was used by the NASA Cosmic Background Explorer (COBE) project; it is an approximately +equal-area projection and is not the same as the QSC projection.</p> +<p>See also <span id="id5">[<a class="reference internal" href="../../zreferences.html#id5" title="Calabretta, M. R. and Greisen, E. W. Representations of celestial coordinates in FITS. Astronomy & Astrophysics, 395(3):1077–1122, 2002. doi:10.1051/0004-6361:20021327.">CalabrettaGreisen2002</a>]</span> Sec. 5.6.2 and 5.6.3 for a description of both and +some analysis.</p> +<p>In this implementation, the QSC projection projects onto one side of a circumscribed +cube. The cube side is selected by choosing one of the following six projection centers:</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 56%" /> +<col style="width: 44%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=0</span></code></p></td> +<td><p>front cube side</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=90</span></code></p></td> +<td><p>right cube side</p></td> +</tr> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=180</span></code></p></td> +<td><p>back cube side</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=-90</span></code></p></td> +<td><p>left cube side</p></td> +</tr> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=90</span></code></p></td> +<td><p>top cube side</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=-90</span></code></p></td> +<td><p>bottom cube side</p></td> +</tr> +</tbody> +</table> +<p>Furthermore, this implementation allows the projection to be applied to ellipsoids. +A preceding shift to a sphere is performed automatically; see <span id="id6">[<a class="reference internal" href="../../zreferences.html#id25" title="Lambers, M. and Kolb, A. Ellipsoidal cube maps for accurate rendering of planetary-scale terrain data. In Bregler, C., Sander, P., and Wimmer, M., editors, Pacific Graphics Short Papers. The Eurographics Association, 2012. doi:10.2312/PE/PG/PG2012short/005-010.">LambersKolb2012</a>]</span> for details.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The following example uses QSC projection via GDAL to create the six cube side +maps from a world map for the WGS84 ellipsoid:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=0" \ + -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ + worldmap.tiff frontside.tiff + +gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=90" \ + -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ + worldmap.tiff rightside.tiff + +gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=180" \ + -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ + worldmap.tiff backside.tiff + +gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=-90" \ + -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ + worldmap.tiff leftside.tiff + +gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=90 +lon_0=0" \ + -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ + worldmap.tiff topside.tiff + +gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=-90 +lon_0=0" \ + -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ + worldmap.tiff bottomside.tiff +</pre></div> +</div> +<p>Explanation:</p> +<ul class="simple"> +<li><p>QSC projection is selected with <code class="docutils literal notranslate"><span class="pre">+wktext</span> <span class="pre">+proj=qsc</span></code>.</p></li> +<li><p>The WGS84 ellipsoid is specified with <code class="docutils literal notranslate"><span class="pre">+ellps=WGS84</span></code>.</p></li> +<li><p>The cube side is selected with <code class="docutils literal notranslate"><span class="pre">+lat_0=...</span> <span class="pre">+lon_0=...</span></code>.</p></li> +<li><p>The <code class="docutils literal notranslate"><span class="pre">-wo</span></code> options are necessary for GDAL to avoid holes in the output maps.</p></li> +<li><p>The <code class="docutils literal notranslate"><span class="pre">-te</span></code> option limits the extends of the output map to the major axis diameter +(from -radius to +radius in both x and y direction). These are the dimensions of one side +of the circumscribing cube.</p></li> +</ul> +<p>The resulting images can be laid out in a grid like below.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 24%" /> +<col style="width: 27%" /> +<col style="width: 25%" /> +<col style="width: 24%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td></td> +<td><p><a class="reference internal" href="../../_images/qsc_topside.jpg"><img alt="Top side" class="align-middle" src="../../_images/qsc_topside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td> +<td></td> +<td></td> +</tr> +<tr class="row-even"><td><p><a class="reference internal" href="../../_images/qsc_leftside.jpg"><img alt="Left side" class="align-middle" src="../../_images/qsc_leftside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td> +<td><p><a class="reference internal" href="../../_images/qsc_frontside.jpg"><img alt="Front side" class="align-middle" src="../../_images/qsc_frontside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td> +<td><p><a class="reference internal" href="../../_images/qsc_rightside.jpg"><img alt="Right side" class="align-middle" src="../../_images/qsc_rightside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td> +<td><p><a class="reference internal" href="../../_images/qsc_backside.jpg"><img alt="Back side" class="align-middle" src="../../_images/qsc_backside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td> +</tr> +<tr class="row-odd"><td></td> +<td><p><a class="reference internal" href="../../_images/qsc_bottomside.jpg"><img alt="Bottom side" class="align-middle" src="../../_images/qsc_bottomside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td> +<td></td> +<td></td> +</tr> +</tbody> +</table> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Quadrilateralized_spherical_cube">Wikipedia</a></p></li> +<li><p><a class="reference external" href="https://lambda.gsfc.nasa.gov/product/cobe/skymap_info_new.cfm">NASA</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="qua_aut.html" class="btn btn-neutral float-left" title="Quartic Authalic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="robin.html" class="btn btn-neutral float-right" title="Robinson" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a 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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Quartic Authalic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/qua_aut.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="putp6p.html" class="btn btn-neutral float-left" title="Putnins P6’" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="qsc.html" class="btn btn-neutral float-right" title="Quadrilateralized Spherical Cube" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="quartic-authalic"> +<span id="qua-aut"></span><h1>Quartic Authalic<a class="headerlink" href="#quartic-authalic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>qua_aut</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/qua_aut.png"><img alt="Quartic Authalic" src="../../_images/qua_aut.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=qua_aut</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Quartic Authalic projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="putp6p.html" class="btn btn-neutral float-left" title="Putnins P6’" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="qsc.html" class="btn btn-neutral float-right" title="Quadrilateralized Spherical Cube" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>rHEALPix</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/rhealpix.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="healpix.html" class="btn btn-neutral float-left" title="HEALPix" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="igh.html" class="btn btn-neutral float-right" title="Interrupted Goode Homolosine" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="rhealpix"> +<span id="id1"></span><h1>rHEALPix<a class="headerlink" href="#rhealpix" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>rhealpix</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<a class="reference internal image-reference" href="../../_images/rhealpix.png"><img alt="rHEALPix" src="../../_images/rhealpix.png" style="width: 621.0px; height: 455.25px;" /></a> +<p>rHEALPix is a projection based on the HEALPix projection. The implementation of +rHEALPix uses the HEALPix projection. The rHEALPix combines the peaks of the +HEALPix into a square. The square’s position can be translated and rotated across +the x-axis which is a novel approach for the rHEALPix projection. The initial +intention of using rHEALPix in the Spatial Computation Engine Science Collaboration +Environment (SCENZGrid).</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>To run a rHEALPix projection on a WGS84 ellipsoidal model, use the following +command:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj +proj=rhealpix -f '%.2f' +ellps=WGS84 +south_square=0 +north_square=2 -E << EOF +> 55 12 +> EOF +55 12 6115727.86 1553840.13 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-north_square"> +<span id="cmdoption-arg-north-square"></span><span class="sig-name descname"><span class="pre">+north_square</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-north_square" title="Permalink to this definition">¶</a></dt> +<dd><p>Position of the north polar square. Valid inputs are 0–3.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-south_square"> +<span id="cmdoption-arg-south-square"></span><span class="sig-name descname"><span class="pre">+south_square</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-south_square" title="Permalink to this definition">¶</a></dt> +<dd><p>Position of the south polar square. Valid inputs are 0–3.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="http://healpix.jpl.nasa.gov/">NASA</a></p></li> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/HEALPix">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="healpix.html" class="btn btn-neutral float-left" title="HEALPix" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="igh.html" class="btn btn-neutral float-right" title="Interrupted Goode Homolosine" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Robinson</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/robin.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="qsc.html" class="btn btn-neutral float-left" title="Quadrilateralized Spherical Cube" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="rouss.html" class="btn btn-neutral float-right" title="Roussilhe Stereographic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="robinson"> +<span id="robin"></span><h1>Robinson<a class="headerlink" href="#robinson" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>robin</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/robin.png"><img alt="Robinson" src="../../_images/robin.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=robin</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="qsc.html" class="btn btn-neutral float-left" title="Quadrilateralized Spherical Cube" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="rouss.html" class="btn btn-neutral float-right" title="Roussilhe Stereographic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins 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Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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href="robin.html" class="btn btn-neutral float-left" title="Robinson" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="rpoly.html" class="btn btn-neutral float-right" title="Rectangular Polyconic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="roussilhe-stereographic"> +<span id="rouss"></span><h1>Roussilhe Stereographic<a class="headerlink" href="#roussilhe-stereographic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>rouss</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/rouss.png"><img alt="Roussilhe Stereographic" src="../../_images/rouss.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=rouss</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="robin.html" class="btn btn-neutral float-left" title="Robinson" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="rpoly.html" class="btn btn-neutral float-right" title="Rectangular Polyconic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="fahey.html">Fahey</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc.html">Foucaut</a></li> +<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li> +<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li> +<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li> +<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li> +<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li> +<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Rectangular Polyconic</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Rectangular Polyconic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/rpoly.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="rouss.html" class="btn btn-neutral float-left" title="Roussilhe Stereographic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="s2.html" class="btn btn-neutral float-right" title="S2" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="rectangular-polyconic"> +<span id="rpoly"></span><h1>Rectangular Polyconic<a class="headerlink" href="#rectangular-polyconic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudoconical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>rpoly</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/rpoly.png"><img alt="Rectangular Polyconic" src="../../_images/rpoly.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=rpoly</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="rouss.html" class="btn btn-neutral float-left" title="Roussilhe Stereographic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="s2.html" class="btn btn-neutral float-right" title="S2" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">S2</a><ul> +<li 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class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li 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href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/s2.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="rpoly.html" class="btn btn-neutral float-left" title="Rectangular Polyconic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="sch.html" class="btn btn-neutral float-right" title="Spherical Cross-track Height" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="s2"> +<span id="id1"></span><h1>S2<a class="headerlink" href="#s2" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>s2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 8.2.</span></p> +</div> +<p>The S2 projection, like the Quadrilateralized Spherical Cube (QSC) projection, projects +a sphere surface onto the six sides of a cube:</p> +<a class="reference internal image-reference" href="../../_images/qsc_concept.jpg"><img alt="Quadrilateralized Spherical Cube" class="align-center" src="../../_images/qsc_concept.jpg" style="width: 500px;" /></a> +<p>S2 was created by Google to represent geographic data on the whole earth. The documentation can be found +at <a class="reference external" href="https://s2geometry.io/">S2 Geometry</a> It works by first +projecting a point on the sphere to a face of the cube. These are called u,v-coordinates, and they are in [-1,1] x [-1,1]. +This step is followed by a non-linear transformation to normalize the area of rectangles on the sphere. There are three +different choices available for this transformation, meaning that S2 is a family of projections. The final output is in +s,t-coordinates, which are in [0,1] x [0,1]. +See the comments in <a class="reference external" href="https://github.com/google/s2geometry/blob/0c4c460bdfe696da303641771f9def900b3e440f/src/s2/s2coords.h#L226">S2 Code</a> +for an explanation of the tradeoff between speed and area-preservation. Note that the projection is azimuthal when “none” or +“linear” is selected for the area-normalization, but it is not azimuthal when “quadratic” or “tangent” is chosen. See +S2’s <a class="reference external" href="https://s2geometry.io/resources/earthcube">Earthcube page</a> +to visualize the unfolded cube and the orientation of each face.</p> +<p>In this implementation, the cube side is selected by choosing one of the following six projection centers:</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 56%" /> +<col style="width: 44%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=0</span></code></p></td> +<td><p>front cube side</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=90</span></code></p></td> +<td><p>right cube side</p></td> +</tr> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=180</span></code></p></td> +<td><p>back cube side</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=-90</span></code></p></td> +<td><p>left cube side</p></td> +</tr> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=90</span></code></p></td> +<td><p>top cube side</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=-90</span></code></p></td> +<td><p>bottom cube side</p></td> +</tr> +</tbody> +</table> +<p>The specific transformation can be chosen with the UVtoST parameter:</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 46%" /> +<col style="width: 54%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+UVtoST=linear</span></code></p></td> +<td><p>fastest, no normalization</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+UVtoST=quadratic</span></code></p></td> +<td><p>fast, good normalization</p></td> +</tr> +<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+UVtoST=tangent</span></code></p></td> +<td><p>slowest, best normalization</p></td> +</tr> +<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+UVtoST=none</span></code></p></td> +<td><p>returns u,v-coordinates</p></td> +</tr> +</tbody> +</table> +<p>Furthermore, this implementation allows the projection to be applied to ellipsoids. +A preceding shift to a sphere is performed automatically; see <span id="id2">[<a class="reference internal" href="../../zreferences.html#id25" title="Lambers, M. and Kolb, A. Ellipsoidal cube maps for accurate rendering of planetary-scale terrain data. In Bregler, C., Sander, P., and Wimmer, M., editors, Pacific Graphics Short Papers. The Eurographics Association, 2012. doi:10.2312/PE/PG/PG2012short/005-010.">LambersKolb2012</a>]</span> for details. +The output of the projection is in s,t-coordinates ([0,1] x [0,1]), so only the +eccentricity of the ellipse is taken into account: the absolute value of the axes does +not affect the output.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The following example uses S2 on the right face:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 90 0 | ../bin/proj +proj=s2 +lat_0=0 +lon_0=90 +ellps=WGS84 +UVtoST=linear + +0.5 0.5 +</pre></div> +</div> +<p>Explanation:</p> +<ul class="simple"> +<li><p>S2 projection is selected with <code class="docutils literal notranslate"><span class="pre">+proj=s2</span></code>.</p></li> +<li><p>The WGS84 ellipsoid is specified with <code class="docutils literal notranslate"><span class="pre">+ellps=WGS84</span></code>.</p></li> +<li><p>The cube side is selected with <code class="docutils literal notranslate"><span class="pre">+lat_0=...</span> <span class="pre">+lon_0=...</span></code>.</p></li> +<li><p>The normalization transformation is selected with <code class="docutils literal notranslate"><span class="pre">+UVtoST=...</span></code>.</p></li> +</ul> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-UVtoST"> +<span id="cmdoption-arg-uvtost"></span><span class="sig-name descname"><span class="pre">+UVtoST</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-UVtoST" title="Permalink to this definition">¶</a></dt> +<dd><p>The area-normalization transformation. Choose from {linear, quadratic, tangent, none}</p> +<p><em>Defaults to “quadratic”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://s2geometry.io/">S2’s Website</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="rpoly.html" class="btn btn-neutral float-left" title="Rectangular Polyconic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="sch.html" class="btn btn-neutral float-right" title="Spherical Cross-track Height" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Spherical Cross-track Height</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/sch.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="s2.html" class="btn btn-neutral float-left" title="S2" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="sinu.html" class="btn btn-neutral float-right" title="Sinusoidal (Sanson-Flamsteed)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="spherical-cross-track-height"> +<span id="sch"></span><h1>Spherical Cross-track Height<a class="headerlink" href="#spherical-cross-track-height" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse.</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>sch</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>3D coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<blockquote> +<div><p>proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=sch</span> <span class="pre">+plat_0=XX</span> <span class="pre">+plon_0=XX</span> <span class="pre">+phdg_0=XX</span></code></p> +</div></blockquote> +<p>The SCH coordinate system is a sensor aligned coordinate system developed at +JPL (Jet Propulsion Laboratory) for radar mapping missions.</p> +<p>See <span id="id1">[<a class="reference internal" href="../../zreferences.html#id16" title="Hensley, S., Chapin, E., Freedman, A., and Michel, T. Improved processing of AIRSAR data based on the GeoSAR processor. In AIRSAR Earth Science and Application Workshop. Pasadena, California, 2002. Jet Propulsion Laboratory. URL: https://airsar.jpl.nasa.gov/documents/workshop2002/papers/T3.pdf.">Hensley2002</a>]</span></p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-plat_0"> +<span id="cmdoption-arg-plat-0"></span><span class="sig-name descname"><span class="pre">+plat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-plat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Peg latitude (in degree)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-plon_0"> +<span id="cmdoption-arg-plon-0"></span><span class="sig-name descname"><span class="pre">+plon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-plon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Peg longitude (in degree)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-phdg_0"> +<span id="cmdoption-arg-phdg-0"></span><span class="sig-name descname"><span class="pre">+phdg_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-phdg_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Peg heading (in degree)</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-h_0"> +<span id="cmdoption-arg-h-0"></span><span class="sig-name descname"><span class="pre">+h_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-h_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Average height (in metre)</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="s2.html" class="btn btn-neutral float-left" title="S2" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="sinu.html" class="btn btn-neutral float-right" title="Sinusoidal (Sanson-Flamsteed)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-label="Sequential page navigation"> + <a href="sch.html" class="btn btn-neutral float-left" title="Spherical Cross-track Height" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="somerc.html" class="btn btn-neutral float-right" title="Swiss Oblique Mercator" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="sinusoidal-sanson-flamsteed"> +<span id="sinu"></span><h1>Sinusoidal (Sanson-Flamsteed)<a class="headerlink" href="#sinusoidal-sanson-flamsteed" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>sinu</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/sinu.png"><img alt="Sinusoidal (Sanson-Flamsteed)" src="../../_images/sinu.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=sinu</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>MacBryde and Thomas developed generalized formulas for several of the +pseudocylindricals with sinusoidal meridians:</p> +<div class="math notranslate nohighlight"> +\[x = C\lambda(m+cos\theta) / ( m + 1)\]</div> +<div class="math notranslate nohighlight"> +\[y = C\theta\]</div> +<div class="math notranslate nohighlight"> +\[C = \sqrt { (m + 1 ) / n }\]</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Sinusoidal projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="sch.html" class="btn btn-neutral float-left" title="Spherical Cross-track Height" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="somerc.html" class="btn btn-neutral float-right" title="Swiss Oblique Mercator" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference 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P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Swiss Oblique Mercator</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Swiss Oblique Mercator</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/somerc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="sinu.html" class="btn btn-neutral float-left" title="Sinusoidal (Sanson-Flamsteed)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="stere.html" class="btn btn-neutral float-right" title="Stereographic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="swiss-oblique-mercator"> +<span id="somerc"></span><h1>Swiss Oblique Mercator<a class="headerlink" href="#swiss-oblique-mercator" title="Permalink to this headline">¶</a></h1> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/somerc.png"><img alt="Swiss Oblique Mercator" src="../../_images/somerc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=somerc</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="sinu.html" class="btn btn-neutral float-left" title="Sinusoidal (Sanson-Flamsteed)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="stere.html" class="btn btn-neutral float-right" title="Stereographic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Stereographic</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/stere.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="somerc.html" class="btn btn-neutral float-left" title="Swiss Oblique Mercator" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="sterea.html" class="btn btn-neutral float-right" title="Oblique Stereographic Alternative" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="stereographic"> +<span id="stere"></span><h1>Stereographic<a class="headerlink" href="#stereographic" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>stere</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/stere.png"><img alt="Stereographic" src="../../_images/stere.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=stere</span> <span class="pre">+lat_0=90</span> <span class="pre">+lat_ts=75</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Defines the latitude where scale is not distorted. It is only taken into +account for Polar Stereographic formulations (<code class="docutils literal notranslate"><span class="pre">+lat_0</span></code> = +/- 90 ), and +then defaults to the <code class="docutils literal notranslate"><span class="pre">+lat_0</span></code> value. +If set to a value different from +/- 90, it takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> +if both options are used together.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="somerc.html" class="btn btn-neutral float-left" title="Swiss Oblique Mercator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="sterea.html" class="btn btn-neutral float-right" title="Oblique Stereographic Alternative" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a 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class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Oblique Stereographic Alternative</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal 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navigation"> + <a href="stere.html" class="btn btn-neutral float-left" title="Stereographic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gstmerc.html" class="btn btn-neutral float-right" title="Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="oblique-stereographic-alternative"> +<span id="sterea"></span><h1>Oblique Stereographic Alternative<a class="headerlink" href="#oblique-stereographic-alternative" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>sterea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/sterea.png"><img alt="Oblique Stereographic Alternative" src="../../_images/sterea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=sterea</span> <span class="pre">+lat_0=90</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="stere.html" class="btn btn-neutral float-left" title="Stereographic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="gstmerc.html" class="btn btn-neutral float-right" title="Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-label="Sequential page navigation"> + <a href="gstmerc.html" class="btn btn-neutral float-left" title="Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tcea.html" class="btn btn-neutral float-right" title="Transverse Cylindrical Equal Area" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="transverse-central-cylindrical"> +<span id="tcc"></span><h1>Transverse Central Cylindrical<a class="headerlink" href="#transverse-central-cylindrical" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>tcc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/tcc.png"><img alt="Transverse Central Cylindrical" src="../../_images/tcc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tcc</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="gstmerc.html" class="btn btn-neutral float-left" title="Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tcea.html" class="btn btn-neutral float-right" title="Transverse Cylindrical Equal Area" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Transverse Cylindrical Equal Area</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/tcea.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="tcc.html" class="btn btn-neutral float-left" title="Transverse Central Cylindrical" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="times.html" class="btn btn-neutral float-right" title="Times" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="transverse-cylindrical-equal-area"> +<span id="tcea"></span><h1>Transverse Cylindrical Equal Area<a class="headerlink" href="#transverse-cylindrical-equal-area" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>tcea</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/tcea.png"><img alt="Transverse Cylindrical Equal Area" src="../../_images/tcea.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tcea</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tcc.html" class="btn btn-neutral float-left" title="Transverse Central Cylindrical" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="times.html" class="btn btn-neutral float-right" title="Times" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Previous</a> + <a href="tissot.html" class="btn btn-neutral float-right" title="Tissot" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="times"> +<span id="id1"></span><h1>Times<a class="headerlink" href="#times" title="Permalink to this headline">¶</a></h1> +<p>See <span id="id2">[<a class="reference internal" href="../../zreferences.html#id35" title="Snyder, J. P. Flattening the Earth. University of Chicago Press, 1993.">Snyder1993</a>]</span>, p.213-214.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>times</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id3"> +<a class="reference internal image-reference" href="../../_images/times.png"><img alt="Times" src="../../_images/times.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=times</span></code></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tcea.html" class="btn btn-neutral float-left" title="Transverse Cylindrical Equal Area" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tissot.html" class="btn btn-neutral float-right" title="Tissot" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Tissot</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li 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href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Tissot</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/tissot.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="times.html" class="btn btn-neutral float-left" title="Times" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tmerc.html" class="btn btn-neutral float-right" title="Transverse Mercator" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="tissot"> +<span id="id1"></span><h1>Tissot<a class="headerlink" href="#tissot" title="Permalink to this headline">¶</a></h1> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/tissot.png"><img alt="Tissot" src="../../_images/tissot.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tissot</span> <span class="pre">+lat_1=60</span> <span class="pre">+lat_2=65</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="times.html" class="btn btn-neutral float-left" title="Times" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tmerc.html" class="btn btn-neutral float-right" title="Transverse Mercator" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> 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internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Transverse Mercator</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#usage">Usage</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +<li class="toctree-l4"><a class="reference internal" href="#mathematical-definition">Mathematical definition</a></li> +<li class="toctree-l4"><a class="reference internal" href="#further-reading">Further reading</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Transverse Mercator</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/tmerc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="tissot.html" class="btn btn-neutral float-left" title="Tissot" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tobmerc.html" class="btn btn-neutral float-right" title="Tobler-Mercator" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="transverse-mercator"> +<span id="tmerc"></span><h1>Transverse Mercator<a class="headerlink" href="#transverse-mercator" title="Permalink to this headline">¶</a></h1> +<p>The transverse Mercator projection in its various forms is the most widely used projected coordinate system for world topographical and offshore mapping. +It is a conformal projection in which a chosen meridian projects to a +straight line at constant scale.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Transverse and oblique cylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical and ellipsoidal</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, with full accuracy within 3900 km +of the central meridian</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>tmerc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id10"> +<a class="reference internal image-reference" href="../../_images/tmerc.png"><img alt="Transverse Mercator" src="../../_images/tmerc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tmerc</span></code></span><a class="headerlink" href="#id10" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the interwar period. +Calculating the distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem) than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude. +In the post-war years, these concepts were extended into the Universal Transverse Mercator/Universal Polar Stereographic (UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps.</p> +<p>The following table gives special cases of the Transverse Mercator projection.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 21%" /> +<col style="width: 30%" /> +<col style="width: 18%" /> +<col style="width: 24%" /> +<col style="width: 8%" /> +</colgroup> +<thead> +<tr class="row-odd"><th class="head"><p>Projection Name</p></th> +<th class="head"><p>Areas</p></th> +<th class="head"><p>Central meridian</p></th> +<th class="head"><p>Zone width</p></th> +<th class="head"><p>Scale Factor</p></th> +</tr> +</thead> +<tbody> +<tr class="row-even"><td><p>Transverse Mercator</p></td> +<td><p>World wide</p></td> +<td><p>Various</p></td> +<td><p>less than 1000 km</p></td> +<td><p>Various</p></td> +</tr> +<tr class="row-odd"><td><p>Transverse Mercator south oriented</p></td> +<td><p>Southern Africa</p></td> +<td><p>2° intervals E of 11°E</p></td> +<td><p>2°</p></td> +<td><p>1.000</p></td> +</tr> +<tr class="row-even"><td><p>UTM North hemisphere</p></td> +<td><p>World wide equator to 84°N</p></td> +<td><p>6° intervals E & W of 3° E & W</p></td> +<td><p>Usually 6°, wider for Norway and Svalbard</p></td> +<td><p>0.9996</p></td> +</tr> +<tr class="row-odd"><td><p>UTM South hemisphere</p></td> +<td><p>World wide north of 80°S to equator</p></td> +<td><p>6° intervals E & W of 3° E & W</p></td> +<td><p>Always 6°</p></td> +<td><p>0.9996</p></td> +</tr> +<tr class="row-even"><td><p>Gauss-Kruger</p></td> +<td><p>Former USSR, Yugoslavia, Germany, S. America, China</p></td> +<td><p>Various, according to area</p></td> +<td><p>Usually less than 6°, often less than 4°</p></td> +<td><p>1.0000</p></td> +</tr> +<tr class="row-odd"><td><p>Gauss Boaga</p></td> +<td><p>Italy</p></td> +<td><p>Various, according to area</p></td> +<td><p>6°</p></td> +<td><p>0.9996</p></td> +</tr> +</tbody> +</table> +<p>Example using Gauss-Kruger on Germany area (aka EPSG:31467)</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 9 51 | proj +proj=tmerc +lat_0=0 +lon_0=9 +k_0=1 +x_0=3500000 +y_0=0 +ellps=bessel +units=m +3500000.00 5651505.56 +</pre></div> +</div> +<p>Example using Gauss Boaga on Italy area (EPSG:3004)</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 15 42 | proj +proj=tmerc +lat_0=0 +lon_0=15 +k_0=0.9996 +x_0=2520000 +y_0=0 +ellps=intl +units=m +2520000.00 4649858.60 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-approx"> +<span class="sig-name descname"><span class="pre">+approx</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-approx" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>Use the Evenden-Snyder algorithm described below under “Legacy +ellipsoidal form”. It is faster than the default algorithm, but is +less accurate and diverges beyond 3° from the central meridian.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-algo"> +<span class="sig-name descname"><span class="pre">+algo</span></span><span class="sig-prename descclassname"><span class="pre">=auto/evenden_snyder/poder_engsager</span></span><a class="headerlink" href="#cmdoption-arg-algo" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 7.1.</span></p> +</div> +<p>Selects the algorithm to use. The hardcoded value and the one defined in +<a class="reference internal" href="../../resource_files.html#proj-ini"><span class="std std-ref">proj.ini</span></a> default to <code class="docutils literal notranslate"><span class="pre">poder_engsager</span></code>; that is the most precise +one.</p> +<p>When using auto, a heuristics based on the input coordinate to transform +is used to determine if the faster Evenden-Snyder method can be used, for +faster computation, without causing an error greater than 0.1 mm (for an +ellipsoid of the size of Earth)</p> +<p>Note that <a class="reference internal" href="utm.html#cmdoption-arg-approx"><code class="xref std std-option docutils literal notranslate"><span class="pre">+approx</span></code></a> and <a class="reference internal" href="utm.html#cmdoption-arg-algo"><code class="xref std std-option docutils literal notranslate"><span class="pre">+algo</span></code></a> are mutually exclusive.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulation given here for the Transverse Mercator projection is due +to Krüger <span id="id1">[<a class="reference internal" href="../../zreferences.html#id24" title="Krüger, J. H. L. Konforme Abbildung des Erdellipsoids in der Ebene. New Series 52, Royal Prussian Geodetic Institute, Potsdam, 1912. doi:10.2312/GFZ.b103-krueger28.">Krueger1912</a>]</span> who gave the series expansions accurate to +<span class="math notranslate nohighlight">\(n^4\)</span>, where <span class="math notranslate nohighlight">\(n = (a-b)/(a+b)\)</span> is the third flattening. +These series were extended to sixth order by Engsager and Poder in +<span id="id2">[<a class="reference internal" href="../../zreferences.html#id29" title="Poder, K. and Engsager, K. Some conformal mappings and transformations for geodesy and topographic cartography. National Survey and Cadastre Publications, National Survey and Cadastre, Copenhagen, Denmark, 1998.">Poder1998</a>]</span> and <span id="id3">[<a class="reference internal" href="../../zreferences.html#id10" title="Engsager, K. E. and Poder, K. A highly accurate world wide algorithm for the transverse Mercator mapping (almost). In Proc. XXIII Intl. Cartographic Conf. (ICC2007), Moscow, 2.1.2. August 2007.">Engsager2007</a>]</span>. This gives full +double-precision accuracy within 3900 km of the central meridian (about +57% of the surface of the earth) <span id="id4">[<a class="reference internal" href="../../zreferences.html#id21" title="Karney, C. F. F. Transverse Mercator with an accuracy of a few nanometers. J. Geod., 85(8):475-485, August 2011. arXiv:1002.1417, doi:10.1007/s00190-011-0445-3.">Karney2011tm</a>]</span>. The error is +less than 0.1 mm within 7000 km of the central meridian (about 89% of +the surface of the earth).</p> +<p>This formulation consists of three steps: a conformal projection from +the ellipsoid to a sphere, the spherical transverse Mercator +projection, rectifying this projection to give constant scale on the +central meridian.</p> +<p>The scale on the central meridian is <span class="math notranslate nohighlight">\(k_0\)</span> and is set by <code class="docutils literal notranslate"><span class="pre">+k_0</span></code>.</p> +<p>Option <a class="reference internal" href="wintri.html#cmdoption-arg-lon_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lon_0</span></code></a> sets the central meridian; in the formulation +below <span class="math notranslate nohighlight">\(\lambda\)</span> is the longitude relative to the central meridian.</p> +<p>Options <a class="reference internal" href="tpers.html#cmdoption-arg-lat_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+lat_0</span></code></a>, <a class="reference internal" href="wintri.html#cmdoption-arg-x_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+x_0</span></code></a>, and <a class="reference internal" href="wintri.html#cmdoption-arg-y_0"><code class="xref std std-option docutils literal notranslate"><span class="pre">+y_0</span></code></a> serve to +translate the projected coordinates so that at <span class="math notranslate nohighlight">\((\phi, \lambda) = +(\phi_0, \lambda_0)\)</span>, the projected coordinates are <span class="math notranslate nohighlight">\((x,y) = +(x_0,y_0)\)</span>. To simplify the formulas below, these options are set to +zero (their default values).</p> +<p>Because the projection is conformal, the formulation is most +conveniently given in terms of complex numbers. In particular, the +unscaled projected coordinates <span class="math notranslate nohighlight">\(\eta\)</span> (proportional to the +easting, <span class="math notranslate nohighlight">\(x\)</span>) and <span class="math notranslate nohighlight">\(\xi\)</span> (proportional to the northing, +<span class="math notranslate nohighlight">\(y\)</span>) are combined into the single complex quantity <span class="math notranslate nohighlight">\(\zeta = +\xi + i\eta\)</span>, where <span class="math notranslate nohighlight">\(i=\sqrt{-1}\)</span>. Then any analytic function +<span class="math notranslate nohighlight">\(f(\zeta)\)</span> defines a conformal mapping (this follows from the +Cauchy-Riemann conditions).</p> +<section id="spherical-form"> +<h3>Spherical form<a class="headerlink" href="#spherical-form" title="Permalink to this headline">¶</a></h3> +<p>Because the full (ellipsoidal) projection includes the spherical +projection as one of the components, we present the spherical form first +with the coordinates tagged with primes, <span class="math notranslate nohighlight">\(\phi'\)</span>, +<span class="math notranslate nohighlight">\(\lambda'\)</span>, <span class="math notranslate nohighlight">\(\zeta' = \xi' + i\eta'\)</span>, <span class="math notranslate nohighlight">\(x'\)</span>, +<span class="math notranslate nohighlight">\(y'\)</span>, so that they can be distinguished from the corresponding +ellipsoidal coordinates (without the primes). The projected coordinates +for the sphere are given by</p> +<div class="math notranslate nohighlight"> +\[x' = k_0 R \eta';\qquad y' = k_0 R \xi'\]</div> +<section id="forward-projection"> +<h4>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\xi' = \tan^{-1}\biggl(\frac{\tan\phi'}{\cos\lambda'}\biggr)\]</div> +<div class="math notranslate nohighlight"> +\[\eta' = \sinh^{-1}\biggl(\frac{\sin\lambda'} +{\sqrt{\tan^2\phi' + \cos^2\lambda'}}\biggr)\]</div> +</section> +<section id="inverse-projection"> +<h4>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\phi' = \tan^{-1}\biggl(\frac{\sin\xi'} +{\sqrt{\sinh^2\eta' + \cos^2\xi'}}\biggr)\]</div> +<div class="math notranslate nohighlight"> +\[\lambda' = \tan^{-1}\biggl(\frac{\sinh\eta'}{\cos\xi'}\biggr)\]</div> +</section> +</section> +<section id="ellipsoidal-form"> +<h3>Ellipsoidal form<a class="headerlink" href="#ellipsoidal-form" title="Permalink to this headline">¶</a></h3> +<p>The projected coordinates are given by</p> +<div class="math notranslate nohighlight"> +\[\zeta = \xi + i\eta;\qquad x = k_0 A \eta;\qquad y = k_0 A \xi\]</div> +<div class="math notranslate nohighlight"> +\[A = \frac a{1+n}\biggl(1 + \frac14 n^2 + \frac1{64} n^4 + +\frac1{256}n^6\biggr)\]</div> +<p>The series for conversion between ellipsoidal and spherical geographic +coordinates and ellipsoidal and spherical projected coordinates are +given in matrix notation where <span class="math notranslate nohighlight">\(\mathbf S(\theta)\)</span> and +<span class="math notranslate nohighlight">\(\mathbf N\)</span> are the row and column vectors of length 6</p> +<div class="math notranslate nohighlight"> +\[\mathbf S(\theta) = \begin{pmatrix} +\sin 2\theta & +\sin 4\theta & +\sin 6\theta & +\sin 8\theta & +\sin 10\theta & +\sin 12\theta +\end{pmatrix}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\mathbf N = \begin{pmatrix} +n \\ n^2 \\ n^3\\ n^4 \\ n^5 \\ n^6 +\end{pmatrix}\end{split}\]</div> +<p>and <span class="math notranslate nohighlight">\(\mathsf C_{\alpha,\beta}\)</span> are upper triangular +<span class="math notranslate nohighlight">\(6\times6\)</span> matrices.</p> +<section id="relation-between-geographic-coordinates"> +<h4>Relation between geographic coordinates<a class="headerlink" href="#relation-between-geographic-coordinates" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\lambda' = \lambda\]</div> +<div class="math notranslate nohighlight"> +\[\phi' = \tan^{-1}\sinh\bigl(\sinh^{-1}\tan\phi +- e \tanh^{-1}(e\sin\phi)\bigr)\]</div> +<p>Instead of using this analytical formula for <span class="math notranslate nohighlight">\(\phi'\)</span>, the +conversions between <span class="math notranslate nohighlight">\(\phi\)</span> and <span class="math notranslate nohighlight">\(\phi'\)</span> use the series +approximations:</p> +<div class="math notranslate nohighlight"> +\[\phi' = \phi + \mathbf S(\phi) \cdot \mathsf C_{\chi,\phi} \cdot \mathbf N\]</div> +<div class="math notranslate nohighlight"> +\[\phi = \phi' + \mathbf S(\phi') \cdot \mathsf C_{\phi,\chi} \cdot \mathbf N\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\mathsf C_{\chi,\phi} = \begin{pmatrix} +-2& \frac{2}{3}& \frac{4}{3}& -\frac{82}{45}& \frac{32}{45}& \frac{4642}{4725} \\ +& \frac{5}{3}& -\frac{16}{15}& -\frac{13}{9}& \frac{904}{315}& -\frac{1522}{945} \\ +& & -\frac{26}{15}& \frac{34}{21}& \frac{8}{5}& -\frac{12686}{2835} \\ +& & & \frac{1237}{630}& -\frac{12}{5}& -\frac{24832}{14175} \\ +& & & & -\frac{734}{315}& \frac{109598}{31185} \\ +& & & & & \frac{444337}{155925} \\ +\end{pmatrix}\end{split}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\mathsf C_{\phi,\chi} = \begin{pmatrix} +2& -\frac{2}{3}& -2& \frac{116}{45}& \frac{26}{45}& -\frac{2854}{675} \\ +& \frac{7}{3}& -\frac{8}{5}& -\frac{227}{45}& \frac{2704}{315}& \frac{2323}{945} \\ +& & \frac{56}{15}& -\frac{136}{35}& -\frac{1262}{105}& \frac{73814}{2835} \\ +& & & \frac{4279}{630}& -\frac{332}{35}& -\frac{399572}{14175} \\ +& & & & \frac{4174}{315}& -\frac{144838}{6237} \\ +& & & & & \frac{601676}{22275} \\ +\end{pmatrix}\end{split}\]</div> +<p>Here <span class="math notranslate nohighlight">\(\phi'\)</span> is the conformal latitude (sometimes denoted by +<span class="math notranslate nohighlight">\(\chi\)</span>) and <span class="math notranslate nohighlight">\(\mathsf C_{\chi,\phi}\)</span> and <span class="math notranslate nohighlight">\(\mathsf +C_{\phi,\chi}\)</span> are the coefficients in the trigonometric series for +converting between <span class="math notranslate nohighlight">\(\phi\)</span> and <span class="math notranslate nohighlight">\(\chi\)</span>.</p> +</section> +<section id="relation-between-projected-coordinates"> +<h4>Relation between projected coordinates<a class="headerlink" href="#relation-between-projected-coordinates" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\zeta = \zeta' + \mathbf S(\zeta') \cdot \mathsf C_{\mu,\chi} \cdot \mathbf N\]</div> +<div class="math notranslate nohighlight"> +\[\zeta' = \zeta + \mathbf S(\zeta) \cdot \mathsf C_{\chi,\mu} \cdot \mathbf N\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\mathsf C_{\mu,\chi} = \begin{pmatrix} +\frac{1}{2}& -\frac{2}{3}& \frac{5}{16}& \frac{41}{180}& -\frac{127}{288}& \frac{7891}{37800} \\ +& \frac{13}{48}& -\frac{3}{5}& \frac{557}{1440}& \frac{281}{630}& -\frac{1983433}{1935360} \\ +& & \frac{61}{240}& -\frac{103}{140}& \frac{15061}{26880}& \frac{167603}{181440} \\ +& & & \frac{49561}{161280}& -\frac{179}{168}& \frac{6601661}{7257600} \\ +& & & & \frac{34729}{80640}& -\frac{3418889}{1995840} \\ +& & & & & \frac{212378941}{319334400} \\ +\end{pmatrix}\end{split}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\mathsf C_{\chi,\mu} = \begin{pmatrix} +-\frac{1}{2}& \frac{2}{3}& -\frac{37}{96}& \frac{1}{360}& \frac{81}{512}& -\frac{96199}{604800} \\ +& -\frac{1}{48}& -\frac{1}{15}& \frac{437}{1440}& -\frac{46}{105}& \frac{1118711}{3870720} \\ +& & -\frac{17}{480}& \frac{37}{840}& \frac{209}{4480}& -\frac{5569}{90720} \\ +& & & -\frac{4397}{161280}& \frac{11}{504}& \frac{830251}{7257600} \\ +& & & & -\frac{4583}{161280}& \frac{108847}{3991680} \\ +& & & & & -\frac{20648693}{638668800} \\ +\end{pmatrix}\end{split}\]</div> +<p>On the central meridian (<span class="math notranslate nohighlight">\(\lambda = \lambda' = 0\)</span>), <span class="math notranslate nohighlight">\(\zeta' += \phi'\)</span> is the conformal latitude <span class="math notranslate nohighlight">\(\chi\)</span> and <span class="math notranslate nohighlight">\(\zeta\)</span> plays +the role of the rectifying latitude (sometimes denoted by <span class="math notranslate nohighlight">\(\mu\)</span>). +<span class="math notranslate nohighlight">\(\mathsf C_{\mu,\chi}\)</span> and <span class="math notranslate nohighlight">\(\mathsf C_{\chi,\mu}\)</span> are the +coefficients in the trigonometric series for converting between +<span class="math notranslate nohighlight">\(\chi\)</span> and <span class="math notranslate nohighlight">\(\mu\)</span>.</p> +</section> +</section> +<section id="legacy-ellipsoidal-form"> +<h3>Legacy ellipsoidal form<a class="headerlink" href="#legacy-ellipsoidal-form" title="Permalink to this headline">¶</a></h3> +<p>The formulas below describe the algorithm used when giving the +<a class="reference internal" href="utm.html#cmdoption-arg-approx"><code class="xref std std-option docutils literal notranslate"><span class="pre">+approx</span></code></a> option. They are originally from <span id="id5">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>, +but here quoted from <span id="id6">[<a class="reference internal" href="../../zreferences.html#id12" title="Evenden, G. I. Cartographic Projection Procedures for the UNIX Environment — A User's Manual. 1995. URL: https://pubs.usgs.gov/of/1990/of90-284/ofr90-284.pdf.">Evenden1995</a>]</span> and <span id="id7">[<a class="reference internal" href="../../zreferences.html#id11" title="Evenden, G. I. libproj4: A Comprehensive Library of Cartographic Projection Functions (Preliminary Draft). 2005. URL: https://github.com/OSGeo/PROJ/blob/master/docs/old/libproj.pdf.">Evenden2005</a>]</span>. These +are less accurate that the formulation above and are only valid within +about 5 degrees of the central meridian. Here <span class="math notranslate nohighlight">\(M(\phi)\)</span> is the +meridional distance.</p> +<section id="id8"> +<h4>Forward projection<a class="headerlink" href="#id8" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[N = \frac{k_0}{(1 - e^2 \sin^2\phi)^{1/2}}\]</div> +<div class="math notranslate nohighlight"> +\[R = \frac{k_0(1-e^2)}{(1-e^2 \sin^2\phi)^{3/2}}\]</div> +<div class="math notranslate nohighlight"> +\[t = \tan\phi\]</div> +<div class="math notranslate nohighlight"> +\[\eta = \frac{e^2}{1-e^2} \cos^2\phi\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}x &= k_0 \lambda \cos \phi \\ + &+ \frac{k_0 \lambda^3 \cos^3\phi}{3!}(1-t^2+\eta^2) \\ + &+ \frac{k_0 \lambda^5 \cos^5\phi}{5!}(5-18t^2+t^4+14\eta^2-58t^2\eta^2) \\ + &+\frac{k_0 \lambda^7 \cos^7\phi}{7!}(61-479t^2+179t^4-t^6)\end{split}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}y &= M(\phi) \\ + &+ \frac{k_0 \lambda^2 \sin\phi \cos \phi}{2!} \\ + &+ \frac{k_0 \lambda^4 \sin\phi \cos^3\phi}{4!}(5-t^2+9\eta^2+4\eta^4) \\ + &+ \frac{k_0 \lambda^6 \sin\phi \cos^5\phi}{6!}(61-58t^2+t^4+270\eta^2-330t^2\eta^2) \\ + &+ \frac{k_0 \lambda^8 \sin\phi \cos^7\phi}{8!}(1385-3111t^2+543t^4-t^6)\end{split}\]</div> +</section> +<section id="id9"> +<h4>Inverse projection<a class="headerlink" href="#id9" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\phi_1 = M^{-1}(y)\]</div> +<div class="math notranslate nohighlight"> +\[N_1 = \frac{k_0}{1 - e^2 \sin^2\phi_1)^{1/2}}\]</div> +<div class="math notranslate nohighlight"> +\[R_1 = \frac{k_0(1-e^2)}{(1-e^2 \sin^2\phi_1)^{3/2}}\]</div> +<div class="math notranslate nohighlight"> +\[t_1 = \tan(\phi_1)\]</div> +<div class="math notranslate nohighlight"> +\[\eta_1 = \frac{e^2}{1-e^2} \cos^2\phi_1\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\phi &= \phi_1 \\ + &- \frac{t_1 x^2}{2! R_1 N_1} \\ + &+ \frac{t_1 x^4}{4! R_1 N_1^3}(5+3t_1^2+\eta_1^2-4\eta_1^4-9\eta_1^2t_1^2) \\ + &- \frac{t_1 x^6}{6! R_1 N_1^5}(61+90t_1^2+46\eta_1^2+45t_1^4-252t_1^2\eta_1^2) \\ + &+ \frac{t_1 x^8}{8! R_1 N_1^7}(1385+3633t_1^2+4095t_1^4+1575t_1^6)\end{split}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\lambda &= \frac{x}{\cos \phi N_1} \\ + &- \frac{x^3}{3! \cos \phi N_1^3}(1+2t_1^2+\eta_1^2) \\ + &+ \frac{x^5}{5! \cos \phi N_1^5}(5+6\eta_1^2+28t_1^2-3\eta_1^2+8t_1^2\eta_1^2) \\ + &- \frac{x^7}{7! \cos \phi N_1^7}(61+662t_1^2+1320t_1^4+720t_1^6)\end{split}\]</div> +</section> +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Transverse_Mercator_projection">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tissot.html" class="btn btn-neutral float-left" title="Tissot" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tobmerc.html" class="btn btn-neutral float-right" title="Tobler-Mercator" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/tobmerc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="tmerc.html" class="btn btn-neutral float-left" title="Transverse Mercator" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tpeqd.html" class="btn btn-neutral float-right" title="Two Point Equidistant" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="tobler-mercator"> +<span id="tobmerc"></span><h1>Tobler-Mercator<a class="headerlink" href="#tobler-mercator" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>Equal area cylindrical projection with the same latitudinal spacing as +Mercator projection.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical equal area</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical only</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global, conventionally truncated at about 80 degrees +north and south</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>tobmerc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2"> +<a class="reference internal image-reference" href="../../_images/tobmerc.png"><img alt="Tobler-Mercator" src="../../_images/tobmerc.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tobmerc</span></code></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>The inappropriate use of the Mercator projection has declined but still +occasionally occurs. One method of contrasting the Mercator projection is to +present an alternative in the form of an equal area projection. The map +projection derived here is thus not simply a pretty Christmas tree ornament: +it is instead a complement to Mercator’s conformal navigation anamorphosis +and can be displayed as an alternative. The equations for the new map +projection preserve the latitudinal stretching of the Mercator while +adjusting the longitudinal spacing. This allows placement of the new map +adjacent to that of Mercator. The surface area, while drastically warped, +maintains the correct magnitude.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-k_0"> +<span id="cmdoption-arg-k-0"></span><span class="sig-name descname"><span class="pre">+k_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-k_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor. Determines scale factor used in the projection.</p> +<p><em>Defaults to 1.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the Tobler-Mercator are taken from Waldo Tobler’s +article <span id="id1">[<a class="reference internal" href="../../zreferences.html#id39" title="Tobler, W. A new companion for Mercator. Cartography and Geographic Information Science, 45(3):284–285, 2018. doi:10.1080/15230406.2017.1308837.">Tobler2018</a>]</span></p> +<section id="spherical-form"> +<h3>Spherical form<a class="headerlink" href="#spherical-form" title="Permalink to this headline">¶</a></h3> +<p>For the spherical form of the projection we introduce the scaling factor:</p> +<div class="math notranslate nohighlight"> +\[k_0 = \cos^2 \phi_{ts}\]</div> +<section id="forward-projection"> +<h4>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[x = k_0 \lambda\]</div> +<div class="math notranslate nohighlight"> +\[y = k_0 \ln \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right]\]</div> +</section> +<section id="inverse-projection"> +<h4>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight"> +\[\lambda = \frac{x}{k_0}\]</div> +<div class="math notranslate nohighlight"> +\[\phi = \frac{\pi}{2} - 2 \arctan \left[ e^{-y/k_0} \right]\]</div> +</section> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tmerc.html" class="btn btn-neutral float-left" title="Transverse Mercator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tpeqd.html" class="btn btn-neutral float-right" title="Two Point Equidistant" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="tobmerc.html" class="btn btn-neutral float-left" title="Tobler-Mercator" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tpers.html" class="btn btn-neutral float-right" title="Tilted perspective" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="two-point-equidistant"> +<span id="tpeqd"></span><h1>Two Point Equidistant<a class="headerlink" href="#two-point-equidistant" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>tpeqd</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/tpeqd.png"><img alt="Two Point Equidistant" src="../../_images/tpeqd.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tpeqd</span> <span class="pre">+lat_1=60</span> <span class="pre">+lat_2=65</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_1"> +<span id="cmdoption-arg-lon-1"></span><span class="sig-name descname"><span class="pre">+lon_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of first point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_2"> +<span id="cmdoption-arg-lon-2"></span><span class="sig-name descname"><span class="pre">+lon_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of second point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of second point.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tobmerc.html" class="btn btn-neutral float-left" title="Tobler-Mercator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tpers.html" class="btn btn-neutral float-right" title="Tilted perspective" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="tpeqd.html" class="btn btn-neutral float-left" title="Two Point Equidistant" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ups.html" class="btn btn-neutral float-right" title="Universal Polar Stereographic" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="tilted-perspective"> +<span id="tpers"></span><h1>Tilted perspective<a class="headerlink" href="#tilted-perspective" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Azimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>tpers</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/tpers.png"><img alt="Tilted perspective" src="../../_images/tpers.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=tpers</span> <span class="pre">+h=5500000</span> <span class="pre">+lat_0=40</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>Tilted Perspective is similar to <a class="reference internal" href="nsper.html#nsper"><span class="std std-ref">Near-sided perspective</span></a> (<code class="docutils literal notranslate"><span class="pre">nsper</span></code>) in that it simulates a +perspective view from a height. Where <code class="docutils literal notranslate"><span class="pre">nsper</span></code> projects onto a plane tangent to +the surface, Tilted Perspective orients the plane towards the direction of the +view. Thus, extra parameters specifying azimuth and tilt are required beyond +<cite>nsper`</cite>’s <code class="docutils literal notranslate"><span class="pre">h</span></code>. As with <code class="docutils literal notranslate"><span class="pre">nsper</span></code>, <code class="docutils literal notranslate"><span class="pre">lat_0</span></code> & <code class="docutils literal notranslate"><span class="pre">lon_0</span></code> are +also required for satellite position.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-h"> +<span class="sig-name descname"><span class="pre">+h</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-h" title="Permalink to this definition">¶</a></dt> +<dd><p>Height of the view point above the Earth and must be in the same units as +the radius of the sphere or semimajor axis of the ellipsoid.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-azi"> +<span class="sig-name descname"><span class="pre">+azi</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-azi" title="Permalink to this definition">¶</a></dt> +<dd><p>Bearing in degrees away from north.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-tilt"> +<span class="sig-name descname"><span class="pre">+tilt</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-tilt" title="Permalink to this definition">¶</a></dt> +<dd><p>Angle in degrees away from nadir.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_0"> +<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tpeqd.html" class="btn btn-neutral float-left" title="Two Point Equidistant" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="ups.html" class="btn btn-neutral float-right" title="Universal Polar Stereographic" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" 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P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li 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+<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" 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href="tpers.html" class="btn btn-neutral float-left" title="Tilted perspective" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="urm5.html" class="btn btn-neutral float-right" title="Urmaev V" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="universal-polar-stereographic"> +<span id="ups"></span><h1>Universal Polar Stereographic<a class="headerlink" href="#universal-polar-stereographic" title="Permalink to this headline">¶</a></h1> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/ups.png"><img alt="Universal Polar Stereographic" src="../../_images/ups.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=ups</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-south"> +<span class="sig-name descname"><span class="pre">+south</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-south" title="Permalink to this definition">¶</a></dt> +<dd><p>South polar aspect.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tpers.html" class="btn btn-neutral float-left" title="Tilted perspective" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="urm5.html" class="btn btn-neutral float-right" title="Urmaev V" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li 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+<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a 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internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Urmaev V</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" 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href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Urmaev V</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/urm5.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="ups.html" class="btn btn-neutral float-left" title="Universal Polar Stereographic" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="urmfps.html" class="btn btn-neutral float-right" title="Urmaev Flat-Polar Sinusoidal" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="urmaev-v"> +<span id="urm5"></span><h1>Urmaev V<a class="headerlink" href="#urmaev-v" title="Permalink to this headline">¶</a></h1> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/urm5.png"><img alt="Urmaev V" src="../../_images/urm5.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=urm5</span> <span class="pre">+n=0.9</span> <span class="pre">+alpha=2</span> <span class="pre">+q=4</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required-parameters"> +<h3>Required parameters<a class="headerlink" href="#required-parameters" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-n"> +<span class="sig-name descname"><span class="pre">+n</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-n" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the <span class="math notranslate nohighlight">\(n\)</span> constant. Value between 0 and 1.</p> +</dd></dl> + +</section> +<section id="optional-parameters"> +<h3>Optional parameters<a class="headerlink" href="#optional-parameters" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-q"> +<span class="sig-name descname"><span class="pre">+q</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-q" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the <span class="math notranslate nohighlight">\(q\)</span> constant.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-alpha"> +<span class="sig-name descname"><span class="pre">+alpha</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-alpha" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the <span class="math notranslate nohighlight">\(\alpha\)</span> constant.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="ups.html" class="btn btn-neutral float-left" title="Universal Polar Stereographic" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="urmfps.html" class="btn btn-neutral float-right" title="Urmaev Flat-Polar Sinusoidal" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-label="Sequential page navigation"> + <a href="urm5.html" class="btn btn-neutral float-left" title="Urmaev V" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="utm.html" class="btn btn-neutral float-right" title="Universal Transverse Mercator (UTM)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="urmaev-flat-polar-sinusoidal"> +<span id="urmfps"></span><h1>Urmaev Flat-Polar Sinusoidal<a class="headerlink" href="#urmaev-flat-polar-sinusoidal" title="Permalink to this headline">¶</a></h1> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/urmfps.png"><img alt="Urmaev Flat-Polar Sinusoidal" src="../../_images/urmfps.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=urmfps</span> <span class="pre">+n=0.5</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-n"> +<span class="sig-name descname"><span class="pre">+n</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-n" title="Permalink to this definition">¶</a></dt> +<dd><p>Set the <span class="math notranslate nohighlight">\(n\)</span> constant. Value between 0 and 1.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="urm5.html" class="btn btn-neutral float-left" title="Urmaev V" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="utm.html" class="btn btn-neutral float-right" title="Universal Transverse Mercator (UTM)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins 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class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Universal Transverse Mercator (UTM)</a><ul> +<li class="toctree-l4"><a class="reference internal" 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Mercator (UTM)</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/utm.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="urmfps.html" class="btn btn-neutral float-left" title="Urmaev Flat-Polar Sinusoidal" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg.html" class="btn btn-neutral float-right" title="van der Grinten (I)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="universal-transverse-mercator-utm"> +<span id="utm"></span><h1>Universal Transverse Mercator (UTM)<a class="headerlink" href="#universal-transverse-mercator-utm" title="Permalink to this headline">¶</a></h1> +<p>The Universal Transverse Mercator is a system of map projections divided into +sixty zones across the globe, with each zone corresponding to 6 degrees of +longitude.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Transverse cylindrical, conformal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, ellipsoidal only</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Within the used zone, but transformations of coordinates +in adjacent zones can be expected to be accurate as well</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>utm</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id2" style="width: 100%"> +<img alt="Universal Transverse Mercator (UTM) zones" src="../../_images/utm_zones.png" /> +<figcaption> +<p><span class="caption-text">UTM zones.</span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<p>UTM projections are really the <a class="reference internal" href="tmerc.html#tmerc"><span class="std std-ref">Transverse Mercator</span></a> +to which specific parameters, such as central meridians, have been applied. +The Earth is divided into 60 zones each generally 6° wide in longitude. +Bounding meridians are evenly divisible by 6°, and zones are +numbered from 1 to 60 proceeding east from the 180th meridian from Greenwich +with minor exceptions <span id="id1">[<a class="reference internal" href="../../zreferences.html#id37" title="Snyder, J. P. Map projections — A working manual. Professional Paper 1395, U.S. Geological Survey, 1987. doi:10.3133/pp1395.">Snyder1987</a>]</span>.</p> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Convert geodetic coordinate to UTM Zone 32 on the northern hemisphere:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 12 56 | proj +proj=utm +zone=32 +687071.44 6210141.33 +</pre></div> +</div> +<p>Convert geodetic coordinate to UTM Zone 59 on the southern hemisphere:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 174 -44 | proj +proj=utm +zone=59 +south +740526.32 5123750.87 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-zone"> +<span class="sig-name descname"><span class="pre">+zone</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-zone" title="Permalink to this definition">¶</a></dt> +<dd><p>Select which UTM zone to use. Can be a value between 1-60.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-south"> +<span class="sig-name descname"><span class="pre">+south</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-south" title="Permalink to this definition">¶</a></dt> +<dd><p>Add this flag when using the UTM on the southern hemisphere.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-approx"> +<span class="sig-name descname"><span class="pre">+approx</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-approx" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>Use faster, less accurate algorithm for the Transverse Mercator.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-algo"> +<span class="sig-name descname"><span class="pre">+algo</span></span><span class="sig-prename descclassname"><span class="pre">=auto/evenden_snyder/poder_engsager</span></span><a class="headerlink" href="#cmdoption-arg-algo" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 7.1.</span></p> +</div> +<p>Selects the algorithm to use. The hardcoded value and the one defined in +<a class="reference internal" href="../../resource_files.html#proj-ini"><span class="std std-ref">proj.ini</span></a> default to <code class="docutils literal notranslate"><span class="pre">poder_engsager</span></code>, that is the most precise +one.</p> +<p>When using auto, a heuristics based on the input coordinate to transform +is used to determine if the faster Evenden-Snyder method can be used, for +faster computation, without causing an error greater than 0.1 mm (for an +ellipsoid of the size of Earth)</p> +<p>Note that <a class="reference internal" href="#cmdoption-arg-approx"><code class="xref std std-option docutils literal notranslate"><span class="pre">+approx</span></code></a> and <a class="reference internal" href="#cmdoption-arg-algo"><code class="xref std std-option docutils literal notranslate"><span class="pre">+algo</span></code></a> are mutually exclusive.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="urmfps.html" class="btn btn-neutral float-left" title="Urmaev Flat-Polar Sinusoidal" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg.html" class="btn btn-neutral float-right" title="van der Grinten (I)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="utm.html" class="btn btn-neutral float-left" title="Universal Transverse Mercator (UTM)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg2.html" class="btn btn-neutral float-right" title="van der Grinten II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="van-der-grinten-i"> +<span id="vandg"></span><h1>van der Grinten (I)<a class="headerlink" href="#van-der-grinten-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>vandg</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/vandg.png"><img alt="van der Grinten (I)" src="../../_images/vandg.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=vandg</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="utm.html" class="btn btn-neutral float-left" title="Universal Transverse Mercator (UTM)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg2.html" class="btn btn-neutral float-right" title="van der Grinten II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="vandg.html" class="btn btn-neutral float-left" title="van der Grinten (I)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg3.html" class="btn btn-neutral float-right" title="van der Grinten III" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="van-der-grinten-ii"> +<span id="vandg2"></span><h1>van der Grinten II<a class="headerlink" href="#van-der-grinten-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>vandg2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/vandg2.png"><img alt="van der Grinten II" src="../../_images/vandg2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=vandg2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="vandg.html" class="btn btn-neutral float-left" title="van der Grinten (I)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg3.html" class="btn btn-neutral float-right" title="van der Grinten III" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins 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class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li 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href="vandg2.html" class="btn btn-neutral float-left" title="van der Grinten II" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg4.html" class="btn btn-neutral float-right" title="van der Grinten IV" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="van-der-grinten-iii"> +<span id="vandg3"></span><h1>van der Grinten III<a class="headerlink" href="#van-der-grinten-iii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>vandg3</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/vandg3.png"><img alt="van der Grinten III" src="../../_images/vandg3.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=vandg3</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="vandg2.html" class="btn btn-neutral float-left" title="van der Grinten II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vandg4.html" class="btn btn-neutral float-right" title="van der Grinten IV" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li 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(I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">van der Grinten IV</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>van der Grinten IV</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/vandg4.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="vandg3.html" class="btn btn-neutral float-left" title="van der Grinten III" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vitk1.html" class="btn btn-neutral float-right" title="Vitkovsky I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="van-der-grinten-iv"> +<span id="vandg4"></span><h1>van der Grinten IV<a class="headerlink" href="#van-der-grinten-iv" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Miscellaneous</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>vandg4</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/vandg4.png"><img alt="van der Grinten IV" src="../../_images/vandg4.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=vandg4</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="vandg3.html" class="btn btn-neutral float-left" title="van der Grinten III" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vitk1.html" class="btn btn-neutral float-right" title="Vitkovsky I" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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(I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Vitkovsky I</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li 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operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Vitkovsky I</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/vitk1.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="vandg4.html" class="btn btn-neutral float-left" title="van der Grinten IV" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag1.html" class="btn btn-neutral float-right" title="Wagner I (Kavrayskiy VI)" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="vitkovsky-i"> +<span id="vitk1"></span><h1>Vitkovsky I<a class="headerlink" href="#vitkovsky-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Conical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>vitk1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/vitk1.png"><img alt="Vitkovsky I" src="../../_images/vitk1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=vitk1</span> <span class="pre">+lat_1=45</span> <span class="pre">+lat_2=55</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_2"> +<span id="cmdoption-arg-lat-2"></span><span class="sig-name descname"><span class="pre">+lat_2</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_2" title="Permalink to this definition">¶</a></dt> +<dd><p>Second standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="vandg4.html" class="btn btn-neutral float-left" title="van der Grinten IV" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag1.html" class="btn btn-neutral float-right" title="Wagner I (Kavrayskiy VI)" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="vitk1.html" class="btn btn-neutral float-left" title="Vitkovsky I" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag2.html" class="btn btn-neutral float-right" title="Wagner II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="wagner-i-kavrayskiy-vi"> +<span id="wag1"></span><h1>Wagner I (Kavrayskiy VI)<a class="headerlink" href="#wagner-i-kavrayskiy-vi" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wag1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag1.png"><img alt="Wagner I (Kavrayskiy VI)" src="../../_images/wag1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag1</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>This projection name may also be transliterated as Kavraisky VI.</p> +</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="vitk1.html" class="btn btn-neutral float-left" title="Vitkovsky I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag2.html" class="btn btn-neutral float-right" title="Wagner II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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navigation"> + <a href="wag1.html" class="btn btn-neutral float-left" title="Wagner I (Kavrayskiy VI)" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag3.html" class="btn btn-neutral float-right" title="Wagner III" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="wagner-ii"> +<span id="wag2"></span><h1>Wagner II<a class="headerlink" href="#wagner-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wag2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag2.png"><img alt="Wagner II" src="../../_images/wag2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}x &= 0.92483 \lambda \cos \theta\\y &= 1.38725\theta\\\sin \theta &= 0.88022 \sin(0.8855\phi)\end{aligned}\end{align} \]</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag1.html" class="btn btn-neutral float-left" title="Wagner I (Kavrayskiy VI)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag3.html" class="btn btn-neutral float-right" title="Wagner III" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a 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class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Wagner III</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Wagner III</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/wag3.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="wag2.html" class="btn btn-neutral float-left" title="Wagner II" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag4.html" class="btn btn-neutral float-right" title="Wagner IV" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="wagner-iii"> +<span id="wag3"></span><h1>Wagner III<a class="headerlink" href="#wagner-iii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wag3</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag3.png"><img alt="Wagner III" src="../../_images/wag3.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag3</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}x &= [\cos\phi_{ts} / \cos ( 2\phi_{ts} / 3)] \lambda \cos (2\phi /3)\\y = \phi\end{aligned}\end{align} \]</div> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag2.html" class="btn btn-neutral float-left" title="Wagner II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag4.html" class="btn btn-neutral float-right" title="Wagner IV" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="wag5.html" class="btn btn-neutral float-right" title="Wagner V" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="wagner-iv"> +<span id="wag4"></span><h1>Wagner IV<a class="headerlink" href="#wagner-iv" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wag4</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag4.png"><img alt="Wagner IV" src="../../_images/wag4.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag4</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag3.html" class="btn btn-neutral float-left" title="Wagner III" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag5.html" class="btn btn-neutral float-right" title="Wagner V" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Wagner V</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/wag5.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="wag4.html" class="btn btn-neutral float-left" title="Wagner IV" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag6.html" class="btn btn-neutral float-right" title="Wagner VI" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="wagner-v"> +<span id="wag5"></span><h1>Wagner V<a class="headerlink" href="#wagner-v" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wag5</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag5.png"><img alt="Wagner V" src="../../_images/wag5.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag5</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag4.html" class="btn btn-neutral float-left" title="Wagner IV" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag6.html" class="btn btn-neutral float-right" title="Wagner VI" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" 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aria-hidden="true"></span> Previous</a> + <a href="wag7.html" class="btn btn-neutral float-right" title="Wagner VII" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="wagner-vi"> +<span id="wag6"></span><h1>Wagner VI<a class="headerlink" href="#wagner-vi" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wag6</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag6.png"><img alt="Wagner VI" src="../../_images/wag6.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag6</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the Wagner VI projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag5.html" class="btn btn-neutral float-left" title="Wagner V" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wag7.html" class="btn btn-neutral float-right" title="Wagner VII" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference 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class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wag7.png"><img alt="Wagner VII" src="../../_images/wag7.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wag7</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag6.html" class="btn btn-neutral float-left" title="Wagner VI" accesskey="p" rel="prev"><span 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+<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li 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+<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference 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href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Web Mercator / Pseudo Mercator</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#usage">Usage</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +<li class="toctree-l4"><a class="reference internal" href="#mathematical-definition">Mathematical definition</a></li> +<li class="toctree-l4"><a class="reference internal" href="#further-reading">Further reading</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li 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href="index.html">Projections</a> »</li> + <li>Web Mercator / Pseudo Mercator</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/webmerc.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="wag7.html" class="btn btn-neutral float-left" title="Wagner VII" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="weren.html" class="btn btn-neutral float-right" title="Werenskiold I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="web-mercator-pseudo-mercator"> +<span id="webmerc"></span><h1>Web Mercator / Pseudo Mercator<a class="headerlink" href="#web-mercator-pseudo-mercator" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<p>The Web Mercator / Pseudo Mercator projection is a cylindrical map projection. +This is a variant of the regular <a class="reference internal" href="merc.html#merc"><span class="std std-ref">Mercator</span></a> projection, except that the computation +is done on a sphere, using the semi-major axis of the ellipsoid.</p> +<p>From <a class="reference external" href="https://en.wikipedia.org/wiki/Web_Mercator">Wikipedia</a>:</p> +<blockquote> +<div><p>This projection is widely used by the Web Mercator, Google Web Mercator, +Spherical Mercator, WGS 84 Web Mercator[1] or WGS 84/Pseudo-Mercator is a +variant of the Mercator projection and is the de facto standard for Web +mapping applications. […] +It is used by virtually all major online map providers […] +Its official EPSG identifier is EPSG:3857, although others have been used +historically.</p> +</div></blockquote> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Cylindrical (non conformant if used with ellipsoid)</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>webmerc</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<section id="usage"> +<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2> +<p>Example:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 2 49 | proj +proj=webmerc +datum=WGS84 +222638.98 6274861.39 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters for the projection are optional, except the ellipsoid +definition, which is WGS84 for the typical use case of EPSG:3857. +In which case, the other parameters are set to their default 0 value.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +<section id="mathematical-definition"> +<h2>Mathematical definition<a class="headerlink" href="#mathematical-definition" title="Permalink to this headline">¶</a></h2> +<p>The formulas describing the Mercator projection are all taken from G. Evenden’s libproj manuals <span id="id1">[<a class="reference internal" href="../../zreferences.html#id11" title="Evenden, G. I. libproj4: A Comprehensive Library of Cartographic Projection Functions (Preliminary Draft). 2005. URL: https://github.com/OSGeo/PROJ/blob/master/docs/old/libproj.pdf.">Evenden2005</a>]</span>.</p> +<section id="forward-projection"> +<h3>Forward projection<a class="headerlink" href="#forward-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[x = \lambda\]</div> +<div class="math notranslate nohighlight"> +\[y = \ln \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right]\]</div> +</section> +<section id="inverse-projection"> +<h3>Inverse projection<a class="headerlink" href="#inverse-projection" title="Permalink to this headline">¶</a></h3> +<div class="math notranslate nohighlight"> +\[\lambda = {x}\]</div> +<div class="math notranslate nohighlight"> +\[\phi = \frac{\pi}{2} - 2 \arctan \left[ e^{-y} \right]\]</div> +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Web_Mercator">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wag7.html" class="btn btn-neutral float-left" title="Wagner VII" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="weren.html" class="btn btn-neutral float-right" title="Werenskiold I" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wink1.html" class="btn btn-neutral float-right" title="Winkel I" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="werenskiold-i"> +<span id="weren"></span><h1>Werenskiold I<a class="headerlink" href="#werenskiold-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>weren</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/weren.png"><img alt="Werenskiold I" src="../../_images/weren.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=weren</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="webmerc.html" class="btn btn-neutral float-left" title="Web Mercator / Pseudo Mercator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wink1.html" class="btn btn-neutral float-right" title="Winkel I" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a 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href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li> +<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li> +<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" 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class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" 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href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Winkel I</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Winkel I</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/wink1.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="weren.html" class="btn btn-neutral float-left" title="Werenskiold I" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wink2.html" class="btn btn-neutral float-right" title="Winkel II" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="winkel-i"> +<span id="wink1"></span><h1>Winkel I<a class="headerlink" href="#winkel-i" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wink1</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wink1.png"><img alt="Winkel I" src="../../_images/wink1.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wink1</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="weren.html" class="btn btn-neutral float-left" title="Werenskiold I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wink2.html" class="btn btn-neutral float-right" title="Winkel II" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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aria-hidden="true"></span> Previous</a> + <a href="wintri.html" class="btn btn-neutral float-right" title="Winkel Tripel" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="winkel-ii"> +<span id="wink2"></span><h1>Winkel II<a class="headerlink" href="#winkel-ii" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudocylindrical</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse, spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wink2</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wink2.png"><img alt="Winkel II" src="../../_images/wink2.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wink2</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_ts"> +<span id="cmdoption-arg-lat-ts"></span><span class="sig-name descname"><span class="pre">+lat_ts</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_ts" title="Permalink to this definition">¶</a></dt> +<dd><p>Latitude of true scale. Defines the latitude where scale is not distorted. +Takes precedence over <code class="docutils literal notranslate"><span class="pre">+k_0</span></code> if both options are used together.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wink1.html" class="btn btn-neutral float-left" title="Winkel I" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="wintri.html" class="btn btn-neutral float-right" title="Winkel Tripel" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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Semi-Elliptical</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li> +<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li> +<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li> +<li class="toctree-l3"><a 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class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li> +<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li> +<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li> +<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li> +<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li> +<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li> +<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li> +<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li> +<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li> +<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li> +<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li> +<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li> +<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li> +<li class="toctree-l3"><a class="reference 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href="natearth2.html">Natural Earth II</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li> +<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li> +<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li> +<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li> +<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li> +<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li> +<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li> +<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li> +<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li> +<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li> +<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li> +<li class="toctree-l3"><a class="reference internal" href="qsc.html">Quadrilateralized Spherical Cube</a></li> +<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li> +<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li> +<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li> +<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li> +<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li> +<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li> +<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li> +<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li> +<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li> +<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li> +<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li> +<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li> +<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li> +<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li> +<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li> +<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li> +<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li> +<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li> +<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li> +<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li> +<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Winkel Tripel</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +</ul> +</li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2"><a class="reference internal" href="../transformations/index.html">Transformations</a></li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Projections</a> »</li> + <li>Winkel Tripel</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/projections/wintri.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="wink2.html" class="btn btn-neutral float-left" title="Winkel II" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../conversions/index.html" class="btn btn-neutral float-right" title="Conversions" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="winkel-tripel"> +<span id="wintri"></span><h1>Winkel Tripel<a class="headerlink" href="#winkel-tripel" title="Permalink to this headline">¶</a></h1> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Classification</strong></p></td> +<td><p>Pseudoazimuthal</p></td> +</tr> +<tr class="row-even"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward spherical projection</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Defined area</strong></p></td> +<td><p>Global</p></td> +</tr> +<tr class="row-even"><td><p><strong>Alias</strong></p></td> +<td><p>wintri</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Domain</strong></p></td> +<td><p>2D</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected coordinates</p></td> +</tr> +</tbody> +</table> +<figure class="align-center" id="id1"> +<a class="reference internal image-reference" href="../../_images/wintri.png"><img alt="Winkel Tripel" src="../../_images/wintri.png" style="width: 500px;" /></a> +<figcaption> +<p><span class="caption-text">proj-string: <code class="docutils literal notranslate"><span class="pre">+proj=wintri</span></code></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p> +</figcaption> +</figure> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional for the projection.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lat_1"> +<span id="cmdoption-arg-lat-1"></span><span class="sig-name descname"><span class="pre">+lat_1</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_1" title="Permalink to this definition">¶</a></dt> +<dd><p>First standard parallel.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-lon_0"> +<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt> +<dd><p>Longitude of projection center.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-R"> +<span id="cmdoption-arg-r"></span><span class="sig-name descname"><span class="pre">+R</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-R" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the sphere, given in meters. If used in conjunction with +<code class="docutils literal notranslate"><span class="pre">+ellps</span></code>, <a class="reference internal" href="../../usage/ellipsoids.html#cmdoption-arg-R"><code class="xref std std-option docutils literal notranslate"><span class="pre">+R</span></code></a> takes precedence.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoid-size-parameters"><span class="std std-ref">Ellipsoid size parameters</span></a> for more information.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x_0"> +<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False easting.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y_0"> +<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt> +<dd><p>False northing.</p> +<p><em>Defaults to 0.0.</em></p> +</dd></dl> + +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="wink2.html" class="btn btn-neutral float-left" title="Winkel II" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../conversions/index.html" class="btn btn-neutral float-right" title="Conversions" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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transformation</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/affine.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="index.html" class="btn btn-neutral float-left" title="Transformations" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="defmodel.html" class="btn btn-neutral float-right" title="Multi-component time-based deformation model" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="affine-transformation"> +<span id="affine"></span><h1>Affine transformation<a class="headerlink" href="#affine-transformation" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>The affine transformation applies translation and scaling/rotation terms on the +x,y,z coordinates, and translation and scaling on the temporal coordinate.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>affine</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>XYZT</p></td> +</tr> +<tr class="row-even"><td><p><strong>output type</strong></p></td> +<td><p>XYZT</p></td> +</tr> +</tbody> +</table> +<p>By default, the parameters are set for an identity transforms. The transformation +is reversible unless the determinant of the sji matrix is 0, or <cite>tscale</cite> is 0</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-xoff"> +<span class="sig-name descname"><span class="pre">+xoff</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-xoff" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in X. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-yoff"> +<span class="sig-name descname"><span class="pre">+yoff</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-yoff" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in Y. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-zoff"> +<span class="sig-name descname"><span class="pre">+zoff</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-zoff" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in Z. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-toff"> +<span class="sig-name descname"><span class="pre">+toff</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-toff" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in T. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s11"> +<span class="sig-name descname"><span class="pre">+s11</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s11" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 1</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s12"> +<span class="sig-name descname"><span class="pre">+s12</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s12" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s13"> +<span class="sig-name descname"><span class="pre">+s13</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s13" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s21"> +<span class="sig-name descname"><span class="pre">+s21</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s21" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s22"> +<span class="sig-name descname"><span class="pre">+s22</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s22" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 1</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s23"> +<span class="sig-name descname"><span class="pre">+s23</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s23" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s31"> +<span class="sig-name descname"><span class="pre">+s31</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s31" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s32"> +<span class="sig-name descname"><span class="pre">+s32</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s32" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 0</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s33"> +<span class="sig-name descname"><span class="pre">+s33</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s33" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation/scaling term. Default value: 1</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-tscale"> +<span class="sig-name descname"><span class="pre">+tscale</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-tscale" title="Permalink to this definition">¶</a></dt> +<dd><p>Time scaling term. Default value: 1</p> +</dd></dl> + +<section id="mathematical-description"> +<h4>Mathematical description<a class="headerlink" href="#mathematical-description" title="Permalink to this headline">¶</a></h4> +<div class="math notranslate nohighlight" id="equation-formula"> +<span class="eqno">(1)<a class="headerlink" href="#equation-formula" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + T \\ + \end{bmatrix}^{dest} = + \begin{bmatrix} + xoff \\ + yoff \\ + zoff \\ + toff \\ + \end{bmatrix} + + \begin{bmatrix} + s11 & s12 & s13 & 0 \\ + s21 & s22 & s23 & 0 \\ + s31 & s32 & s33 & 0 \\ + 0 & 0 & 0 & tscale \\ + \end{bmatrix} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + T \\ + \end{bmatrix}^{source} +\end{align}\end{split}\]</div> +</section> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="index.html" class="btn btn-neutral float-left" title="Transformations" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="defmodel.html" class="btn btn-neutral float-right" title="Multi-component time-based deformation model" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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time-based deformation model</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/defmodel.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="affine.html" class="btn btn-neutral float-left" title="Affine transformation" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="deformation.html" class="btn btn-neutral float-right" title="Kinematic datum shifting utilizing a deformation model" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="multi-component-time-based-deformation-model"> +<span id="defmodel"></span><h1>Multi-component time-based deformation model<a class="headerlink" href="#multi-component-time-based-deformation-model" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 7.1.0.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 24%" /> +<col style="width: 76%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>defmodel</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic or projected coordinates (horizontal), meters (vertical), +decimalyear (temporal)</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Geodetic or projected coordinates (horizontal), meters (vertical), +decimalyear (temporal)</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse</p></td> +</tr> +</tbody> +</table> +<p>The defmodel transformation can be used to represent most deformation models +currently in use, in particular for areas subject to complex deformation, including +large scale secular crustal deformation near plate boundaries and vertical deformation +due to Glacial Isostatic Adjustment (GIA). These can often be represented by a constant +velocity model. Additionally, many areas suffer episodic deformation events such as +earthquakes and aseismic slow slip event.</p> +<p>The transformation relies on a “master” JSON file, describing general metadata on +the deformation model, its spatial and temporal extent, and listing spatial +components whose values are stored in <a class="reference internal" href="../../specifications/geodetictiffgrids.html#geodetictiffgrids"><span class="std std-ref">Geodetic TIFF grids (GTG)</span></a>. +The valuation of each component is modulated by a time function (constant, step, +reverse step, velocity, piecewise, exponential).</p> +<p>All details on the content of this JSON file are given in the <a class="reference external" href="https://github.com/linz/deformation-model-format/blob/master/doc/JsonGeotiffDeformationModelFormat_20200501.pdf">Proposal for encoding +of a Deformation Model</a></p> +<p>If input coordinates are given in the geographic domain (resp. projected domain), +the output will also be in the geographic domain (resp. projected domain). +The domain should be the corresponding to the source_crs metadata of the model.</p> +<p>This transformation is a generalization of the <a class="reference internal" href="deformation.html#deformation"><span class="std std-ref">Kinematic datum shifting utilizing a deformation model</span></a> transformation.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-model"> +<span class="sig-name descname"><span class="pre">+model</span></span><span class="sig-prename descclassname"><span class="pre">=<filename></span></span><a class="headerlink" href="#cmdoption-arg-model" title="Permalink to this definition">¶</a></dt> +<dd><p>Filename to the JSON master file for the deformation model.</p> +</dd></dl> + +</section> +</section> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>Transforming a point with the LINZ NZGD2000 deformation model:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 166.7133850980 -44.5105886020 293.3700 2007.689 | cct +proj=defmodel +model=nzgd2000-20180701.json +</pre></div> +</div> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="affine.html" class="btn btn-neutral float-left" title="Affine transformation" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="deformation.html" class="btn btn-neutral float-right" title="Kinematic datum shifting utilizing a deformation model" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="current reference internal" href="#">Kinematic datum shifting utilizing a deformation model</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#example">Example</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +<li class="toctree-l4"><a class="reference internal" href="#mathematical-description">Mathematical description</a></li> +<li class="toctree-l4"><a class="reference internal" href="#see-also">See also</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="geogoffset.html">Geographic offsets</a></li> +<li class="toctree-l3"><a class="reference internal" href="helmert.html">Helmert transform</a></li> +<li class="toctree-l3"><a class="reference internal" href="horner.html">Horner polynomial evaluation</a></li> +<li class="toctree-l3"><a class="reference internal" href="molodensky.html">Molodensky transform</a></li> +<li class="toctree-l3"><a class="reference internal" 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<span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="kinematic-datum-shifting-utilizing-a-deformation-model"> +<span id="deformation"></span><h1>Kinematic datum shifting utilizing a deformation model<a class="headerlink" href="#kinematic-datum-shifting-utilizing-a-deformation-model" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Perform datum shifts means of a deformation/velocity model.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>deformation</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Cartesian coordinates (spatial), decimalyears (temporal).</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Cartesian coordinates (spatial), decimalyears (temporal).</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geodetic coordinates</p></td> +</tr> +</tbody> +</table> +<p>The deformation operation is used to adjust coordinates for intraplate deformations. +Usually the transformation parameters for regional plate-fixed reference frames such as +the ETRS89 does not take intraplate deformation into account. It is assumed that +tectonic plate of the region is rigid. Often times this is true, but near the plate +boundary and in areas with post-glacial uplift the assumption breaks. Intraplate +deformations can be modelled and then applied to the coordinates so that +they represent the physical world better. In PROJ this is done with the deformation +operation.</p> +<p>The horizontal grid is stored in CTable2 format and the vertical grid is stored in the +GTX format. Both grids are expected to contain grid-values in units of +mm/year. GDAL both reads and writes both file formats. Using GDAL for +construction of new grids is recommended.</p> +<p>Starting with PROJ 7.0, use of a GeoTIFF format is recommended to store both +the horizontal and vertical velocities.</p> +<p>More complex deformations can be done with the <a class="reference internal" href="defmodel.html#defmodel"><span class="std std-ref">Multi-component time-based deformation model</span></a> transformation.</p> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>In <span id="id1">[<a class="reference internal" href="../../zreferences.html#id14" title="Häkli, P., Lidberg, M., Jivall, L., Nørbech, T., Tangen, O., Weber, M., Pihlak, P., Aleksejenko, I., and Paršeliunas, E. The NKG2008 GPS campaign – final transformation results and a new common Nordic reference frame. Journal of Geodetic Science, 6(1):1–33, 2016. doi:10.1515/jogs-2016-0001.">Hakli2016</a>]</span> coordinate transformation including a deformation model is described. +The paper describes how coordinates from the global ITRFxx frames are transformed to the +local Nordic realisations of ETRS89. Scandinavia is an area with significant post-glacial +rebound. The deformations from the post-glacial uplift is not accounted for in the +official ETRS89 transformations so in order to get accurate transformations in the Nordic +countries it is necessary to apply the deformation model. The transformation from ITRF2008 +to the Danish realisation of ETRS89 is in PROJ described as:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj = pipeline ellps = GRS80 + # ITRF2008@t_obs -> ITRF2000@t_obs +step init = ITRF2008:ITRF2000 + # ITRF2000@t_obs -> ETRF2000@t_obs +step proj=helmert t_epoch = 2000.0 convention=position_vector + x = 0.054 rx = 0.000891 drx = 8.1e-05 + y = 0.051 ry = 0.00539 dry = 0.00049 + z = -0.048 rz = -0.008712 drz = -0.000792 + # ETRF2000@t_obs -> NKG_ETRF00@2000.0 +step proj = deformation t_epoch = 2000.0 + grids = ./eur_nkg_nkgrf03vel_realigned.tif + inv + # NKG_ETRF@2000.0 -> ETRF92@2000.0 +step proj=helmert convention=position_vector s = -0.009420e + x = 0.03863 rx = 0.00617753 + y = 0.147 ry = 5.064e-05 + z = 0.02776 rz = 4.729e-05 + # ETRF92@2000.0 -> ETRF92@1994.704 +step proj = deformation dt = -5.296 + grids = ./eur_nkg_nkgrf03vel_realigned.tif +</pre></div> +</div> +<p>From this we can see that the transformation from ITRF2008 to the Danish realisation of +ETRS89 is a combination of Helmert transformations and adjustments with a deformation +model. The first use of the deformation operation is:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj = deformation t_epoch = 2000.0 grids = ./eur_nkg_nkgrf03vel_realigned.tif +</pre></div> +</div> +<p>Here we set the central epoch of the transformation, 2000.0. The observation epoch +is expected as part of the input coordinate tuple. The deformation model is +described by two grids, specified with <a class="reference internal" href="#cmdoption-arg-xy_grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+xy_grids</span></code></a> and <a class="reference internal" href="#cmdoption-arg-z_grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+z_grids</span></code></a>. +The first is the horizontal part of the model and the second is the vertical +component.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-xy_grids"> +<span id="cmdoption-arg-xy-grids"></span><span class="sig-name descname"><span class="pre">+xy_grids</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-xy_grids" title="Permalink to this definition">¶</a></dt> +<dd><p>Comma-separated list of grids to load. If a grid is prefixed by an <code class="docutils literal notranslate"><span class="pre">@</span></code> the +grid is considered optional and PROJ will the not complain if the grid is +not available.</p> +<p>Grids for the horizontal component of a deformation model is expected to be +in CTable2 format.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><a class="reference internal" href="#cmdoption-arg-xy_grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+xy_grids</span></code></a> is mutually exclusive with <a class="reference internal" href="xyzgridshift.html#cmdoption-arg-grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+grids</span></code></a></p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-z_grids"> +<span id="cmdoption-arg-z-grids"></span><span class="sig-name descname"><span class="pre">+z_grids</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-z_grids" title="Permalink to this definition">¶</a></dt> +<dd><p>Comma-separated list of grids to load. If a grid is prefixed by an <cite>@</cite> the +grid is considered optional and PROJ will the not complain if the grid is +not available.</p> +<p>Grids for the vertical component of a deformation model is expected to be +in either GTX format.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><a class="reference internal" href="#cmdoption-arg-z_grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+z_grids</span></code></a> is mutually exclusive with <a class="reference internal" href="xyzgridshift.html#cmdoption-arg-grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+grids</span></code></a></p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-grids"> +<span class="sig-name descname"><span class="pre">+grids</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-grids" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 7.0.0.</span></p> +</div> +<p>Comma-separated list of grids to load. If a grid is prefixed by an <cite>@</cite> the +grid is considered optional and PROJ will the not complain if the grid is +not available.</p> +<p>Grids should be in GeoTIFF format with the first 3 components being +respectively the easting, northing and up velocities in mm/year. +Setting the Description and Unit Type GDAL band metadata items is strongly +recommended, so that gdalinfo reports:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>Band 1 Block=... Type=Float32, ColorInterp=Gray + Description = east_velocity + Unit Type: mm/year +Band 2 Block=... Type=Float32, ColorInterp=Undefined + Description = north_velocity + Unit Type: mm/year +Band 3 Block=... Type=Float32, ColorInterp=Undefined + Description = up_velocity + Unit Type: mm/year +</pre></div> +</div> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><a class="reference internal" href="xyzgridshift.html#cmdoption-arg-grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+grids</span></code></a> is mutually exclusive with <a class="reference internal" href="#cmdoption-arg-xy_grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+xy_grids</span></code></a> +and <a class="reference internal" href="#cmdoption-arg-z_grids"><code class="xref std std-option docutils literal notranslate"><span class="pre">+z_grids</span></code></a></p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_epoch"> +<span id="cmdoption-arg-t-epoch"></span><span class="sig-name descname"><span class="pre">+t_epoch</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-t_epoch" title="Permalink to this definition">¶</a></dt> +<dd><p>Central epoch of transformation given in decimalyears. Will be used in +conjunction with the observation time from the input coordinate to +determine <span class="math notranslate nohighlight">\(dt\)</span> as used in eq. <a class="reference internal" href="#equation-apply-velocity">(1)</a> below.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><a class="reference internal" href="vgridshift.html#cmdoption-arg-t_epoch"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_epoch</span></code></a> is mutually exclusive with <a class="reference internal" href="#cmdoption-arg-dt"><code class="xref std std-option docutils literal notranslate"><span class="pre">+dt</span></code></a></p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dt"> +<span class="sig-name descname"><span class="pre">+dt</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dt" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p><span class="math notranslate nohighlight">\(dt\)</span> as used in eq. <a class="reference internal" href="#equation-apply-velocity">(1)</a> below. Is useful when +no observation time is available in the input coordinate or when +a deformation for a specific timespan needs to be applied in a +transformation. <span class="math notranslate nohighlight">\(dt\)</span> is given in units of decimalyears.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p><a class="reference internal" href="#cmdoption-arg-dt"><code class="xref std std-option docutils literal notranslate"><span class="pre">+dt</span></code></a> is mutually exclusive with <a class="reference internal" href="vgridshift.html#cmdoption-arg-t_epoch"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_epoch</span></code></a></p> +</div> +</dd></dl> + +</section> +<section id="mathematical-description"> +<h2>Mathematical description<a class="headerlink" href="#mathematical-description" title="Permalink to this headline">¶</a></h2> +<p>Mathematically speaking, application of a deformation model is simple. The deformation model is +represented as a grid of velocities in three dimensions. Coordinate corrections are +applied in cartesian space. For a given coordinate, <span class="math notranslate nohighlight">\((X, Y, Z)\)</span>, velocities +<span class="math notranslate nohighlight">\((V_X, V_Y, V_Z)\)</span> can be interpolated from the gridded model. The time span +between <span class="math notranslate nohighlight">\(t_{obs}\)</span> and <span class="math notranslate nohighlight">\(t_c\)</span> determine the magnitude of the coordinate +correction as seen in eq. <a class="reference internal" href="#equation-apply-velocity">(1)</a> below.</p> +<div class="math notranslate nohighlight" id="equation-apply-velocity"> +<span class="eqno">(1)<a class="headerlink" href="#equation-apply-velocity" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{pmatrix} + X \\ + Y \\ + Z \\ + \end{pmatrix}_B = + \begin{pmatrix} + X \\ + Y \\ + Z \\ + \end{pmatrix}_A + + (t_{obs} - t_c) + \begin{pmatrix} + V_X \\ + V_Y \\ + V_Z \\ + \end{pmatrix} +\end{align}\end{split}\]</div> +<p>Corrections are done in cartesian space.</p> +<p>Coordinates of the gridded model are in ENU (east, north, up) space because it +would otherwise require an enormous 3 dimensional grid to handle the corrections +in cartesian space. Keeping the correction in lat/long space reduces the +complexity of the grid significantly. Consequently though, the input coordinates +needs to be converted to lat/long space when searching for corrections in the +grid. This is done with the <a class="reference internal" href="../conversions/cart.html#cart"><span class="std std-ref">cart</span></a> operation. The converted grid +corrections can then be applied to the input coordinates in cartesian space. The +conversion from ENU space to cartesian space is done in the following way:</p> +<div class="math notranslate nohighlight" id="equation-enu2xyz"> +<span class="eqno">(2)<a class="headerlink" href="#equation-enu2xyz" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{pmatrix} + X \\ + Y \\ + Z \\ + \end{pmatrix} = + \begin{pmatrix} + -\sin\phi \cos\lambda N - \sin\lambda E + \cos\phi \cos\lambda U \\ + -\sin\phi \sin\lambda N + \sin\lambda E + \cos\phi \sin\lambda U \\ + \cos\phi N + \sin\phi U \\ + \end{pmatrix} +\end{align}\end{split}\]</div> +<p>where <span class="math notranslate nohighlight">\(\phi\)</span> and <span class="math notranslate nohighlight">\(\lambda\)</span> are the latitude and longitude of the coordinate +that is searched for in the grid. <span class="math notranslate nohighlight">\((E, N, U)\)</span> are the grid values in ENU-space and +<span class="math notranslate nohighlight">\((X, Y, Z)\)</span> are the corrections converted to cartesian space.</p> +</section> +<section id="see-also"> +<h2>See also<a class="headerlink" href="#see-also" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference internal" href="../../usage/differences.html#differences-deformation"><span class="std std-ref">Behavioural changes from version 5 to 6</span></a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="defmodel.html" class="btn btn-neutral float-left" title="Multi-component time-based deformation model" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="geogoffset.html" class="btn btn-neutral float-right" title="Geographic offsets" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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+ <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/geogoffset.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="deformation.html" class="btn btn-neutral float-left" title="Kinematic datum shifting utilizing a deformation model" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="helmert.html" class="btn btn-neutral float-right" title="Helmert transform" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="geographic-offsets"> +<span id="geogoffset"></span><h1>Geographic offsets<a class="headerlink" href="#geographic-offsets" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>The Geographic offsets transformation adds an offset to the geographic longitude, +latitude coordinates, and an offset to the ellipsoidal height.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>geogoffset</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical)</p></td> +</tr> +<tr class="row-even"><td><p><strong>output type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical)</p></td> +</tr> +</tbody> +</table> +<p>This method is normally only used when low accuracy is tolerated. It is documented +as coordinate operation method code 9619 (for geographic 2D) and 9660 (for +geographic 3D) in the EPSG dataset (<span id="id1">[<a class="reference internal" href="../../zreferences.html#id17" title="IOGP. Geomatics guidance note 7, part 2: coordinate conversions & transformations including formulas. IOGP Publication 373-7-2, International Association For Oil And Gas Producers, 2018. URL: https://www.iogp.org/bookstore/product/coordinate-conversions-and-transformation-including-formulas/.">IOGP2018</a>]</span>)</p> +<p>It can also be used to implement the method Geographic2D with Height Offsets +(code 9618) by noting that the input vertical component is a gravity-related +height and the output vertical component is the ellipsoid height (dh being +the geoid undulation).</p> +<p>It can also be used to implement the method Vertical offset (code 9616)</p> +<p>The reverse transformation simply consists in subtracting the offsets.</p> +<p>This method is a conveniency wrapper for the more general <a class="reference internal" href="affine.html#affine"><span class="std std-ref">Affine transformation</span></a>.</p> +<section id="examples"> +<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2> +<p>Geographic offset from the old Greek geographic 2D CRS to the newer GGRS87 CRS:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=geogoffset dlon=0.28 dlat=-5.86 +</pre></div> +</div> +<p>Conversion from Tokyo + JSLD69 height to WGS 84:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=geogoffset dlon=-13.97 dlat=7.94 dh=26.9 +</pre></div> +</div> +<p>Conversion from Baltic 1977 height to Black Sea height:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=geogoffset dh=0.4 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dlon"> +<span class="sig-name descname"><span class="pre">+dlon</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dlon" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in longitude, expressed in arc-second, to add.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dlat"> +<span class="sig-name descname"><span class="pre">+dlat</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dlat" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in latitude, expressed in arc-second, to add.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dh"> +<span class="sig-name descname"><span class="pre">+dh</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dh" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset in height, expressed in meter, to add.</p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="deformation.html" class="btn btn-neutral float-left" title="Kinematic datum shifting utilizing a deformation model" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="helmert.html" class="btn btn-neutral float-right" title="Helmert transform" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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model</a></li> +<li class="toctree-l3"><a class="reference internal" href="geogoffset.html">Geographic offsets</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Helmert transform</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#examples">Examples</a></li> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +<li class="toctree-l4"><a class="reference internal" href="#mathematical-description">Mathematical description</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="horner.html">Horner polynomial evaluation</a></li> +<li class="toctree-l3"><a class="reference internal" href="molodensky.html">Molodensky transform</a></li> +<li class="toctree-l3"><a class="reference internal" href="molobadekas.html">Molodensky-Badekas transform</a></li> +<li class="toctree-l3"><a class="reference internal" href="hgridshift.html">Horizontal grid shift</a></li> +<li 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<li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Transformations</a> »</li> + <li>Helmert transform</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/helmert.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="geogoffset.html" class="btn btn-neutral float-left" title="Geographic offsets" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="horner.html" class="btn btn-neutral float-right" title="Horner polynomial evaluation" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="helmert-transform"> +<span id="helmert"></span><h1>Helmert transform<a class="headerlink" href="#helmert-transform" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>The Helmert transformation changes coordinates from one reference frame to +another by means of 3-, 4-and 7-parameter shifts, or one of their 6-, 8- and +14-parameter kinematic counterparts.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>helmert</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D, 3D and 4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Cartesian coordinates (spatial), decimalyears (temporal).</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Cartesian coordinates (spatial), decimalyears (temporal).</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Cartesian coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Cartesian coordinates</p></td> +</tr> +</tbody> +</table> +<p>The Helmert transform, in all its various incarnations, is used to perform reference +frame shifts. The transformation operates in cartesian space. It can be used to transform +planar coordinates from one datum to another, transform 3D cartesian +coordinates from one static reference frame to another or it can be used to do fully +kinematic transformations from global reference frames to local static frames.</p> +<p>All of the parameters described in the table above are marked as optional. This is true +as long as at least one parameter is defined in the setup of the transformation. +The behavior of the transformation depends on which parameters are used in the setup. +For instance, if a rate of change parameter is specified a kinematic version of the +transformation is used.</p> +<p>The kinematic transformations require an observation time of the coordinate, as well +as a central epoch for the transformation. The latter is usually documented +alongside the rest of the transformation parameters for a given transformation. +The central epoch is controlled with the parameter <cite>t_epoch</cite>. The observation +time is given as part of the coordinate when using PROJ’s 4D-functionality.</p> +<section id="examples"> +<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2> +<p>Transforming coordinates from NAD72 to NAD83 using the 4 parameter 2D Helmert:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=helmert convention=coordinate_frame x=-9597.3572 y=.6112 s=0.304794780637 theta=-1.244048 +</pre></div> +</div> +<p>Simplified transformations from ITRF2008/IGS08 to ETRS89 using 7 parameters:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=helmert convention=coordinate_frame x=0.67678 y=0.65495 z=-0.52827 + rx=-0.022742 ry=0.012667 rz=0.022704 s=-0.01070 +</pre></div> +</div> +<p>Transformation from <cite>ITRF2000</cite> to <cite>ITRF93</cite> using 15 parameters:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=helmert convention=position_vector + x=0.0127 y=0.0065 z=-0.0209 s=0.00195 + dx=-0.0029 dy=-0.0002 dz=-0.0006 ds=0.00001 + rx=-0.00039 ry=0.00080 rz=-0.00114 + drx=-0.00011 dry=-0.00019 drz=0.00007 + t_epoch=1988.0 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters are optional but at least one should be used, otherwise the +operation will return the coordinates unchanged.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-convention"> +<span class="sig-name descname"><span class="pre">+convention</span></span><span class="sig-prename descclassname"><span class="pre">=coordinate_frame/position_vector</span></span><a class="headerlink" href="#cmdoption-arg-convention" title="Permalink to this definition">¶</a></dt> +<dd><div class="versionadded"> +<p><span class="versionmodified added">New in version 5.2.0.</span></p> +</div> +<p>Indicates the convention to express the rotational terms when a 3D-Helmert / +7-parameter more transform is involved. As soon as a rotational parameter +is specified (one of <code class="docutils literal notranslate"><span class="pre">rx</span></code>, <code class="docutils literal notranslate"><span class="pre">ry</span></code>, <code class="docutils literal notranslate"><span class="pre">rz</span></code>, <code class="docutils literal notranslate"><span class="pre">drx</span></code>, <code class="docutils literal notranslate"><span class="pre">dry</span></code>, <code class="docutils literal notranslate"><span class="pre">drz</span></code>), +<code class="docutils literal notranslate"><span class="pre">convention</span></code> is required.</p> +<p>The two conventions are equally popular and a frequent source of confusion. +The coordinate frame convention is also described as an clockwise +rotation of the coordinate frame. It corresponds to EPSG method code +1032 (in the geocentric domain) or 9607 (in the geographic domain) +The position vector convention is also described as an anticlockwise +(counter-clockwise) rotation of the coordinate frame. +It corresponds to as EPSG method code 1033 (in the geocentric domain) or +9606 (in the geographic domain).</p> +<p>This parameter is ignored when only a 3-parameter +(translation terms only: <code class="docutils literal notranslate"><span class="pre">x</span></code>, <code class="docutils literal notranslate"><span class="pre">y</span></code>, <code class="docutils literal notranslate"><span class="pre">z</span></code>) , 4-parameter (3-parameter +and <code class="docutils literal notranslate"><span class="pre">theta</span></code>) or 6-parameter (3-parameter and their derivative terms) +is used.</p> +<p>The result obtained with parameters specified in a given convention +can be obtained in the other convention by negating the rotational parameters +(<code class="docutils literal notranslate"><span class="pre">rx</span></code>, <code class="docutils literal notranslate"><span class="pre">ry</span></code>, <code class="docutils literal notranslate"><span class="pre">rz</span></code>, <code class="docutils literal notranslate"><span class="pre">drx</span></code>, <code class="docutils literal notranslate"><span class="pre">dry</span></code>, <code class="docutils literal notranslate"><span class="pre">drz</span></code>)</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>This parameter obsoletes <code class="docutils literal notranslate"><span class="pre">transpose</span></code> which was present in +PROJ 5.0 and 5.1, and is forbidden starting with PROJ 5.2</p> +</div> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x"> +<span class="sig-name descname"><span class="pre">+x</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation of the x-axis given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y"> +<span class="sig-name descname"><span class="pre">+y</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation of the y-axis given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-z"> +<span class="sig-name descname"><span class="pre">+z</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-z" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation of the z-axis given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s"> +<span class="sig-name descname"><span class="pre">+s</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor given in ppm.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-rx"> +<span class="sig-name descname"><span class="pre">+rx</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-rx" title="Permalink to this definition">¶</a></dt> +<dd><p>X-axis rotation in the 3D Helmert given arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ry"> +<span class="sig-name descname"><span class="pre">+ry</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ry" title="Permalink to this definition">¶</a></dt> +<dd><p>Y-axis rotation in the 3D Helmert given in arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-rz"> +<span class="sig-name descname"><span class="pre">+rz</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-rz" title="Permalink to this definition">¶</a></dt> +<dd><p>Z-axis rotation in the 3D Helmert given in arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-theta"> +<span class="sig-name descname"><span class="pre">+theta</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-theta" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation angle in the 2D Helmert given in arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dx"> +<span class="sig-name descname"><span class="pre">+dx</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dx" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation rate of the x-axis given in m/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dy"> +<span class="sig-name descname"><span class="pre">+dy</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dy" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation rate of the y-axis given in m/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dz"> +<span class="sig-name descname"><span class="pre">+dz</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dz" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation rate of the z-axis given in m/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ds"> +<span class="sig-name descname"><span class="pre">+ds</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ds" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale rate factor given in ppm/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-drx"> +<span class="sig-name descname"><span class="pre">+drx</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-drx" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation rate of the x-axis given in arc seconds/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dry"> +<span class="sig-name descname"><span class="pre">+dry</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dry" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation rate of the y-axis given in arc seconds/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-drz"> +<span class="sig-name descname"><span class="pre">+drz</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-drz" title="Permalink to this definition">¶</a></dt> +<dd><p>Rotation rate of the y-axis given in arc seconds/year.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_epoch"> +<span id="cmdoption-arg-t-epoch"></span><span class="sig-name descname"><span class="pre">+t_epoch</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-t_epoch" title="Permalink to this definition">¶</a></dt> +<dd><p>Central epoch of transformation given in decimalyear. Only used +spatiotemporal transformations.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-exact"> +<span class="sig-name descname"><span class="pre">+exact</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-exact" title="Permalink to this definition">¶</a></dt> +<dd><p>Use exact transformation equations.</p> +<p>See <a class="reference internal" href="#equation-rot-exact">(5)</a></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-transpose"> +<span class="sig-name descname"><span class="pre">+transpose</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-transpose" title="Permalink to this definition">¶</a></dt> +<dd><div class="deprecated"> +<p><span class="versionmodified deprecated">Deprecated since version 5.2.0: </span>(removed)</p> +</div> +<p>Transpose rotation matrix and follow the <strong>Position Vector</strong> rotation +convention. If <a class="reference internal" href="#cmdoption-arg-transpose"><code class="xref std std-option docutils literal notranslate"><span class="pre">+transpose</span></code></a> is not added the <strong>Coordinate Frame</strong> +rotation convention is used.</p> +</dd></dl> + +</section> +<section id="mathematical-description"> +<h2>Mathematical description<a class="headerlink" href="#mathematical-description" title="Permalink to this headline">¶</a></h2> +<p>In the notation used below, <span class="math notranslate nohighlight">\(\hat{P}\)</span> is the rate of change of a given transformation +parameter <span class="math notranslate nohighlight">\(P\)</span>. <span class="math notranslate nohighlight">\(\dot{P}\)</span> is the kinematically adjusted version of <span class="math notranslate nohighlight">\(P\)</span>, +described by</p> +<div class="math notranslate nohighlight" id="equation-propagation"> +<span class="eqno">(1)<a class="headerlink" href="#equation-propagation" title="Permalink to this equation">¶</a></span>\[\dot{P}= P + \hat{P}\left(t - t_{central}\right)\]</div> +<p>where <span class="math notranslate nohighlight">\(t\)</span> is the observation time of the coordinate and <span class="math notranslate nohighlight">\(t_{central}\)</span> is +the central epoch of the transformation. Equation <a class="reference internal" href="#equation-propagation">(1)</a> can be used to +propagate all transformation parameters in time.</p> +<p>Superscripts of vectors denote the reference frame the coordinates in the vector belong to.</p> +<section id="d-helmert"> +<h3>2D Helmert<a class="headerlink" href="#d-helmert" title="Permalink to this headline">¶</a></h3> +<p>The simplest version of the Helmert transform is the 2D case. In the 2-dimensional +case only the horizontal coordinates are changed. The coordinates can be +translated, rotated and scale. Translation is controlled with the <cite>x</cite> and <cite>y</cite> +parameters. The rotation is determined by <cite>theta</cite> and the scale is controlled with +the <cite>s</cite> parameters.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The scaling parameter <cite>s</cite> is unitless for the 2D Helmert, as opposed to the +3D version where the scaling parameter is given in units of ppm.</p> +</div> +<p>Mathematically the 2D Helmert is described as:</p> +<div class="math notranslate nohighlight" id="equation-4param"> +<span class="eqno">(2)<a class="headerlink" href="#equation-4param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + \end{bmatrix}^B = + \begin{bmatrix} + T_x \\ + T_y \\ + \end{bmatrix} + + s + \begin{bmatrix} + \hphantom{-}\cos \theta & \sin \theta \\ + -\sin \theta & \cos \theta \\ + \end{bmatrix} + \begin{bmatrix} + X \\ + Y \\ + \end{bmatrix}^A +\end{align}\end{split}\]</div> +<p><a class="reference internal" href="#equation-4param">(2)</a> can be extended to a time-varying kinematic version by +adjusting the parameters with <a class="reference internal" href="#equation-propagation">(1)</a> to <a class="reference internal" href="#equation-4param">(2)</a>, which yields +the kinematic 2D Helmert transform:</p> +<div class="math notranslate nohighlight" id="equation-8param"> +<span class="eqno">(3)<a class="headerlink" href="#equation-8param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + \end{bmatrix}^B = + \begin{bmatrix} + \dot{T_x} \\ + \dot{T_y} \\ + \end{bmatrix} + + s(t) + \begin{bmatrix} + \hphantom{-}\cos \dot{\theta} & \sin \dot{\theta} \\ + -\sin\ \dot{\theta} & \cos \dot{\theta} \\ + \end{bmatrix} + \begin{bmatrix} + X \\ + Y \\ + \end{bmatrix}^A +\end{align}\end{split}\]</div> +<p>All parameters in <a class="reference internal" href="#equation-8param">(3)</a> are determined by the use of <a class="reference internal" href="#equation-propagation">(1)</a>, +which applies the rate of change to each individual parameter for a given +timespan between <span class="math notranslate nohighlight">\(t\)</span> and <span class="math notranslate nohighlight">\(t_{central}\)</span>.</p> +</section> +<section id="id1"> +<h3>3D Helmert<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3> +<p>The general form of the 3D Helmert is</p> +<div class="math notranslate nohighlight" id="equation-general-helmert"> +<span class="eqno">(4)<a class="headerlink" href="#equation-general-helmert" title="Permalink to this equation">¶</a></span>\[\begin{align} + V^B = T + \left(1 + s \times 10^{-6}\right) \mathbf{R} V^A +\end{align}\]</div> +<p>Where <span class="math notranslate nohighlight">\(T\)</span> is a vector consisting of the three translation parameters, <span class="math notranslate nohighlight">\(s\)</span> +is the scaling factor and <span class="math notranslate nohighlight">\(\mathbf{R}\)</span> is a rotation matrix. <span class="math notranslate nohighlight">\(V^A\)</span> and +<span class="math notranslate nohighlight">\(V^B\)</span> are coordinate vectors, with <span class="math notranslate nohighlight">\(V^A\)</span> being the input coordinate and +<span class="math notranslate nohighlight">\(V^B\)</span> is the output coordinate.</p> +<p>In the <em>Position Vector</em> convention, we define <span class="math notranslate nohighlight">\(R_x = radians \left( rx \right)\)</span>, +<span class="math notranslate nohighlight">\(R_z = radians \left( ry \right)\)</span> and <span class="math notranslate nohighlight">\(R_z = radians \left( rz \right)\)</span></p> +<p>In the <em>Coordinate Frame</em> convention, <span class="math notranslate nohighlight">\(R_x = - radians \left( rx \right)\)</span>, +<span class="math notranslate nohighlight">\(R_z = - radians \left( ry \right)\)</span> and <span class="math notranslate nohighlight">\(R_z = - radians \left( rz \right)\)</span></p> +<p>The rotation matrix is composed of three rotation matrices, one for each axis.</p> +<div class="math notranslate nohighlight"> +\[\begin{split}\begin{align} + \mathbf{R}_X &= \begin{bmatrix} 1 & 0 & 0\\ 0 & \cos R_x & -\sin R_x \\ 0 & \sin R_x & \cos R_x \end{bmatrix} +\end{align}\end{split}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\begin{align} + \mathbf{R}_Y &= \begin{bmatrix} \cos R_y & 0 & \sin R_y\\ 0 & 1 & 0\\ -\sin R_y & 0 & \cos R_y \end{bmatrix} +\end{align}\end{split}\]</div> +<div class="math notranslate nohighlight"> +\[\begin{split}\begin{align} + \mathbf{R}_Z &= \begin{bmatrix} \cos R_z & -\sin R_z & 0\\ \sin R_z & \cos R_z & 0\\ 0 & 0 & 1 \end{bmatrix} +\end{align}\end{split}\]</div> +<p>The three rotation matrices can be combined in one:</p> +<div class="math notranslate nohighlight"> +\[\begin{align} + \mathbf{R} = \mathbf{R_X} \mathbf{R_Y} \mathbf{R_Y} +\end{align}\]</div> +<p>For <span class="math notranslate nohighlight">\(\mathbf{R}\)</span>, this yields:</p> +<div class="math notranslate nohighlight" id="equation-rot-exact"> +<span class="eqno">(5)<a class="headerlink" href="#equation-rot-exact" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{bmatrix} + \cos R_y \cos R_z & -\cos R_x \sin R_z + & \sin R_x \sin R_z + \\ + & \sin R_x \sin R_y \cos R_z & \cos R_x \sin R_y \cos R_z \\ + \cos R_y\sin R_z & \cos R_x \cos R_z + & - \sin R_x \cos R_z + \\ + & \sin R_x \sin R_y \sin R_z & \cos R_x \sin R_y \sin R_z \\ + -\sin R_y & \sin R_x \cos R_y & \cos R_x \cos R_y \\ + \end{bmatrix}\end{split}\]</div> +<p>Using the small angle approximation the rotation matrix can be simplified to</p> +<div class="math notranslate nohighlight" id="equation-rot-approx"> +<span class="eqno">(6)<a class="headerlink" href="#equation-rot-approx" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} \mathbf{R} = + \begin{bmatrix} + 1 & -R_z & R_y \\ + Rz & 1 & -R_x \\ + -Ry & R_x & 1 \\ + \end{bmatrix} +\end{align}\end{split}\]</div> +<p>Which allow us to express the most common version of the Helmert transform, +using the approximated rotation matrix:</p> +<div class="math notranslate nohighlight" id="equation-7param"> +<span class="eqno">(7)<a class="headerlink" href="#equation-7param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^B = + \begin{bmatrix} + T_x \\ + T_y \\ + T_z \\ + \end{bmatrix} + + \left(1 + s \times 10^{-6}\right) + \begin{bmatrix} + 1 & -R_z & R_y \\ + Rz & 1 & -R_x \\ + -Ry & R_x & 1 \\ + \end{bmatrix} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^A +\end{align}\end{split}\]</div> +<p>If the rotation matrix is transposed, or the sign of the rotation terms negated, +the rotational part of the transformation is effectively reversed. +This is what happens when switching between the 2 conventions <code class="docutils literal notranslate"><span class="pre">position_vector</span></code> +and <code class="docutils literal notranslate"><span class="pre">coordinate_frame</span></code></p> +<p>Applying <a class="reference internal" href="#equation-propagation">(1)</a> we get the kinematic version of the approximated +3D Helmert:</p> +<div class="math notranslate nohighlight" id="equation-14param"> +<span class="eqno">(8)<a class="headerlink" href="#equation-14param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^B = + \begin{bmatrix} + \dot{T_x} \\ + \dot{T_y} \\ + \dot{T_z} \\ + \end{bmatrix} + + \left(1 + \dot{s} \times 10^{-6}\right) + \begin{bmatrix} + 1 & -\dot{R_z} & \dot{R_y} \\ + \dot{R_z} & 1 & -\dot{R_x} \\ + -\dot{R_y} & \dot{R_x} & 1 \\ + \end{bmatrix} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^A +\end{align}\end{split}\]</div> +<p>The Helmert transformation can be applied without using the rotation parameters, +in which case it becomes a simple translation of the origin of the coordinate +system. When using the Helmert in this version equation <a class="reference internal" href="#equation-general-helmert">(4)</a> +simplifies to:</p> +<div class="math notranslate nohighlight" id="equation-3param"> +<span class="eqno">(9)<a class="headerlink" href="#equation-3param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^B = + \begin{bmatrix} + T_x \\ + T_y \\ + T_z \\ + \end{bmatrix} + + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^A +\end{align}\end{split}\]</div> +<p>That after application of <a class="reference internal" href="#equation-propagation">(1)</a> has the following kinematic +counterpart:</p> +<div class="math notranslate nohighlight" id="equation-6param"> +<span class="eqno">(10)<a class="headerlink" href="#equation-6param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^B = + \begin{bmatrix} + \dot{T_x} \\ + \dot{T_y} \\ + \dot{T_z} \\ + \end{bmatrix} + + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^A +\end{align}\end{split}\]</div> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="geogoffset.html" class="btn btn-neutral float-left" title="Geographic offsets" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="horner.html" class="btn btn-neutral float-right" title="Horner polynomial evaluation" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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shift</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/hgridshift.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="molobadekas.html" class="btn btn-neutral float-left" title="Molodensky-Badekas transform" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tinshift.html" class="btn btn-neutral float-right" title="Triangulated Irregular Network based transformation" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="horizontal-grid-shift"> +<span id="hgridshift"></span><h1>Horizontal grid shift<a class="headerlink" href="#horizontal-grid-shift" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Change of horizontal datum by grid shift.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>hgridshift</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D, 3D and 4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical), +decimalyear (temporal)</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical), +decimalyear (temporal)</p></td> +</tr> +</tbody> +</table> +<p>The horizontal grid shift is done by offsetting the planar input coordinates by +a specific amount determined by the loaded grids. The simplest use case of the +horizontal grid shift is applying a single grid:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=hgridshift +grids=nzgr2kgrid0005.gsb +</pre></div> +</div> +<p>More than one grid can be loaded at the same time, for instance in case the +dataset needs to be transformed spans several countries. In this example grids +of the continental US, Alaska and Canada is loaded at the same time:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=hgridshift +grids=@conus,@alaska,@ntv2_0.gsb,@ntv_can.dat +</pre></div> +</div> +<p>The <code class="docutils literal notranslate"><span class="pre">@</span></code> in the above example states that the grid is optional, in case the grid +is not found in the PROJ search path. The list of grids is prioritized so that +grids in the start of the list takes precedence over the grids in the back of the +list.</p> +<p>PROJ supports CTable2, NTv1 and NTv2 files for horizontal grid corrections. Details +about all three formats can be found in the GDAL documentation and/or driver source +code. GDAL reads and writes all three formats. Using GDAL for construction of +new grids is recommended.</p> +<section id="temporal-gridshifting"> +<h2>Temporal gridshifting<a class="headerlink" href="#temporal-gridshifting" title="Permalink to this headline">¶</a></h2> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<p>By initializing the horizontal gridshift operation with a central epoch, it can be +used as a step function applying the grid offsets only if a coordinate is +transformed from an epoch before grids central epoch to an epoch after. This is +handy in transformations where it is necessary to handle deformations caused by +seismic activity.</p> +<p>The central epoch of the grid is controlled with <a class="reference internal" href="vgridshift.html#cmdoption-arg-t_epoch"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_epoch</span></code></a> and the final +epoch of the coordinate is set with <a class="reference internal" href="vgridshift.html#cmdoption-arg-t_final"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_final</span></code></a>. The observation epoch of +the coordinate is part of the coordinate tuple.</p> +<p>Suppose we want to model the deformation of the 2008 earthquake in Iceland in +a transformation of data from 2005 to 2009:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 63.992 -21.014 10.0 2005.0 | cct +proj=hgridshift +grids=iceland2008.gsb +t_epoch=2008.4071 +t_final=2009.0 +63.9920021 -21.0140013 10.0 2005.0 +</pre></div> +</div> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The timestamp of the resulting coordinate is still 2005.0. The observation +time is always kept unchanged as it would otherwise be impossible to do the +inverse transformation.</p> +</div> +<p>Temporal gridshifting is especially powerful in transformation pipelines where +several gridshifts can be chained together, effectively acting as a series of +step functions that can be applied to a coordinate that is propagated through +time. In the following example we establish a pipeline that allows transformation +of coordinates from any given epoch up until the current date, applying only +those gridshifts that have central epochs between the observation epoch and +the final epoch:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +t_final=now ++step +proj=hgridshift +grids=earthquake_1.gsb +t_epoch=2010.421 ++step +proj=hgridshift +grids=earthquake_2.gsb +t_epoch=2013.853 ++step +proj=hgridshift +grids=earthquake_3.gsb +t_epoch=2017.713 +</pre></div> +</div> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The special epoch <em>now</em> is used when specifying the final epoch with +<a class="reference internal" href="vgridshift.html#cmdoption-arg-t_final"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_final</span></code></a>. This results in coordinates being transformed to the +current date. Additionally, <a class="reference internal" href="vgridshift.html#cmdoption-arg-t_final"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_final</span></code></a> is used as a +<a class="reference internal" href="../pipeline.html#global-pipeline-parameter"><span class="std std-ref">global pipeline parameter</span></a>, which means +that it is applied to all the steps in the pipeline.</p> +</div> +<p>In the above transformation, a coordinate with observation epoch 2009.32 would +be subject to all three gridshift steps in the pipeline. A coordinate with +observation epoch 2014.12 would only by offset by the last step in the pipeline.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-grids"> +<span class="sig-name descname"><span class="pre">+grids</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-grids" title="Permalink to this definition">¶</a></dt> +<dd><p>Comma-separated list of grids to load. If a grid is prefixed by an <cite>@</cite> the +grid is considered optional and PROJ will the not complain if the grid is +not available.</p> +<p>Grids are expected to be in CTable2, NTv1 or NTv2 format.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_epoch"> +<span id="cmdoption-arg-t-epoch"></span><span class="sig-name descname"><span class="pre">+t_epoch</span></span><span class="sig-prename descclassname"><span class="pre">=<time></span></span><a class="headerlink" href="#cmdoption-arg-t_epoch" title="Permalink to this definition">¶</a></dt> +<dd><p>Central epoch of the transformation.</p> +</dd></dl> + +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_final"> +<span id="cmdoption-arg-t-final"></span><span class="sig-name descname"><span class="pre">+t_final</span></span><span class="sig-prename descclassname"><span class="pre">=<time></span></span><a class="headerlink" href="#cmdoption-arg-t_final" title="Permalink to this definition">¶</a></dt> +<dd><p>Final epoch that the coordinate will be propagated to after transformation. +The special epoch <em>now</em> can be used instead of writing a specific period in +time. When <em>now</em> is used, it is replaced internally with the epoch of the +transformation. This means that the resulting coordinate will be slightly +different if carried out again at a later date.</p> +</dd></dl> + +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="molobadekas.html" class="btn btn-neutral float-left" title="Molodensky-Badekas transform" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="tinshift.html" class="btn btn-neutral float-right" title="Triangulated Irregular Network based transformation" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Transformations</a> »</li> + <li>Horner polynomial evaluation</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/horner.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="helmert.html" class="btn btn-neutral float-left" title="Helmert transform" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="molodensky.html" class="btn btn-neutral float-right" title="Molodensky transform" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="horner-polynomial-evaluation"> +<span id="horner"></span><h1>Horner polynomial evaluation<a class="headerlink" href="#horner-polynomial-evaluation" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>horner</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D and 3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic and projected coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geodetic and projected coordinates</p></td> +</tr> +</tbody> +</table> +<p>The Horner polynomial evaluation scheme is used for transformations between reference +frames where one or both are inhomogeneous or internally distorted. This will typically +be reference frames created before the introduction of space geodetic techniques such +as GPS.</p> +<p>Horner polynomials, or Multiple Regression Equations as they are also known as, have +their strength in being able to create complicated mappings between coordinate +reference frames while still being lightweight in both computational cost and disk +space used.</p> +<p>PROJ implements two versions of the Horner evaluation scheme: Real and complex +polynomial evaluation. Below both are briefly described. For more details consult +<span id="id1">[<a class="reference internal" href="../../zreferences.html#id31" title="Ruffhead, A. C. Introduction to multiple regression equations in datum transformations and their reversibility. Survey Review, 50(358):82–90, 2016. doi:10.1080/00396265.2016.1244143.">Ruffhead2016</a>]</span> and <span id="id2">[<a class="reference internal" href="../../zreferences.html#id17" title="IOGP. Geomatics guidance note 7, part 2: coordinate conversions & transformations including formulas. IOGP Publication 373-7-2, International Association For Oil And Gas Producers, 2018. URL: https://www.iogp.org/bookstore/product/coordinate-conversions-and-transformation-including-formulas/.">IOGP2018</a>]</span>.</p> +<p>The polynomial evaluation in real number space is defined by the following equations:</p> +<div class="math notranslate nohighlight" id="equation-real-poly"> +<span class="eqno">(1)<a class="headerlink" href="#equation-real-poly" title="Permalink to this equation">¶</a></span>\[ \begin{align}\begin{aligned}\Delta X = \sum_{i,j} u_{i,j} U^i V^j\\\Delta Y = \sum_{i,j} v_{i,j} U^i V^j\end{aligned}\end{align} \]</div> +<p>where</p> +<div class="math notranslate nohighlight" id="equation-uv"> +<span class="eqno">(2)<a class="headerlink" href="#equation-uv" title="Permalink to this equation">¶</a></span>\[ \begin{align}\begin{aligned}U = X_{in} - X_{origin}\\V = Y_{in} - Y_{origin}\end{aligned}\end{align} \]</div> +<p>and <span class="math notranslate nohighlight">\(u_{i,j}\)</span> and <span class="math notranslate nohighlight">\(v_{i,j}\)</span> are coefficients that make up +the polynomial.</p> +<p>The final coordinates are determined as</p> +<div class="math notranslate nohighlight" id="equation-xy-out"> +<span class="eqno">(3)<a class="headerlink" href="#equation-xy-out" title="Permalink to this equation">¶</a></span>\[ \begin{align}\begin{aligned}X_{out} = X_{in} + \Delta X\\Y_{out} = Y_{in} + \Delta Y\end{aligned}\end{align} \]</div> +<p>The inverse transform is the same as the above but requires a different set of +coefficients.</p> +<p>Evaluation of the complex polynomials are defined by the following equations:</p> +<div class="math notranslate nohighlight" id="equation-complex-poly"> +<span class="eqno">(4)<a class="headerlink" href="#equation-complex-poly" title="Permalink to this equation">¶</a></span>\[\Delta X + i \Delta Y = \sum_{j=1}^n (c_{2j-1} + i c_{2j}) (U + i V)^j\]</div> +<p>Where <span class="math notranslate nohighlight">\(n\)</span> is the degree of the polynomial. <span class="math notranslate nohighlight">\(U\)</span> and <span class="math notranslate nohighlight">\(V\)</span> are +defined as in <a class="reference internal" href="#equation-uv">(2)</a> and the resulting coordinates are again determined +by <a class="reference internal" href="#equation-xy-out">(3)</a>.</p> +<section id="examples"> +<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2> +<p>Mapping between Danish TC32 and ETRS89/UTM zone 32 using polynomials in real +number space:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=horner ++ellps=intl ++range=500000 ++fwd_origin=877605.269066,6125810.306769 ++inv_origin=877605.760036,6125811.281773 ++deg=4 ++fwd_v=6.1258112678e+06,9.9999971567e-01,1.5372750011e-10,5.9300860915e-15,2.2609497633e-19,4.3188227445e-05,2.8225130416e-10,7.8740007114e-16,-1.7453997279e-19,1.6877465415e-10,-1.1234649773e-14,-1.7042333358e-18,-7.9303467953e-15,-5.2906832535e-19,3.9984284847e-19 ++fwd_u=8.7760574982e+05,9.9999752475e-01,2.8817299305e-10,5.5641310680e-15,-1.5544700949e-18,-4.1357045890e-05,4.2106213519e-11,2.8525551629e-14,-1.9107771273e-18,3.3615590093e-10,2.4380247154e-14,-2.0241230315e-18,1.2429019719e-15,5.3886155968e-19,-1.0167505000e-18 ++inv_v=6.1258103208e+06,1.0000002826e+00,-1.5372762184e-10,-5.9304261011e-15,-2.2612705361e-19,-4.3188331419e-05,-2.8225549995e-10,-7.8529116371e-16,1.7476576773e-19,-1.6875687989e-10,1.1236475299e-14,1.7042518057e-18,7.9300735257e-15,5.2881862699e-19,-3.9990736798e-19 ++inv_u=8.7760527928e+05,1.0000024735e+00,-2.8817540032e-10,-5.5627059451e-15,1.5543637570e-18,4.1357152105e-05,-4.2114813612e-11,-2.8523713454e-14,1.9109017837e-18,-3.3616407783e-10,-2.4382678126e-14,2.0245020199e-18,-1.2441377565e-15,-5.3885232238e-19,1.0167203661e-18 +</pre></div> +</div> +<p>Mapping between Danish System Storebælt and ETRS89/UTM zone 32 using complex +polynomials:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=horner ++ellps=intl ++range=500000 ++fwd_origin=4.94690026817276e+05,6.13342113183056e+06 ++inv_origin=6.19480258923588e+05,6.13258568148837e+06 ++deg=3 ++fwd_c=6.13258562111350e+06,6.19480105709997e+05,9.99378966275206e-01,-2.82153291753490e-02,-2.27089979140026e-10,-1.77019590701470e-09,1.08522286274070e-14,2.11430298751604e-15 ++inv_c=6.13342118787027e+06,4.94690181709311e+05,9.99824464710368e-01,2.82279070814774e-02,7.66123542220864e-11,1.78425334628927e-09,-1.05584823306400e-14,-3.32554258683744e-15 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<p>Setting up Horner polynomials requires many coefficients being explicitly +written, even for polynomials of low degree. For this reason it is recommended +to store the polynomial definitions in an <a class="reference internal" href="../../resource_files.html#init-files"><span class="std std-ref">init file</span></a> for +easier writing and reuse.</p> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<p>Below is a list of required parameters that can be set for the Horner polynomial +transformation. As stated above, the transformation takes to forms, either using +real or complex polynomials. These are divided into separate sections below. +Parameters from the two sections are mutually exclusive, that is parameters +describing real and complex polynomials can’t be mixed.</p> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-deg"> +<span class="sig-name descname"><span class="pre">+deg</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-deg" title="Permalink to this definition">¶</a></dt> +<dd><p>Degree of polynomial</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-fwd_origin"> +<span id="cmdoption-arg-fwd-origin"></span><span class="sig-name descname"><span class="pre">+fwd_origin</span></span><span class="sig-prename descclassname"><span class="pre">=<northing,easting></span></span><a class="headerlink" href="#cmdoption-arg-fwd_origin" title="Permalink to this definition">¶</a></dt> +<dd><p>Coordinate of origin for the forward mapping</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-inv_origin"> +<span id="cmdoption-arg-inv-origin"></span><span class="sig-name descname"><span class="pre">+inv_origin</span></span><span class="sig-prename descclassname"><span class="pre">=<northing,easting></span></span><a class="headerlink" href="#cmdoption-arg-inv_origin" title="Permalink to this definition">¶</a></dt> +<dd><p>Coordinate of origin for the inverse mapping</p> +</dd></dl> + +<section id="real-polynomials"> +<h4>Real polynomials<a class="headerlink" href="#real-polynomials" title="Permalink to this headline">¶</a></h4> +<p>The following parameters has to be set if the transformation consists of +polynomials in real space. Each parameter takes a comma-separated list of +coefficients. The number of coefficients is governed by the degree, <span class="math notranslate nohighlight">\(d\)</span>, +of the polynomial:</p> +<div class="math notranslate nohighlight"> +\[N = \frac{(d + 1)(d + 2)}{2}\]</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-fwd_u"> +<span id="cmdoption-arg-fwd-u"></span><span class="sig-name descname"><span class="pre">+fwd_u</span></span><span class="sig-prename descclassname"><span class="pre">=<u_11,u_12,...,u_ij,..,u_mn></span></span><a class="headerlink" href="#cmdoption-arg-fwd_u" title="Permalink to this definition">¶</a></dt> +<dd><p>Coefficients for the forward transformation i.e. latitude to northing +as described in <a class="reference internal" href="#equation-real-poly">(1)</a>.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-fwd_v"> +<span id="cmdoption-arg-fwd-v"></span><span class="sig-name descname"><span class="pre">+fwd_v</span></span><span class="sig-prename descclassname"><span class="pre">=<v_11,v_12,...,v_ij,..,v_mn></span></span><a class="headerlink" href="#cmdoption-arg-fwd_v" title="Permalink to this definition">¶</a></dt> +<dd><p>Coefficients for the forward transformation i.e. longitude to easting +as described in <a class="reference internal" href="#equation-real-poly">(1)</a>.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-inv_u"> +<span id="cmdoption-arg-inv-u"></span><span class="sig-name descname"><span class="pre">+inv_u</span></span><span class="sig-prename descclassname"><span class="pre">=<u_11,u_12,...,u_ij,..,u_mn></span></span><a class="headerlink" href="#cmdoption-arg-inv_u" title="Permalink to this definition">¶</a></dt> +<dd><p>Coefficients for the inverse transformation i.e. latitude to northing +as described in <a class="reference internal" href="#equation-real-poly">(1)</a>.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-inv_v"> +<span id="cmdoption-arg-inv-v"></span><span class="sig-name descname"><span class="pre">+inv_v</span></span><span class="sig-prename descclassname"><span class="pre">=<v_11,v_12,...,v_ij,..,v_mn></span></span><a class="headerlink" href="#cmdoption-arg-inv_v" title="Permalink to this definition">¶</a></dt> +<dd><p>Coefficients for the inverse transformation i.e. longitude to easting +as described in <a class="reference internal" href="#equation-real-poly">(1)</a>.</p> +</dd></dl> + +</section> +<section id="complex-polynomials"> +<h4>Complex polynomials<a class="headerlink" href="#complex-polynomials" title="Permalink to this headline">¶</a></h4> +<p>The following parameters has to be set if the transformation consists of +polynomials in complex space. Each parameter takes a comma-separated list of +coefficients. The number of coefficients is governed by the degree, <span class="math notranslate nohighlight">\(d\)</span>, +of the polynomial:</p> +<div class="math notranslate nohighlight"> +\[N = 2d + 2\]</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-fwd_c"> +<span id="cmdoption-arg-fwd-c"></span><span class="sig-name descname"><span class="pre">+fwd_c</span></span><span class="sig-prename descclassname"><span class="pre">=<c_1,c_2,...,c_N></span></span><a class="headerlink" href="#cmdoption-arg-fwd_c" title="Permalink to this definition">¶</a></dt> +<dd><p>Coefficients for the complex forward transformation +as described in <a class="reference internal" href="#equation-complex-poly">(4)</a>.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-inv_c"> +<span id="cmdoption-arg-inv-c"></span><span class="sig-name descname"><span class="pre">+inv_c</span></span><span class="sig-prename descclassname"><span class="pre">=<c_1,c_2,...,c_N></span></span><a class="headerlink" href="#cmdoption-arg-inv_c" title="Permalink to this definition">¶</a></dt> +<dd><p>Coefficients for the complex inverse transformation +as described in <a class="reference internal" href="#equation-complex-poly">(4)</a>.</p> +</dd></dl> + +</section> +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-range"> +<span class="sig-name descname"><span class="pre">+range</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-range" title="Permalink to this definition">¶</a></dt> +<dd><p>Radius of the region of validity.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-uneg"> +<span class="sig-name descname"><span class="pre">+uneg</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-uneg" title="Permalink to this definition">¶</a></dt> +<dd><p>Express latitude as southing. Only applies for complex polynomials.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-vneg"> +<span class="sig-name descname"><span class="pre">+vneg</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-vneg" title="Permalink to this definition">¶</a></dt> +<dd><p>Express longitude as westing. Only applies for complex polynomials.</p> +</dd></dl> + +</section> +</section> +<section id="further-reading"> +<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2> +<ol class="arabic simple"> +<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Horner%27s_method">Wikipedia</a></p></li> +</ol> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="helmert.html" class="btn btn-neutral float-left" title="Helmert transform" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="molodensky.html" class="btn btn-neutral float-right" title="Molodensky transform" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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href="defmodel.html">Multi-component time-based deformation model</a></li> +<li class="toctree-l1"><a class="reference internal" href="deformation.html">Kinematic datum shifting utilizing a deformation model</a></li> +<li class="toctree-l1"><a class="reference internal" href="geogoffset.html">Geographic offsets</a></li> +<li class="toctree-l1"><a class="reference internal" href="helmert.html">Helmert transform</a></li> +<li class="toctree-l1"><a class="reference internal" href="horner.html">Horner polynomial evaluation</a></li> +<li class="toctree-l1"><a class="reference internal" href="molodensky.html">Molodensky transform</a></li> +<li class="toctree-l1"><a class="reference internal" href="molobadekas.html">Molodensky-Badekas transform</a></li> +<li class="toctree-l1"><a class="reference internal" href="hgridshift.html">Horizontal grid shift</a></li> +<li class="toctree-l1"><a class="reference internal" href="tinshift.html">Triangulated Irregular Network based transformation</a></li> 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<li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Transformations</a> »</li> + <li>Molodensky-Badekas transform</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/molobadekas.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="molodensky.html" class="btn btn-neutral float-left" title="Molodensky transform" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="hgridshift.html" class="btn btn-neutral float-right" title="Horizontal grid shift" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="molodensky-badekas-transform"> +<span id="molobadekas"></span><h1>Molodensky-Badekas transform<a class="headerlink" href="#molodensky-badekas-transform" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 6.0.0.</span></p> +</div> +<p>The Molodensky-Badekas transformation changes coordinates from one reference frame to +another by means of a 10-parameter shift.</p> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>It should not be confused with the <a class="reference internal" href="molodensky.html#molodensky"><span class="std std-ref">Molodensky transform</span></a> transform which +operates directly in the geodetic coordinates. Molodensky-Badekas can rather +be seen as a variation of <a class="reference internal" href="helmert.html#helmert"><span class="std std-ref">Helmert transform</span></a></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>molobadekas</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Cartesian coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Cartesian coordinates</p></td> +</tr> +</tbody> +</table> +<p>The Molodensky-Badekas transformation is a variation of the <a class="reference internal" href="helmert.html#helmert"><span class="std std-ref">Helmert transform</span></a> where +the rotational terms are not directly applied to the ECEF coordinates, but on +cartesian coordinates relative to a reference point (usually close to Earth surface, +and to the area of use of the transformation). When <code class="docutils literal notranslate"><span class="pre">px</span></code> = <code class="docutils literal notranslate"><span class="pre">py</span></code> = <code class="docutils literal notranslate"><span class="pre">pz</span></code> = 0, +this is equivalent to a 7-parameter Helmert transformation.</p> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>Transforming coordinates from La Canoa to REGVEN:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=molobadekas convention=coordinate_frame + x=-270.933 y=115.599 z=-360.226 rx=-5.266 ry=-1.238 rz=2.381 + s=-5.109 px=2464351.59 py=-5783466.61 pz=974809.81 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>All parameters (except convention) are optional but at least one should be +used, otherwise the operation will return the coordinates unchanged.</p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-convention"> +<span class="sig-name descname"><span class="pre">+convention</span></span><span class="sig-prename descclassname"><span class="pre">=coordinate_frame/position_vector</span></span><a class="headerlink" href="#cmdoption-arg-convention" title="Permalink to this definition">¶</a></dt> +<dd><p>Indicates the convention to express the rotational terms when a 3D-Helmert / +7-parameter more transform is involved.</p> +<p>The two conventions are equally popular and a frequent source of confusion. +The coordinate frame convention is also described as an clockwise +rotation of the coordinate frame. It corresponds to EPSG method code +1034 (in the geocentric domain) or 9636 (in the geographic domain) +The position vector convention is also described as an anticlockwise +(counter-clockwise) rotation of the coordinate frame. +It corresponds to as EPSG method code 1061 (in the geocentric domain) or +1063 (in the geographic domain).</p> +<p>The result obtained with parameters specified in a given convention +can be obtained in the other convention by negating the rotational parameters +(<code class="docutils literal notranslate"><span class="pre">rx</span></code>, <code class="docutils literal notranslate"><span class="pre">ry</span></code>, <code class="docutils literal notranslate"><span class="pre">rz</span></code>)</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-x"> +<span class="sig-name descname"><span class="pre">+x</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation of the x-axis given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-y"> +<span class="sig-name descname"><span class="pre">+y</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation of the y-axis given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-z"> +<span class="sig-name descname"><span class="pre">+z</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-z" title="Permalink to this definition">¶</a></dt> +<dd><p>Translation of the z-axis given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-s"> +<span class="sig-name descname"><span class="pre">+s</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-s" title="Permalink to this definition">¶</a></dt> +<dd><p>Scale factor given in ppm.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-rx"> +<span class="sig-name descname"><span class="pre">+rx</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-rx" title="Permalink to this definition">¶</a></dt> +<dd><p>X-axis rotation given arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ry"> +<span class="sig-name descname"><span class="pre">+ry</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ry" title="Permalink to this definition">¶</a></dt> +<dd><p>Y-axis rotation given in arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-rz"> +<span class="sig-name descname"><span class="pre">+rz</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-rz" title="Permalink to this definition">¶</a></dt> +<dd><p>Z-axis rotation given in arc seconds.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-px"> +<span class="sig-name descname"><span class="pre">+px</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-px" title="Permalink to this definition">¶</a></dt> +<dd><p>Coordinate along the x-axis of the reference point given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-py"> +<span class="sig-name descname"><span class="pre">+py</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-py" title="Permalink to this definition">¶</a></dt> +<dd><p>Coordinate along the y-axis of the reference point given in meters.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-pz"> +<span class="sig-name descname"><span class="pre">+pz</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-pz" title="Permalink to this definition">¶</a></dt> +<dd><p>Coordinate along the z-axis of the reference point given in meters.</p> +</dd></dl> + +</section> +<section id="mathematical-description"> +<h2>Mathematical description<a class="headerlink" href="#mathematical-description" title="Permalink to this headline">¶</a></h2> +<p>In the <em>Position Vector</em> convention, we define <span class="math notranslate nohighlight">\(R_x = radians \left( rx \right)\)</span>, +<span class="math notranslate nohighlight">\(R_z = radians \left( ry \right)\)</span> and <span class="math notranslate nohighlight">\(R_z = radians \left( rz \right)\)</span></p> +<p>In the <em>Coordinate Frame</em> convention, <span class="math notranslate nohighlight">\(R_x = - radians \left( rx \right)\)</span>, +<span class="math notranslate nohighlight">\(R_z = - radians \left( ry \right)\)</span> and <span class="math notranslate nohighlight">\(R_z = - radians \left( rz \right)\)</span></p> +<div class="math notranslate nohighlight" id="equation-10param"> +<span class="eqno">(1)<a class="headerlink" href="#equation-10param" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align} + \begin{bmatrix} + X \\ + Y \\ + Z \\ + \end{bmatrix}^{output} = + \begin{bmatrix} + T_x + P_x\\ + T_y + P_y\\ + T_z + P_z\\ + \end{bmatrix} + + \left(1 + s \times 10^{-6}\right) + \begin{bmatrix} + 1 & -R_z & R_y \\ + Rz & 1 & -R_x \\ + -Ry & R_x & 1 \\ + \end{bmatrix} + \begin{bmatrix} + X^{input} - P_x\\ + Y^{input} - P_y\\ + Z^{input} - P_z\\ + \end{bmatrix} +\end{align}\end{split}\]</div> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="molodensky.html" class="btn btn-neutral float-left" title="Molodensky transform" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="hgridshift.html" class="btn btn-neutral float-right" title="Horizontal grid shift" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by 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class="headerlink" href="#molodensky-transform" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>The Molodensky transformation resembles a <a class="reference internal" href="helmert.html#helmert"><span class="std std-ref">Helmert transform</span></a> with zero +rotations and a scale of unity, but converts directly from geodetic coordinates to +geodetic coordinates, without the intermediate shifts to and from cartesian +geocentric coordinates, associated with the Helmert transformation. +The Molodensky transformation is simple to implement and to parametrize, requiring +only the 3 shifts between the input and output frame, and the corresponding +differences between the semimajor axes and flattening parameters of the reference +ellipsoids. Due to its algorithmic simplicity, it was popular prior to the +ubiquity of digital computers. Today, it is mostly interesting for historical +reasons, but nevertheless indispensable due to the large amount of data that has +already been transformed that way <span id="id1">[<a class="reference internal" href="../../zreferences.html#id13" title="Evers, K. and Knudsen, T. Transformation pipelines for PROJ.4. In FIG Working Week 2017 Proceedings. Helsinki, Finland, 2017. URL: http://www.fig.net/resources/proceedings/fig_proceedings/fig2017/papers/iss6b/ISS6B_evers_knudsen_9156.pdf.">EversKnudsen2017</a>]</span>.</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 27%" /> +<col style="width: 73%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>molodensky</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical)</p></td> +</tr> +<tr class="row-even"><td><p><strong>output type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical)</p></td> +</tr> +</tbody> +</table> +<p>The Molodensky transform can be used to perform a datum shift from coordinate +<span class="math notranslate nohighlight">\((\phi_1, \lambda_1, h_1)\)</span> to <span class="math notranslate nohighlight">\((\phi_2, \lambda_2, h_2)\)</span> where the two +coordinates are referenced to different ellipsoids. This is based on three +assumptions:</p> +<blockquote> +<div><ol class="arabic simple"> +<li><p>The cartesian axes, <span class="math notranslate nohighlight">\(X, Y, Z\)</span>, of the two ellipsoids are parallel.</p></li> +<li><p>The offset, <span class="math notranslate nohighlight">\(\delta X, \delta Y, \delta Z\)</span>, between the two ellipsoid +are known.</p></li> +<li><p>The characteristics of the two ellipsoids, expressed as the difference in +semimajor axis (<span class="math notranslate nohighlight">\(\delta a\)</span>) and flattening (<span class="math notranslate nohighlight">\(\delta f\)</span>), are known.</p></li> +</ol> +</div></blockquote> +<p>The Molodensky transform is mostly used for transforming between old systems +dating back to the time before computers. The advantage of the Molodensky transform +is that it is fairly simple to compute by hand. The ease of computation come at the +cost of limited accuracy.</p> +<p>A derivation of the mathematical formulas for the Molodensky transform can be found +in <span id="id2">[<a class="reference internal" href="../../zreferences.html#id8" title="Deakin, R. E. The standard and abridged Molodensky coordinate transformation formulae. Technical Report, Department of Mathematical and Geospatial Sciences, RMIT University, Melborne, Australia, 2004. URL: http://www.mygeodesy.id.au/documents/Molodensky%20V2.pdf.">Deakin2004</a>]</span>.</p> +<section id="examples"> +<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2> +<p>The abridged Molodensky:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=molodensky a=6378160 rf=298.25 da=-23 df=-8.120449e-8 dx=-134 dy=-48 dz=149 abridged +</pre></div> +</div> +<p>The same transformation using the standard Molodensky:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>proj=molodensky a=6378160 rf=298.25 da=-23 df=-8.120449e-8 dx=-134 dy=-48 dz=149 +</pre></div> +</div> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-da"> +<span class="sig-name descname"><span class="pre">+da</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-da" title="Permalink to this definition">¶</a></dt> +<dd><p>Difference in semimajor axis of the defining ellipsoids.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-df"> +<span class="sig-name descname"><span class="pre">+df</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-df" title="Permalink to this definition">¶</a></dt> +<dd><p>Difference in flattening of the defining ellipsoids.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dx"> +<span class="sig-name descname"><span class="pre">+dx</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dx" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset of the X-axes of the defining ellipsoids.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dy"> +<span class="sig-name descname"><span class="pre">+dy</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dy" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset of the Y-axes of the defining ellipsoids.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-dz"> +<span class="sig-name descname"><span class="pre">+dz</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-dz" title="Permalink to this definition">¶</a></dt> +<dd><p>Offset of the Z-axes of the defining ellipsoids.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-abridged"> +<span class="sig-name descname"><span class="pre">+abridged</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-arg-abridged" title="Permalink to this definition">¶</a></dt> +<dd><p>Use the abridged version of the Molodensky transform.</p> +</dd></dl> + +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="horner.html" class="btn btn-neutral float-left" title="Horner polynomial evaluation" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="molobadekas.html" class="btn btn-neutral float-right" title="Molodensky-Badekas transform" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span 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id="triangulated-irregular-network-based-transformation"> +<span id="tinshift"></span><h1>Triangulated Irregular Network based transformation<a class="headerlink" href="#triangulated-irregular-network-based-transformation" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 7.2.0.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 24%" /> +<col style="width: 76%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>tinshift</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Projected or geographic coordinates (horizontal), meters (vertical)</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected or geographic coordinates (horizontal), meters (vertical)</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D or 3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse</p></td> +</tr> +</tbody> +</table> +<p>The <code class="docutils literal notranslate"><span class="pre">tinshift</span></code> transformation takes one mandatory +argument, <code class="docutils literal notranslate"><span class="pre">file</span></code>, that points to a JSON file, which contains the +triangulation and associated metadata. Input and output coordinates must be +geographic or projected coordinates. +Depending on the content of the JSON file, horizontal, vertical or both +components of the coordinates may be transformed.</p> +<p>The transformation is invertible, with the same computational complexity than +the forward transformation.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-file"> +<span class="sig-name descname"><span class="pre">+file</span></span><span class="sig-prename descclassname"><span class="pre">=<filename></span></span><a class="headerlink" href="#cmdoption-arg-file" title="Permalink to this definition">¶</a></dt> +<dd><p>Filename to the JSON file for the TIN.</p> +</dd></dl> + +</section> +</section> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>Transforming a point with the Finland EPSG:2393 (“KKJ / Finland Uniform +Coordinate System”) projected CRS to EPSG:3067 (“ETRS89 / TM35FIN(E,N)”)</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 3210000.0000 6700000.0000 0 2020 | cct +proj=tinshift +file=./triangulation_kkj.json + +209948.3217 6697187.0009 0.0000 2020 +</pre></div> +</div> +<section id="algorithm"> +<h3>Algorithm<a class="headerlink" href="#algorithm" title="Permalink to this headline">¶</a></h3> +<p>Internally, <code class="docutils literal notranslate"><span class="pre">tinshift</span></code> ingest the whole file into memory. It is considered that +triangulation should be small enough for that.</p> +<p>When a point is transformed, one must find the triangle into which it falls into. +Instead of iterating over all triangles, we build a in-memory quadtree to speed-up +the identification of candidates triangles.</p> +<p>To determine if a point falls into a triangle, one computes its 3 +<a class="reference external" href="https://en.wikipedia.org/wiki/Barycentric_coordinate_system#Conversion_between_barycentric_and_Cartesian_coordinates">barycentric coordinates</a> +from its projected coordinates, <span class="math notranslate nohighlight">\(\lambda_i\)</span> for <span class="math notranslate nohighlight">\(i=1,2,3\)</span>. +They are real values (in the [0,1] range for a point inside the triangle), +giving the weight of each of the 3 vertices of the triangles.</p> +<p>Once those weights are known, interpolating the target horizontal +coordinate is a matter of doing the linear combination of those weights with +the target horizontal coordinates at the 3 vertices of the triangle (<span class="math notranslate nohighlight">\(Xt_i\)</span> and <span class="math notranslate nohighlight">\(Yt_i\)</span>):</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}X_{target} = Xt_1 * \lambda_1 + Xt_2 * \lambda_2 + Xt_3 * \lambda_3\\Y_{target} = Yt_1 * \lambda_1 + Yt_2 * \lambda_2 + Yt_3 * \lambda_3\end{aligned}\end{align} \]</div> +<p>This interpolation is exact at the vertices of the triangulation, and has linear properties +inside each triangle. It is completely equivalent to other formulations of +triangular interpolation, such as</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}X_{target} = A + X_{source} * B + Y_{source} * C\\Y_{target} = D + X_{source} * E + Y_{source} * F\end{aligned}\end{align} \]</div> +<p>where the A, B, C, D, E, F constants (for a given triangle) are found by solving +the 2 systems of 3 linear equations, constraint by the source and target coordinate pairs +of the 3 vertices of the triangle:</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}Xt_i = A + Xs_i * B + Ys_i * C\\Yt_i = D + Xs_i * E + Ys_i * F\end{aligned}\end{align} \]</div> +<p>Similarly for a vertical coordinate transformation, where <span class="math notranslate nohighlight">\(Zoff_i\)</span> is the vertical +offset at each vertex of the triangle:</p> +<div class="math notranslate nohighlight"> +\[Z_{target} = Z_{source} + Zoff_1 * \lambda_1 + Zoff_2 * \lambda_2 + Zoff_3 * \lambda_3\]</div> +</section> +<section id="constraints-on-the-triangulation"> +<h3>Constraints on the triangulation<a class="headerlink" href="#constraints-on-the-triangulation" title="Permalink to this headline">¶</a></h3> +<p>No check is done on the consistence of the triangulation. It is highly +recommended that triangles do not overlap each other (when considering the +source coordinates or the forward transformation, or the target coordinates for +the inverse transformation), otherwise which triangle will be selected is +unspecified. Besides that, the triangulation does not need to have particular +properties (like being a Delaunay triangulation)</p> +</section> +<section id="file-format"> +<h3>File format<a class="headerlink" href="#file-format" title="Permalink to this headline">¶</a></h3> +<p>The triangulation is stored in a text-based format, using JSON as a serialization.</p> +<p>Below a minimal example, from the KKJ to ETRS89 transformation, with just a +single triangle:</p> +<div class="highlight-json notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"file_type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"triangulation_file"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"format_version"</span><span class="p">:</span><span class="w"> </span><span class="s2">"1.0"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"name"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Name"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"version"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Version"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"publication_date"</span><span class="p">:</span><span class="w"> </span><span class="s2">"2018-07-01T00:00:00Z"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"license"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Creative Commons Attribution 4.0 International"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"description"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Test triangulation"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"authority"</span><span class="p">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"name"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Authority name"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"url"</span><span class="p">:</span><span class="w"> </span><span class="s2">"http://example.com"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"address"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Adress"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"email"</span><span class="p">:</span><span class="w"> </span><span class="s2">"test@example.com"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="nt">"links"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://example.com/about.html"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"about"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"text/html"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">"About"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://example.com/download"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"source"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"application/zip"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Authoritative source"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://creativecommons.org/licenses/by/4.0/"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"license"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"text/html"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Creative Commons Attribution 4.0 International license"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://example.com/metadata.xml"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"metadata"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"application/xml"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">" ISO 19115 XML encoded metadata regarding the deformation model"</span><span class="w"></span> +<span class="w"> </span><span class="p">}</span><span class="w"></span> +<span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"transformed_components"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="s2">"horizontal"</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"vertices_columns"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="s2">"source_x"</span><span class="p">,</span><span class="w"> </span><span class="s2">"source_y"</span><span class="p">,</span><span class="w"> </span><span class="s2">"target_x"</span><span class="p">,</span><span class="w"> </span><span class="s2">"target_y"</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"triangles_columns"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="s2">"idx_vertex1"</span><span class="p">,</span><span class="w"> </span><span class="s2">"idx_vertex2"</span><span class="p">,</span><span class="w"> </span><span class="s2">"idx_vertex3"</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"vertices"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">49</span><span class="p">,</span><span class="mf">2.1</span><span class="p">,</span><span class="mf">49.1</span><span class="p">],</span><span class="w"> </span><span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="mf">3.1</span><span class="p">,</span><span class="mf">50.1</span><span class="p">],</span><span class="w"> </span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">50</span><span class="p">,</span><span class="w"> </span><span class="mf">2.1</span><span class="p">,</span><span class="mf">50.1</span><span class="p">]</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"triangles"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">]</span><span class="w"></span> +<span class="p">}</span><span class="w"></span> +</pre></div> +</div> +<p>So after the generic metadata, we define the input and output CRS (informative +only), and that the transformation affects horizontal components of +coordinates. We name the columns of the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> and <code class="docutils literal notranslate"><span class="pre">triangles</span></code> arrays. +We defined the source and target coordinates of each vertex, and define a +triangle by referring to the index of its vertices in the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> array.</p> +<p>More formally, the specific items for the triangulation file are:</p> +<dl class="simple"> +<dt>input_crs</dt><dd><p>String identifying the CRS of source coordinates +in the vertices. Typically <code class="docutils literal notranslate"><span class="pre">EPSG:XXXX</span></code>. If the transformation is for vertical +component, this should be the code for a compound CRS (can be EPSG:XXXX+YYYY +where XXXX is the code of the horizontal CRS and YYYY the code of the vertical CRS). +For example, for the KKJ->ETRS89 transformation, this is EPSG:2393 +(<code class="docutils literal notranslate"><span class="pre">KKJ</span> <span class="pre">/</span> <span class="pre">Finland</span> <span class="pre">Uniform</span> <span class="pre">Coordinate</span> <span class="pre">System</span></code>). The input coordinates are assumed +to be passed in the “normalized for visualisation” / “GIS friendly” order, +that is longitude, latitude for geographic coordinates and +easting, northing for projected coordinates.</p> +</dd> +<dt>output_crs</dt><dd><p>String identifying the CRS of target coordinates in the vertices. +Typically <code class="docutils literal notranslate"><span class="pre">EPSG:XXXX</span></code>. If the transformation is for vertical component, +this should be the code for a compound CRS (can be EPSG:XXXX+YYYY where +XXXX is the code of the horizontal CRS and YYYY the code of the vertical CRS). +For example, for the KKJ->ETRS89 transformation, this is EPSG:3067 +("ETRS89 / TM35FIN(E,N)"). The output coordinates will be returned in +the “normalized for visualisation” / “GIS friendly” order, +that is longitude, latitude for geographic coordinates and +easting, northing for projected coordinates.</p> +</dd> +<dt>transformed_components</dt><dd><p>Array which may contain one or two strings: “horizontal” when horizontal +components of the coordinates are transformed and/or “vertical” when the +vertical component is transformed.</p> +</dd> +<dt>fallback_strategy</dt><dd><p>String identifying how to treat points that do not fall into any of the +specified triangles. This item is available for <code class="docutils literal notranslate"><span class="pre">format_version</span></code> >= 1.1. +Possible values are <code class="docutils literal notranslate"><span class="pre">none</span></code>, <code class="docutils literal notranslate"><span class="pre">nearest_side</span></code> and <code class="docutils literal notranslate"><span class="pre">nearest_centroid</span></code>. The +default is <code class="docutils literal notranslate"><span class="pre">none</span></code> and signifies, that points that fall outside the +specified triangles are not transformed. This is also the behaviour for +<code class="docutils literal notranslate"><span class="pre">format_version</span></code> before 1.1. If <code class="docutils literal notranslate"><span class="pre">fallback_strategy</span></code> is set to +<code class="docutils literal notranslate"><span class="pre">nearest_side</span></code>, then points that do not fall into any triangle are +transformed according to the triangle closest to them by euclidean distance. +If <code class="docutils literal notranslate"><span class="pre">fallback_strategy</span></code> is set to <code class="docutils literal notranslate"><span class="pre">nearest_centroid</span></code>, then points that do +not fall into any triangle are transformed according to the triangle with the +closest centroid (intersection of its medians).</p> +</dd> +<dt>vertices_columns</dt><dd><p>Specify the name of the columns of the rows in the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> +array. There must be exactly as many elements in <code class="docutils literal notranslate"><span class="pre">vertices_columns</span></code> as in a +row of <code class="docutils literal notranslate"><span class="pre">vertices</span></code>. The following names have a special meaning: <code class="docutils literal notranslate"><span class="pre">source_x</span></code>, +<code class="docutils literal notranslate"><span class="pre">source_y</span></code>, <code class="docutils literal notranslate"><span class="pre">target_x</span></code>, <code class="docutils literal notranslate"><span class="pre">target_y</span></code>, <code class="docutils literal notranslate"><span class="pre">source_z</span></code>, <code class="docutils literal notranslate"><span class="pre">target_z</span></code> and +<code class="docutils literal notranslate"><span class="pre">offset_z</span></code>. <code class="docutils literal notranslate"><span class="pre">source_x</span></code> and <code class="docutils literal notranslate"><span class="pre">source_y</span></code> are compulsory. +<code class="docutils literal notranslate"><span class="pre">source_x</span></code> is for the source longitude (in degree) or easting. +<code class="docutils literal notranslate"><span class="pre">source_y</span></code> is for the source latitude (in degree) or northing. +<code class="docutils literal notranslate"><span class="pre">target_x</span></code> and <code class="docutils literal notranslate"><span class="pre">target_y</span></code> are compulsory when <code class="docutils literal notranslate"><span class="pre">horizontal</span></code> is specified +in <code class="docutils literal notranslate"><span class="pre">transformed_components</span></code>. (<code class="docutils literal notranslate"><span class="pre">source_z</span></code> and <code class="docutils literal notranslate"><span class="pre">target_z</span></code>) or +<code class="docutils literal notranslate"><span class="pre">offset_z</span></code> are compulsory when <code class="docutils literal notranslate"><span class="pre">vertical</span></code> is specified in <code class="docutils literal notranslate"><span class="pre">transformed_components</span></code></p> +</dd> +<dt>triangles_columns</dt><dd><p>Specify the name of the columns of the rows in the +<code class="docutils literal notranslate"><span class="pre">triangles</span></code> array. There must be exactly as many elements in <code class="docutils literal notranslate"><span class="pre">triangles_columns</span></code> +as in a row of <code class="docutils literal notranslate"><span class="pre">triangles</span></code>. The following names have a special meaning: +<code class="docutils literal notranslate"><span class="pre">idx_vertex1</span></code>, <code class="docutils literal notranslate"><span class="pre">idx_vertex2</span></code>, <code class="docutils literal notranslate"><span class="pre">idx_vertex3</span></code>. They are compulsory.</p> +</dd> +<dt>vertices</dt><dd><p>An array whose items are themselves arrays with as many columns as +described in <code class="docutils literal notranslate"><span class="pre">vertices_columns</span></code>.</p> +</dd> +<dt>triangles</dt><dd><p>An array whose items are themselves arrays with as many columns as +described in <code class="docutils literal notranslate"><span class="pre">triangles_columns</span></code>. +The value of the <code class="docutils literal notranslate"><span class="pre">idx_vertexN</span></code> columns must be indices +(between 0 and len(<code class="docutils literal notranslate"><span class="pre">vertices</span></code>-1) of items of the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> array.</p> +</dd> +</dl> +<p>A <a class="reference external" href="https://proj.org/schemas/triangulation.schema.json">JSON schema</a> is available +for this file format.</p> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="hgridshift.html" class="btn btn-neutral float-left" title="Horizontal grid shift" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vgridshift.html" class="btn btn-neutral float-right" title="Vertical grid shift" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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id="vertical-grid-shift"> +<span id="vgridshift"></span><h1>Vertical grid shift<a class="headerlink" href="#vertical-grid-shift" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.0.0.</span></p> +</div> +<p>Change Vertical datum change by grid shift</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>vgridshift</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D and 4D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical), +decimalyear (temporal)</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Geodetic coordinates (horizontal), meters (vertical), +decimalyear (temporal)</p></td> +</tr> +</tbody> +</table> +<p>The vertical grid shift is done by offsetting the vertical input coordinates by +a specific amount determined by the loaded grids. The simplest use case of the +horizontal grid shift is applying a single grid. Here we change the vertical +reference from the ellipsoid to the global geoid model, EGM96:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=vgridshift +grids=egm96_15.gtx +</pre></div> +</div> +<p>More than one grid can be loaded at the same time, for instance in the case where +a better geoid model than the global is available for a certain area. Here the +gridshift is set up so that the local DVR90 geoid model takes precedence over +the global model:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=vgridshift +grids=@dvr90.gtx,egm96_15.gtx +</pre></div> +</div> +<p>The <code class="docutils literal notranslate"><span class="pre">@</span></code> in the above example states that the grid is optional, in case the grid +is not found in the PROJ search path. The list of grids is prioritized so that +grids in the start of the list takes precedence over the grids in the back of the +list.</p> +<p>PROJ supports the GTX file format for vertical grid corrections. Details +about all the format can be found in the GDAL documentation. GDAL both reads and +writes the format. Using GDAL for construction of new grids is recommended.</p> +<section id="temporal-gridshifting"> +<h2>Temporal gridshifting<a class="headerlink" href="#temporal-gridshifting" title="Permalink to this headline">¶</a></h2> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<p>By initializing the vertical gridshift operation with a central epoch, it can be +used as a step function applying the grid offsets only if a coordinate is +transformed from an epoch before grids central epoch to an epoch after. This is +handy in transformations where it is necessary to handle deformations caused by +seismic activity.</p> +<p>The central epoch of the grid is controlled with <a class="reference internal" href="#cmdoption-arg-t_epoch"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_epoch</span></code></a> and the final +epoch of the coordinate is set with <a class="reference internal" href="#cmdoption-arg-t_final"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_final</span></code></a>. The observation epoch of +the coordinate is part of the coordinate tuple.</p> +<p>Suppose we want to model the deformation of the 2008 earthquake in Iceland in +a transformation of data from 2005 to 2009:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>echo 63.992 -21.014 10.0 2005.0 | cct +proj=vgridshift +grids=iceland2008.gtx +t_epoch=2008.4071 +t_final=2009.0 +63.992 -21.014 10.11 2005.0 +</pre></div> +</div> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The timestamp of the resulting coordinate is still 2005.0. The observation +time is always kept unchanged as it would otherwise be impossible to do the +inverse transformation.</p> +</div> +<p>Temporal gridshifting is especially powerful in transformation pipelines where +several gridshifts can be chained together, effectively acting as a series of +step functions that can be applied to a coordinate that is propagated through +time. In the following example we establish a pipeline that allows transformation +of coordinates from any given epoch up until the current date, applying only +those gridshifts that have central epochs between the observation epoch and +the final epoch:</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline +t_final=now ++step +proj=vgridshift +grids=earthquake_1.gtx +t_epoch=2010.421 ++step +proj=vgridshift +grids=earthquake_2.gtx +t_epoch=2013.853 ++step +proj=vgridshift +grids=earthquake_3.gtx +t_epoch=2017.713 +</pre></div> +</div> +<div class="admonition note"> +<p class="admonition-title">Note</p> +<p>The special epoch <em>now</em> is used when specifying the final epoch with +<a class="reference internal" href="#cmdoption-arg-t_final"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_final</span></code></a>. This results in coordinates being transformed to the +current date. Additionally, <a class="reference internal" href="#cmdoption-arg-t_final"><code class="xref std std-option docutils literal notranslate"><span class="pre">+t_final</span></code></a> is used as a +<a class="reference internal" href="../pipeline.html#global-pipeline-parameter"><span class="std std-ref">global pipeline parameter</span></a>, which means +that it is applied to all the steps in the pipeline.</p> +</div> +<p>In the above transformation, a coordinate with observation epoch 2009.32 would +be subject to all three gridshift steps in the pipeline. A coordinate with +observation epoch 2014.12 would only by offset by the last step in the pipeline.</p> +</section> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-grids"> +<span class="sig-name descname"><span class="pre">+grids</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-grids" title="Permalink to this definition">¶</a></dt> +<dd><p>Comma-separated list of grids to load. If a grid is prefixed by an <cite>@</cite> the +grid is considered optional and PROJ will the not complain if the grid is +not available.</p> +<p>Grids are expected to be in GTX format.</p> +</dd></dl> + +</section> +<section id="optional"> +<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_epoch"> +<span id="cmdoption-arg-t-epoch"></span><span class="sig-name descname"><span class="pre">+t_epoch</span></span><span class="sig-prename descclassname"><span class="pre">=<time></span></span><a class="headerlink" href="#cmdoption-arg-t_epoch" title="Permalink to this definition">¶</a></dt> +<dd><p>Central epoch of the transformation.</p> +</dd></dl> + +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-t_final"> +<span id="cmdoption-arg-t-final"></span><span class="sig-name descname"><span class="pre">+t_final</span></span><span class="sig-prename descclassname"><span class="pre">=<time></span></span><a class="headerlink" href="#cmdoption-arg-t_final" title="Permalink to this definition">¶</a></dt> +<dd><p>Final epoch that the coordinate will be propagated to after transformation. +The special epoch <em>now</em> can be used instead of writing a specific period in +time. When <em>now</em> is used, it is replaced internally with the epoch of the +transformation. This means that the resulting coordinate will be slightly +different if carried out again at a later date.</p> +</dd></dl> + +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.1.0.</span></p> +</div> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-multiplier"> +<span class="sig-name descname"><span class="pre">+multiplier</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-multiplier" title="Permalink to this definition">¶</a></dt> +<dd><p>Specify the multiplier to apply to the grid value in the forward transformation +direction, such that:</p> +<div class="math notranslate nohighlight" id="equation-multiplier-formula"> +<span class="eqno">(1)<a class="headerlink" href="#equation-multiplier-formula" title="Permalink to this equation">¶</a></span>\[Z_{target} = Z_{source} + multiplier \times gridvalue\]</div> +<p>The multiplier can be used to control whether the gridvalue should be added +or subtracted, and if unit conversion must be done (the multiplied gridvalue +must be expressed in metre).</p> +<p>Note that the default is <cite>-1.0</cite> for historical reasons.</p> +</dd></dl> + +<div class="versionadded"> +<p><span class="versionmodified added">New in version 5.2.0.</span></p> +</div> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="tinshift.html" class="btn btn-neutral float-left" title="Triangulated Irregular Network based transformation" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="xyzgridshift.html" class="btn btn-neutral float-right" title="Geocentric grid shift" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="vgridshift.html" class="btn btn-neutral float-left" title="Vertical grid shift" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../pipeline.html" class="btn btn-neutral float-right" title="The pipeline operator" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="geocentric-grid-shift"> +<span id="xyzgridshift"></span><h1>Geocentric grid shift<a class="headerlink" href="#geocentric-grid-shift" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 7.0.0.</span></p> +</div> +<p>Geocentric translation using a grid shift</p> +<table class="docutils align-default"> +<colgroup> +<col style="width: 20%" /> +<col style="width: 80%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>xyzgridshift</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Input type</strong></p></td> +<td><p>Cartesian coordinates</p></td> +</tr> +<tr class="row-even"><td><p><strong>Output type</strong></p></td> +<td><p>Cartesian coordinates</p></td> +</tr> +</tbody> +</table> +<p>Perform a geocentric translation by bilinear interpolation of dx, dy, dz +translation values from a grid. The grid is referenced against either the +2D geographic CRS corresponding to the input (or sometimes output) CRS.</p> +<p>This method is described (in French) in <span id="id1">[<a class="reference internal" href="../../zreferences.html#id26" title="IGN. Grille de parametres de transformation de coordonnees - GR3DF97A - notice d'utilisation. Technical Report, Service de Geodesie et Nivellement, Institut Geographique National, 1997. URL: https://geodesie.ign.fr/contenu/fichiers/documentation/algorithmes/notice/NTG_88.pdf.">NTF_88</a>]</span> +and as EPSG operation method code 9655 in <span id="id2">[<a class="reference internal" href="../../zreferences.html#id17" title="IOGP. Geomatics guidance note 7, part 2: coordinate conversions & transformations including formulas. IOGP Publication 373-7-2, International Association For Oil And Gas Producers, 2018. URL: https://www.iogp.org/bookstore/product/coordinate-conversions-and-transformation-including-formulas/.">IOGP2018</a>]</span> (§2.4.4.1.1 +France geocentric interpolation).</p> +<p>The translation in the grids are added to the input coordinates in the forward direction, +and subtracted in the reverse direction. +By default (if <code class="docutils literal notranslate"><span class="pre">grid_ref=input_crs</span></code>), in the forward direction, the input coordinates +are converted to their geographic equivalent to directly read and interpolate from +the grid. In the reverse direction, an iterative method is used to be able to find +the grid locations to read. +If <code class="docutils literal notranslate"><span class="pre">grid_ref=output_crs</span></code> is used, then the reverse strategy is applied: iterative +method in the forward direction, and direct read in the reverse direction.</p> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>NTF to RGF93 transformation using <code class="file docutils literal notranslate"><span class="pre">gr3df97a.tif</span></code> grid</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>+proj=pipeline + +step +proj=push +v_3 + +step +proj=cart +ellps=clrk80ign + +step +proj=xyzgridshift +grids=gr3df97a.tif +grid_ref=output_crs +ellps=GRS80 + +step +proj=cart +ellps=GRS80 +inv + +step +proj=pop +v_3 +</pre></div> +</div> +<section id="parameters"> +<h3>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h3> +<p>The ellipsoid parameters should be the ones consistent with <code class="docutils literal notranslate"><span class="pre">grid_ref</span></code>. +They are used to perform a geocentric to geographic conversion to find the +translation parameters.</p> +<section id="required"> +<h4>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-ellps"> +<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt> +<dd><p>The name of a built-in ellipsoid definition.</p> +<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute +<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p> +<p><em>Defaults to “GRS80”.</em></p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-grids"> +<span class="sig-name descname"><span class="pre">+grids</span></span><span class="sig-prename descclassname"><span class="pre">=<list></span></span><a class="headerlink" href="#cmdoption-arg-grids" title="Permalink to this definition">¶</a></dt> +<dd><p>Comma-separated list of grids to load. If a grid is prefixed by an <code class="docutils literal notranslate"><span class="pre">@</span></code> the +grid is considered optional and PROJ will the not complain if the grid is +not available.</p> +<p>Grids are expected to be in GeoTIFF format. If no metadata is provided, +the first, second and third samples are assumed to be the geocentric +translation along X, Y and Z axis respectively, in metres.</p> +</dd></dl> + +</section> +<section id="optional"> +<h4>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h4> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-grid_ref"> +<span id="cmdoption-arg-grid-ref"></span><span class="sig-name descname"><span class="pre">+grid_ref</span></span><span class="sig-prename descclassname"><span class="pre">=input_crs/output_crs</span></span><a class="headerlink" href="#cmdoption-arg-grid_ref" title="Permalink to this definition">¶</a></dt> +<dd><p>Specify in which CRS the grid is referenced to. The default value is +input_crs. That is the grid is referenced in the geographic CRS corresponding +to the input geocentric CRS.</p> +<p>If output_crs is specified, the grid is referenced in the geographic CRS corresponding +to the output geocentric CRS. This is for example the case for the French +<code class="file docutils literal notranslate"><span class="pre">gr3df97a.tif</span></code> grid converting from NTF to RGF93, but referenced against RGF93. +Thus in the forward direction (NTF->RGF93), an iterative method is used to find +the appropriate shift.</p> +</dd></dl> + +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-multiplier"> +<span class="sig-name descname"><span class="pre">+multiplier</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-multiplier" title="Permalink to this definition">¶</a></dt> +<dd><p>Specify the multiplier to apply to the grid values. Defaults to 1.0</p> +</dd></dl> + +</section> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="vgridshift.html" class="btn btn-neutral float-left" title="Vertical grid shift" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="../pipeline.html" class="btn btn-neutral float-right" title="The pipeline operator" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
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