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<title>Planimeter -- compute the area of geodesic polygons</title>
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<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="#examples">EXAMPLES</a></li>
<li><a href="#see_also">SEE ALSO</a></li>
<li><a href="#author">AUTHOR</a></li>
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<h1><a name="name">NAME</a></h1>
<p>Planimeter -- compute the area of geodesic polygons</p>
<p>
</p>
<hr />
<h1><a name="synopsis">SYNOPSIS</a></h1>
<p><strong>Planimeter</strong> [ <strong>-s</strong> ] [ <strong>-r</strong> ] [ <strong>-e</strong> <em>a</em> <em>r</em> ]
[ <strong>--version</strong> | <strong>-h</strong> | <strong>--help</strong> ]</p>
<p>
</p>
<hr />
<h1><a name="description">DESCRIPTION</a></h1>
<p>Measure the area of a geodesic polygon. Reads polygon vertices from
standard input, one per line. Vertices may be given as latitude and
longitude, UTM/UPS, or MGRS coordinates, interpreted in the same way as
<a href="GeoConvert.1.html"><code>GeoConvert(1)</code></a>. (MGRS coordinates signify the center of the corresponing
MGRS square.) The end of input, a blank line, or a line which can't be
interpreted as a vertex signals the end of one polygon and the start of
the next. For each polygon print a summary line with the number of
points, the perimeter (in meters), and the area (in meters^2).</p>
<p>By default, areas are traversed in a counter-clockwise sense (in other
words, the included area is to the left of the perimeter) and a positive
area is returned. By this rule, a polygon tranversed in a clockwise
sense will return the area of ellipsoid excluded by the polygon;
however, if the <strong>-s</strong> option is given, the signed area will be returned.
If the <strong>-r</strong> option is given, the included area is to the right of the
perimeter. Only simple polygons are supported for the area computation.
Polygons may include one or both poles.</p>
<p>
</p>
<hr />
<h1><a name="options">OPTIONS</a></h1>
<dl>
<dt><strong><a name="s" class="item"><strong>-s</strong></a></strong></dt>
<dd>
<p>return a signed result for the area. (This is a toggle; repeating the
option undoes this setting.)</p>
</dd>
<dt><strong><a name="r" class="item"><strong>-r</strong></a></strong></dt>
<dd>
<p>reverse the traversal rule so that clockwise traversal yields a positive
result. (This is a toggle; repeating the option undoes this setting.)</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="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="examples">EXAMPLES</a></h1>
<p>Example (the area of the 100km MGRS square 18SWK)</p>
<pre>
Planimeter <<EOF
18N 500000 4400000
18N 600000 4400000
18N 600000 4500000
18N 500000 4500000
EOF
=> 4 400139.53295860 10007388597.1913</pre>
<p>The following code takes the output from gdalinfo and reports the area
covered by the data (assuming the edges of the image are geodesics).</p>
<pre>
#! /bin/sh
egrep '^((Upper|Lower) (Left|Right)|Center) ' |
sed -e 's/d /d/g' -e "s/' /'/g" | tr -s '(),\r\t' ' ' | awk '{
if ($1 $2 == "UpperLeft")
ul = $6 " " $5;
else if ($1 $2 == "LowerLeft")
ll = $6 " " $5;
else if ($1 $2 == "UpperRight")
ur = $6 " " $5;
else if ($1 $2 == "LowerRight")
lr = $6 " " $5;
else if ($1 == "Center") {
printf "%s\n%s\n%s\n%s\n\n", ul, ll, lr, ur;
ul = ll = ur = lr = "";
}
}
' | Planimeter | cut -f3 -d' '</pre>
<p>
</p>
<hr />
<h1><a name="see_also">SEE ALSO</a></h1>
<p><a href="GeoConvert.1.html"><code>GeoConvert(1)</code></a>. <strong>Planimeter</strong> is a part of GeographicLib,
<a href="http://geographiclib.sf.net">http://geographiclib.sf.net</a>. The algorithm for the area of geodesic
polygon is given in Section 15 of 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>Planimeter</strong> was written by Charles Karney.</p>
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