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| author | PROJ deploybot <proj.bot@proj.bot> | 2022-03-22 20:00:06 +0000 |
|---|---|---|
| committer | PROJ deploybot <proj.bot@proj.bot> | 2022-03-22 20:00:06 +0000 |
| commit | a3f43744feec86272fe532124679d3a013ef9a8c (patch) | |
| tree | 27e4198db6011e3097eb7bcfe7197684aba7583a /operations/conversions/geoc.html | |
| download | PROJ-gh-pages.tar.gz PROJ-gh-pages.zip | |
update with results of commit https://github.com/OSGeo/PROJ/commit/53c07a8bd211b7aee4bc07a9c6726005504b7181gh-pages
Diffstat (limited to 'operations/conversions/geoc.html')
| -rw-r--r-- | operations/conversions/geoc.html | 230 |
1 files changed, 230 insertions, 0 deletions
diff --git a/operations/conversions/geoc.html b/operations/conversions/geoc.html new file mode 100644 index 00000000..5cb5b976 --- /dev/null +++ b/operations/conversions/geoc.html @@ -0,0 +1,230 @@ +<!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>Geocentric Latitude — 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/geoc.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="../../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 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 current"><a class="current reference internal" href="#">Geocentric Latitude</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#mathematical-definition">Mathematical definition</a></li> +<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="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" 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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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