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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" 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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 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 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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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