. ./utils.sh
DEFAULTRADIUS=6378137
DEFAULTFLATTENING=1/298.257223563
OPTION=`lookupkey "$QUERY_STRING" option`
if test "$OPTION" = Reset; then
INPUT=
RADIUS=
FLATTENING=
else
INPUT=`lookupcheckkey "$QUERY_STRING" input`
RADIUS=`lookupellipsoid "$QUERY_STRING" radius`
FLATTENING=`lookupellipsoid "$QUERY_STRING" flattening`
NORM=`lookupkey "$QUERY_STRING" norm`
TYPE=`lookupkey "$QUERY_STRING" type`
RHUMB=`lookupkey "$QUERY_STRING" rhumb`
fi
test "$RADIUS" || RADIUS=$DEFAULTRADIUS
test "$FLATTENING" || FLATTENING=$DEFAULTFLATTENING
TAG=
if test "$RADIUS" = "$DEFAULTRADIUS" -a \
"$FLATTENING" = "$DEFAULTFLATTENING"; then
TAG=" (WGS84)"
fi
INPUTENC=`encodevalue "$INPUT"`
if test "$TYPE" = "polyline"; then
LINEFLAG=-l
else
LINEFLAG=
fi
if test "$RHUMB" = "rhumb"; then
RHUMBFLAG=-R
else
RHUMBFLAG=
fi
EXECDIR=../bin
COMMAND="Planimeter"
VERSION=`$EXECDIR/$COMMAND --version | cut -f4 -d" "`
COMMAND="$COMMAND -E -e $RADIUS $FLATTENING"
STATUS=
NUM=
LEN=
AREA=
set -o pipefail
if test "$INPUT"; then
OUTPUT=`echo "$INPUT" | $EXECDIR/$COMMAND $LINEFLAG $RHUMBFLAG 2>&1 |
head -1`
if test $? -eq 0; then
STATUS=OK
NUM="`echo $OUTPUT | cut -f1 -d' '`"
LEN="`echo $OUTPUT | cut -f2 -d' '`"
AREA="`echo $OUTPUT | cut -f3 -d' '`"
if test "$NORM"; then
TRANSFORMEDINPUT=`echo "$INPUT" | $EXECDIR/GeoConvert -p 20 |
sed '/^ERROR/,$d'`
INPUTENC=`encodevalue "$TRANSFORMEDINPUT"`
fi
else
STATUS="$OUTPUT"
fi
fi
echo Content-type: text/html
echo
cat <<EOF
<html>
<head>
<title>
Online geodesic planimeter
</title>
<meta name="description" content="Online geodesic planimeter" />
<meta name="author" content="Charles F. F. Karney" />
<meta name="keywords"
content="geodesics,
geodesic distance,
geodesic area,
geographic distance,
geographic area,
geodesic polygon,
shortest path,
spheroidal triangle,
latitude and longitude,
rhumb lines,
online calculator,
WGS84 ellipsoid,
GeographicLib" />
</head>
<body>
<h3>
Online geodesic polygon calculations using the
<a href="https://geographiclib.sourceforge.io/C++/doc/Planimeter.1.html">
Planimeter</a> utility
</h3>
<form action="/cgi-bin/Planimeter" method="get">
<p>
<table>
<tr>
<td>
Closed/open:
</td>
<td> <label for="c">
<input type="radio" name="type" value="polygon" id="c"
`test "$LINEFLAG" || echo CHECKED`>
Polygon</label>
</td>
<td> <label for="o">
<input type="radio" name="type" value="polyline" id="o"
`test "$LINEFLAG" && echo CHECKED`>
Polyline</label>
</td>
</tr>
<tr>
<td>
Edge type:
</td>
<td> <label for="g">
<input type="radio" name="rhumb" value="geodesic" id="g"
`test "$RHUMBFLAG" || echo CHECKED`>
Geodesic</label>
</td>
<td> <label for="r">
<input type="radio" name="rhumb" value="rhumb" id="r"
`test "$RHUMBFLAG" && echo CHECKED`>
Rhumb line</label>
</td>
</tr>
<tr>
<td>Equatorial radius:</td>
<td>
<input type=text name="radius" size=20 value="$RADIUS">
</td>
<td>meters</td>
</tr>
<tr>
<td>Flattening:</td>
<td>
<input type=text name="flattening" size=20 value="$FLATTENING">
</td>
</tr>
</table>
</p>
<p>
Enter the vertices as latitude longitude pairs, one per line:
<br>
<textarea cols=45 rows=15 name="input">$INPUTENC</textarea>
</p>
<p>
<input type="checkbox" name="norm" value="decdegrees"
`test "$NORM" && echo CHECKED` />
Convert vertices to decimal degrees
</p>
<p>
Select action:<br>
<input type="submit" name="option" value="Submit">
<input type="submit" name="option" value="Reset">
</p>
<p>
Results:<br>
<font size="4"><pre>
ellipsoid (a f) = `encodevalue "$RADIUS"` `encodevalue "$FLATTENING"`$TAG
status = $STATUS
number of vertices = $NUM
Perimeter (m) = $LEN
area (m^2) = $AREA</pre></font>
</p>
</form>
<hr>
<p>
In polygon mode,
<a href="https://geographiclib.sourceforge.io/C++/doc/Planimeter.1.html">
Planimeter (version $VERSION)</a>
calculates the perimeter and area of a polygon whose edges are
either geodesics or rhumb lines on the WGS84 ellipsoid. In
polyline mode, it calculates the length of the geodesic or rhumb
line path joining the points.
</p>
<p>
The edges of the polygon are given by the <i>shortest</i> geodesic
or rhumb line between consecutive vertices. In certain cases,
there may be two or many such shortest paths, and in that case,
the polygon is not uniquely specified by its vertices. In such
cases, insert an additional vertex near the middle of the long
edge to define the boundary of the polygon.
</p>
<p>
Counter-clockwise traversal of a polygon results in a positive
area. Arbitrarily complex polygons are allowed. In the case of
self-intersecting polygons the area is accumulated
"algebraically", i.e., the areas of the 2 loops in a figure-8
polygon will partially cancel. There is no need to close the
polygon. Polygons may include one or both poles.
</p>
<p>
Give the vertices in terms of latitude and longitude, for example
(these all refer to the position of Timbuktu):
<pre>
16.776 -3.009
16d47' -3d1'
W3°0'34" N16°46'33"
3:0:34W 16:46:33N</pre>
A blank line or a coordinate which cannot be understood
causes the reading of vertices to be stopped.
</p>
<p>
The ellipsoid is specified by its equatorial radius, <em>a</em>,
and its flattening, <em>f</em> =
(<em>a</em> − <em>b</em>)/<em>a</em>,
where <em>b</em> is the polar semi-axis. The default values for
these parameters correspond to the WGS84 ellipsoid. The method is
accurate for −99 ≤ <em>f</em> ≤ 0.99
(corresponding to 0.01 ≤ <em>b</em>/<em>a</em> ≤
100). Note that <em>f</em> is negative for a prolate ellipsoid
(<em>b</em> > <em>a</em>) and that it can be entered as a
fraction, e.g., 1/297.
</p>
<p>
For moderately complex polygons, the perimeter is accurate to
about 200 nm and the area is accurate to about
0.1 m<sup>2</sup>.
</p>
<p>
<a href="https://geographiclib.sourceforge.io/C++/doc/Planimeter.1.html">
Planimeter</a>,
which is a simple wrapper of the
<a href="https://geographiclib.sourceforge.io/C++/doc/classGeographicLib_1_1PolygonAreaT.html">
GeographicLib::PolygonAreaT</a> class,
is one of the utilities provided
with <a href="https://geographiclib.sourceforge.io/">
GeographicLib</a>.
Geodesic areas can also be computed using JavaScript; see the
<a href="../scripts/geod-calc.html">JavaScript geodesic
calculator</a>.
If you wish to use Planimeter directly,
<a href="https://sourceforge.net/projects/geographiclib/files/distrib-C++">
download</a>
and compile GeographicLib. The algorithms are described
in C. F. F. Karney,
<a href="https://doi.org/10.1007/s00190-012-0578-z"><i>Algorithms for
geodesics</i></a>,
J. Geodesy <b>87</b>, 43–55 (2013); DOI:
<a href="https://doi.org/10.1007/s00190-012-0578-z">
10.1007/s00190-012-0578-z</a>;
addenda:
<a href="https://geographiclib.sourceforge.io/geod-addenda.html">
geod-addenda.html</a> and
C. F. F. Karney,
<a href="https://doi.org/10.1007/s11200-024-0709-z"><i>The area
of rhumb polygons</i></a>,
Stud. Geophys. Geod. <b>68</b>(3–4), 99–120 (2024); DOI:
<a href="https://doi.org/10.1007/s11200-024-0709-z">
10.1007/s11200-024-0709-z</a>.
</p>
<hr>
<address>Charles Karney
<a href="mailto:karney@alum.mit.edu"><karney@alum.mit.edu></a>
(2022-04-10)</address>
<a href="https://geographiclib.sourceforge.io">
GeographicLib home
</a>
</body>
</html>
EOF