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<section id="geod">
<span id="id1"></span><h1>geod<a class="headerlink" href="#geod" title="Permalink to this headline">¶</a></h1>
<section id="synopsis">
<h2>Synopsis<a class="headerlink" href="#synopsis" title="Permalink to this headline">¶</a></h2>
<blockquote>
<div><p><strong>geod</strong> <em>+ellps=<ellipse></em> [<strong>-afFIlptwW</strong> [args]] [<em>+opt[=arg]</em> …] file …</p>
<p><strong>invgeod</strong> <em>+ellps=<ellipse></em> [<strong>-afFIlptwW</strong> [args]] [<em>+opt[=arg]</em> …] file …</p>
</div></blockquote>
</section>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
<p><strong class="program">geod</strong> (direct) and <strong class="program">invgeod</strong> (inverse) perform geodesic
(Great Circle) computations for determining latitude, longitude and back
azimuth of a terminus point given a initial point latitude, longitude,
azimuth and distance (direct) or the forward and back azimuths and distance
between an initial and terminus point latitudes and longitudes (inverse).
The results are accurate to round off for <span class="math notranslate nohighlight">\(|f| < 1/50\)</span>, where
<span class="math notranslate nohighlight">\(f\)</span> is flattening.</p>
<p><strong class="program">invgeod</strong> may not be available on all platforms; in this case
use <a class="reference internal" href="#cmdoption-geod-I"><code class="xref std std-option docutils literal notranslate"><span class="pre">geod</span> <span class="pre">-I</span></code></a> instead.</p>
<p>The following command-line options can appear in any order:</p>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-I">
<span id="cmdoption-geod-i"></span><span class="sig-name descname"><span class="pre">-I</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-I" title="Permalink to this definition">¶</a></dt>
<dd><p>Specifies that the inverse geodesic computation is to be performed. May be
used with execution of <strong class="program">geod</strong> as an alternative to <strong class="program">invgeod</strong> execution.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-a">
<span class="sig-name descname"><span class="pre">-a</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-a" title="Permalink to this definition">¶</a></dt>
<dd><p>Latitude and longitudes of the initial and terminal points, forward and
back azimuths and distance are output.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-t-a">
<span class="sig-name descname"><span class="pre">-t<a></span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-t-a" title="Permalink to this definition">¶</a></dt>
<dd><p>Where <em>a</em> specifies a character employed as the first character to denote a control
line to be passed through without processing.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-le">
<span class="sig-name descname"><span class="pre">-le</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-le" title="Permalink to this definition">¶</a></dt>
<dd><p>Gives a listing of all the ellipsoids that may be selected with the
<em>+ellps=</em> option.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-lu">
<span class="sig-name descname"><span class="pre">-lu</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-lu" title="Permalink to this definition">¶</a></dt>
<dd><p>Gives a listing of all the units that may be selected with the <em>+units=</em>
option. (Default units are meters.)</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-f">
<span class="sig-name descname"><span class="pre">-f</span></span><span class="sig-prename descclassname"> <span class="pre"><format></span></span><a class="headerlink" href="#cmdoption-geod-f" title="Permalink to this definition">¶</a></dt>
<dd><p>Where <em>format</em> is a printf format string to control the output form of the
geographic coordinate values. The default mode is DMS.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-F">
<span class="sig-name descname"><span class="pre">-F</span></span><span class="sig-prename descclassname"> <span class="pre"><format></span></span><a class="headerlink" href="#cmdoption-geod-F" title="Permalink to this definition">¶</a></dt>
<dd><p>Where <em>format</em> is a printf format string to control the output form of the distance
value. The default mode is <code class="docutils literal notranslate"><span class="pre">"%.3f"</span></code>.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-w-n">
<span class="sig-name descname"><span class="pre">-w<n></span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-w-n" title="Permalink to this definition">¶</a></dt>
<dd><p>Where <em>n</em> is the number of significant fractional digits to employ for seconds
output (when the option is not specified, <code class="docutils literal notranslate"><span class="pre">-w3</span></code> is assumed).</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-W-n">
<span class="sig-name descname"><span class="pre">-W<n></span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-W-n" title="Permalink to this definition">¶</a></dt>
<dd><p>Where <em>n</em> is the number of significant fractional digits to employ for seconds
output. When <code class="docutils literal notranslate"><span class="pre">-W</span></code> is employed the fields will be constant width
with leading zeroes.</p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-geod-p">
<span class="sig-name descname"><span class="pre">-p</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-geod-p" title="Permalink to this definition">¶</a></dt>
<dd><p>This option causes the azimuthal values to be output as unsigned DMS
numbers between 0 and 360 degrees. Also note <a class="reference internal" href="#cmdoption-geod-f"><code class="xref std std-option docutils literal notranslate"><span class="pre">-f</span></code></a>.</p>
</dd></dl>
<p>The <em>+opt</em> command-line options are associated with geodetic
parameters for specifying the ellipsoidal or sphere to use.
controls. The options are processed in left to right order
from the command line. Reentry of an option is ignored with
the first occurrence assumed to be the desired value.</p>
<p>See <a class="reference internal" href="../usage/projections.html#projections-intro"><span class="std std-ref">Cartographic projection</span></a> for full
list of these parameters and controls.</p>
<p>One or more files (processed in left to right order) specify
the source of data to be transformed. A <code class="docutils literal notranslate"><span class="pre">-</span></code> will specify the
location of processing standard input. If no files are specified,
the input is assumed to be from stdin.</p>
<p>For direct determinations input data must be in latitude, longitude,
azimuth and distance order and output will be latitude,
longitude and back azimuth of the terminus point. Latitude,
longitude of the initial and terminus point are input for the
inverse mode and respective forward and back azimuth from the
initial and terminus points are output along with the distance
between the points.</p>
<p>Input geographic coordinates (latitude and longitude) and
azimuthal data must be in decimal degrees or DMS format and
input distance data must be in units consistent with the ellipsoid
major axis or sphere radius units. The latitude must lie
in the range [-90d,90d]. Output geographic coordinates will be
in DMS (if the <a class="reference internal" href="#cmdoption-geod-f"><code class="xref std std-option docutils literal notranslate"><span class="pre">-f</span></code></a> switch is not employed) to 0.001” with trailing,
zero-valued minute-second fields deleted. Output distance
data will be in the same units as the ellipsoid or sphere
radius.</p>
<p>The Earth’s ellipsoidal figure may be selected in the same manner
as program <strong class="program">proj</strong> by using <em>+ellps=</em>, <em>+a=</em>, <em>+es=</em>, etc.</p>
<p><strong class="program">geod</strong> may also be used to determine intermediate points along
either a geodesic line between two points or along an arc of
specified distance from a geographic point. In both cases an
initial point must be specified with <em>+lat_1=lat</em> and <em>+lon_1=lon</em>
parameters and either a terminus point <em>+lat_2=lat</em> and
<em>+lon_2=lon</em> or a distance and azimuth from the initial point
with <em>+S=distance</em> and <em>+A=azimuth</em> must be specified.</p>
<p>If points along a geodesic are to be determined then either
<em>+n_S=integer</em> specifying the number of intermediate points
and/or <em>+del_S=distance</em> specifying the incremental distance
between points must be specified.</p>
<p>To determine points along an arc equidistant from the initial
point both <em>+del_A=angle</em> and <em>+n_A=integer</em> must be specified
which determine the respective angular increments and number of
points to be determined.</p>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
<p>The following script determines the geodesic azimuths and distance in U.S.
statute miles from Boston, MA, to Portland, OR:</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">geod +ellps=clrk66 <<EOF -I +units=us-mi</span>
<span class="go">42d15'N 71d07'W 45d31'N 123d41'W</span>
<span class="go">EOF</span>
</pre></div>
</div>
<p>which gives the results:</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">-66d31'50.141" 75d39'13.083" 2587.504</span>
</pre></div>
</div>
<p>where the first two values are the azimuth from Boston to Portland,
the back azimuth from Portland to Boston followed by the distance.</p>
<p>An example of forward geodesic use is to use the Boston location
and determine Portland’s location by azimuth and distance:</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">geod +ellps=clrk66 <<EOF +units=us-mi</span>
<span class="go">42d15'N 71d07'W -66d31'50.141" 2587.504</span>
<span class="go">EOF</span>
</pre></div>
</div>
<p>which gives:</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">45d31'0.003"N 123d40'59.985"W 75d39'13.094"</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Lack of precision in the distance value compromises the
precision of the Portland location.</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://geographiclib.sourceforge.io">GeographicLib</a>.</p></li>
<li><p>C. F. F. Karney, <a class="reference external" href="https://doi.org/10.1007/s00190-012-0578-z">Algorithms for Geodesics</a>, J. Geodesy <strong>87</strong>(1), 43–55 (2013);
<a class="reference external" href="https://geographiclib.sourceforge.io/geod-addenda.html">addenda</a>.</p></li>
<li><p><a class="reference external" href="https://geographiclib.sourceforge.io/geodesic-papers/biblio.html">A geodesic bibliography</a>.</p></li>
</ol>
</section>
</section>
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