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<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>
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