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<title>Geod -- perform geodesic calculations</title>
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<ul>
<li><a href="#name">NAME</a></li>
<li><a href="#synopsis">SYNOPSIS</a></li>
<li><a href="#description">DESCRIPTION</a></li>
<li><a href="#options">OPTIONS</a></li>
<li><a href="#input">INPUT</a></li>
<li><a href="#auxiliary_sphere">AUXILIARY SPHERE</a></li>
<li><a href="#precision">PRECISION</a></li>
<li><a href="#errors">ERRORS</a></li>
<li><a href="#examples">EXAMPLES</a></li>
<li><a href="#see_also">SEE ALSO</a></li>
<li><a href="#author">AUTHOR</a></li>
</ul>
-->
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<p>
</p>
<hr />
<h1><a name="name">NAME</a></h1>
<p>Geod -- perform geodesic calculations</p>
<p>
</p>
<hr />
<h1><a name="synopsis">SYNOPSIS</a></h1>
<p><strong>Geod</strong> [ <strong>-i</strong> | <strong>-l</strong> <em>lat1</em> <em>lon1</em> <em>azi1</em> ] [ <strong>-a</strong> ] [ <strong>-e</strong> <em>a</em> <em>r</em> ]
[ <strong>-d</strong> ] [ <strong>-b</strong> ] [ <strong>-f</strong> ] [ <strong>-p</strong> <em>prec</em> ]
[ <strong>--version</strong> | <strong>-h</strong> | <strong>--help</strong> ]</p>
<p>
</p>
<hr />
<h1><a name="description">DESCRIPTION</a></h1>
<p>The shortest path between two points on the ellipsoid at (<em>lat1</em>,
<em>lon1</em>) and (<em>lat2</em>, <em>lon2</em>) is called the geodesic. Its length is
<em>s12</em> and the geodesic from point 1 to point 2 has azimuths <em>azi1</em> and
<em>azi2</em> at the two end points. The reduced length of the
geodesic, <em>m12</em>, is defined such that if the initial azimuth is
perturbed by d<em>azi1</em> (radians) then the second point is displaced by
<em>m12</em>*d<em>azi1</em> in the direction perpendicular to the geodesic. On a
flat surface, we have <em>m12</em> = <em>s12</em>.</p>
<p><strong>Geod</strong> operates in one of three modes:</p>
<ol>
<li>
<p>By default, <strong>Geod</strong> accepts lines on the standard input containing
<em>lat1</em> <em>lon1</em> <em>azi1</em> <em>s12</em> and prints <em>lat2</em> <em>lon2</em> <em>azi2</em> <em>m12</em>
on standard output. This is the direct geodesic calculation.</p>
</li>
<li>
<p>Command line arguments <strong>-l</strong> <em>lat1</em> <em>lon1</em> <em>azi1</em> specify a geodesic line.
<strong>Geod</strong> then accepts a sequence of <em>s12</em> values (one per line) on
standard input and prints <em>lat2</em> <em>lon2</em> <em>azi2</em> <em>m12</em> for each. This
generates a sequence of points on a single geodesic.</p>
</li>
<li>
<p>With the <strong>-i</strong> command line argument, <strong>Geod</strong> performs the inverse
geodesic calculation. It reads lines containing <em>lat1</em> <em>lon1</em> <em>lat2</em>
<em>lon2</em> and prints the corresponding values of <em>azi1</em> <em>azi2</em> <em>s12</em> <em>m12</em>.</p>
</li>
</ol>
<p>
</p>
<hr />
<h1><a name="options">OPTIONS</a></h1>
<dl>
<dt><strong><a name="i" class="item"><strong>-i</strong></a></strong></dt>
<dd>
<p>perform an inverse geodesic calculation (see 3 above).</p>
</dd>
<dt><strong><a name="l" class="item"><strong>-l</strong></a></strong></dt>
<dd>
<p>line mode (see 2 above); generate a sequence of points along the
geodesic specified by <em>lat1</em> <em>lon1</em> <em>azi1</em>.</p>
</dd>
<dt><strong><a name="a" class="item"><strong>-a</strong></a></strong></dt>
<dd>
<p>arc mode; on input <em>and</em> output <em>s12</em> is replaced by <em>a12</em> the arc
length (in degrees) on the auxiliary sphere. See <a href="#auxiliary_sphere">AUXILIARY SPHERE</a>.</p>
</dd>
<dt><strong><a name="e" class="item"><strong>-e</strong></a></strong></dt>
<dd>
<p>specify the ellipsoid via <em>a</em> <em>r</em>; the equatorial radius is <em>a</em> and
the reciprocal flattening is <em>r</em>. Setting <em>r</em> = 0 results in a
sphere. Specify <em>r</em> < 0 for a prolate ellipsoid. By default, the
WGS84 ellipsoid is used, <em>a</em> = 6378137m, <em>r</em> = 298.257223563.</p>
</dd>
<dt><strong><a name="d" class="item"><strong>-d</strong></a></strong></dt>
<dd>
<p>output angles as degrees, minutes, seconds instead of decimal degrees.</p>
</dd>
<dt><strong><a name="b" class="item"><strong>-b</strong></a></strong></dt>
<dd>
<p>report the <em>back</em> azimuth at point 2 instead of the forward azimuth.</p>
</dd>
<dt><strong><a name="f" class="item"><strong>-f</strong></a></strong></dt>
<dd>
<p>full output; each line of output consists of 9 quantities: <em>lat1</em>
<em>lon1</em> <em>azi1</em> <em>lat2</em> <em>lon2</em> <em>azi2</em> <em>s12</em> <em>a12</em> <em>m12</em>.</p>
</dd>
<dt><strong><a name="p" class="item"><strong>-p</strong></a></strong></dt>
<dd>
<p>set the precision to <em>prec</em> (default 3); <em>prec</em> is the precision
relative to 1m. See <a href="#precision">PRECISION</a>.</p>
</dd>
<dt><strong><a name="version" class="item"><strong>--version</strong></a></strong></dt>
<dd>
<p>print version.</p>
</dd>
<dt><strong><a name="h" class="item"><strong>-h</strong></a></strong></dt>
<dd>
<p>print usage.</p>
</dd>
<dt><strong><a name="help" class="item"><strong>--help</strong></a></strong></dt>
<dd>
<p>print full documentation.</p>
</dd>
</dl>
<p>
</p>
<hr />
<h1><a name="input">INPUT</a></h1>
<p><strong>Geod</strong> measures all angles in degrees and all lengths (<em>s12</em>, <em>m12</em>)
in meters. On input angles (latitude, longitude, azimuth, arc length)
can be as decimal degrees or degrees (d), minutes ('), seconds ("). A
decimal point can only appear in the least significant component and the
designator (d, ', or ") for this component is optional; thus <code>40d30</code>,
<code>40d30'</code>, <code>40.5d</code>, and <code>40.5</code> are all equivalent. By default,
latitude precedes longitude for each point; however on input either may
be given first by appending (or prepending) <em>N</em> or <em>S</em> to the latitude
and <em>E</em> or <em>W</em> to the longitude. Azimuths are measured clockwise from
north; however this may be overridden with <em>E</em> or <em>W</em>.</p>
<p>
</p>
<hr />
<h1><a name="auxiliary_sphere">AUXILIARY SPHERE</a></h1>
<p>Geodesics on the ellipsoid can be transferred to the <em>auxiliary sphere</em>
on which the distance is measured in terms of the arc length <em>a12</em>
(measured in degrees) instead of <em>s12</em>. In terms of <em>a12</em>, 180
degrees is the distance from one equator crossing to the next or from
the minimum latitude to the maximum latitude. Geodesics with <em>a12</em>
> 180 degrees do not correspond to shortest paths. With the <strong>-a</strong>
flag, <em>s12</em> (on both input and output) is replaced by <em>a12</em>. The
<strong>-a</strong> flag does <em>not</em> affect the full output given by the <strong>-f</strong> flag
(which always includes both <em>s12</em> and <em>a12</em>). <em>m12</em> is always given
in meters.</p>
<p>
</p>
<hr />
<h1><a name="precision">PRECISION</a></h1>
<p><em>prec</em> gives precision of
the output with <em>prec</em> = 0 giving 1m precision, <em>prec</em> = 3 giving 1mm
precision, etc. <em>prec</em> is the number of digits after the decimal point
for lengths. For decimal degrees, the number of digits after the
decimal point is 5 + <em>prec</em>. For DMS (degree, minute, seconds) output,
the number of digits after the decimal point in the seconds component
is 1 + <em>prec</em>. The minimum value of <em>prec</em> is 0 and the maximum is 10.</p>
<p>
</p>
<hr />
<h1><a name="errors">ERRORS</a></h1>
<p>An illegal line of input will print an error message to standard output
beginning with <code>ERROR:</code> and causes <strong>Geod</strong> to return an exit code of 1.
However, an error does not cause <strong>Geod</strong> to terminate; following lines
will be converted.</p>
<p>
</p>
<hr />
<h1><a name="examples">EXAMPLES</a></h1>
<p>Route from JFK Airport to Singapore Changi Airport:</p>
<pre>
echo "40d38'23N" "073d46'44W" "01d21'33N" "103d59'22E" |
Geod -i -d -p 0</pre>
<pre>
003d18'29.9" 177d29'09.2" 15347628 4302458</pre>
<p>Waypoints on the route at intervals of 2000km:</p>
<pre>
for ((i = 0; i <= 16; i += 2)); do echo ${i}000000;done |
Geod -l "40d38'23N" "073d46'44W" "003d18'29.9" -d -p 0</pre>
<pre>
40d38'23.0"N 073d46'44.0"W 003d18'29.9" 0
58d34'45.1"N 071d49'36.7"W 004d48'48.8" 1967419
76d22'28.4"N 065d32'17.8"W 010d41'38.4" 3743642
84d50'28.0"N 075d04'39.2"E 150d55'00.9" 5156905
67d26'20.3"N 098d00'51.2"E 173d27'20.3" 6070415
49d33'03.2"N 101d06'52.6"E 176d07'54.3" 6394568
31d34'16.5"N 102d30'46.3"E 177d03'08.4" 6095725
13d31'56.0"N 103d26'50.7"E 177d24'55.0" 5200700
04d32'05.7"S 104d14'48.7"E 177d28'43.6" 3795596</pre>
<p>
</p>
<hr />
<h1><a name="see_also">SEE ALSO</a></h1>
<p><strong>Geod</strong> is a part of GeographicLib, <a href="http://geographiclib.sf.net">http://geographiclib.sf.net</a>. The
algorithms are described in C. F. F. Karney, <em>Geodesics on an ellipsoid
of revolution</em>, Feb. 2011; preprint <a href="http://arxiv.org/abs/1102.1215">http://arxiv.org/abs/1102.1215</a>.</p>
<p>
</p>
<hr />
<h1><a name="author">AUTHOR</a></h1>
<p><strong>Geod</strong> was written by Charles Karney.</p>
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