. ./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 "$QUERY_STRING" flattening`
FORMAT=`lookupkey "$QUERY_STRING" format`
AZF2=`lookupkey "$QUERY_STRING" azi2`
UNROLL=`lookupkey "$QUERY_STRING" unroll`
PREC=`lookupkey "$QUERY_STRING" prec`
TYPE=`lookupkey "$QUERY_STRING" type`
fi
test "$RADIUS" || RADIUS=$DEFAULTRADIUS
test "$FLATTENING" || FLATTENING=$DEFAULTFLATTENING
test "$FORMAT" || FORMAT=g
test "$AZF2" || AZF2=f
test "$UNROLL" || UNROLL=r
test "$PREC" || PREC=3
test "$TYPE" || TYPE=I
AZIX="fazi2"
test "$AZF2" = b && AZIX="bazi2"
TAG=
if test "$RADIUS" = "$DEFAULTRADIUS" -a \
"$FLATTENING" = "$DEFAULTFLATTENING"; then
TAG=" (WGS84)"
fi
INPUTENC=`encodevalue "$INPUT"`
EXECDIR=../bin
COMMAND="GeodSolve -E -f"
VERSION=`$EXECDIR/$COMMAND --version | cut -f4 -d" "`
F='<font color="blue">'
G='</font>'
S=' '
test $TYPE = I && COMMAND="$COMMAND -i"
COMMANDX="$COMMAND -p 1"
test $FORMAT = d && COMMAND="$COMMAND -$FORMAT"
test $AZF2 = b && COMMAND="$COMMAND -$AZF2"
test $UNROLL = u && COMMAND="$COMMAND -$UNROLL"
test $PREC = 3 || COMMAND="$COMMAND -p $PREC"
STATUS=
POSITION1=
POSITION2=
DIST12=
a12=
m12=
M1221=
S12=
set -o pipefail
if test "$INPUT"; then
OUTPUT=`echo $INPUT | $EXECDIR/$COMMAND -e "$RADIUS" "$FLATTENING" 2>&1 |
head -1`
if test $? -eq 0; then
STATUS=OK
OUTPUTG=`echo $INPUT | $EXECDIR/$COMMANDX -e "$RADIUS" "$FLATTENING" |
head -1`
POS1="`echo $OUTPUT | cut -f1-2 -d' '`"
POS2="`echo $OUTPUT | cut -f4-5 -d' '`"
POSG1="`echo $OUTPUTG | cut -f1-2 -d' '`"
POSG2="`echo $OUTPUTG | cut -f4-5 -d' '`"
AZI1="`echo $OUTPUT | cut -f3 -d' '`"
AZI2="`echo $OUTPUT | cut -f6 -d' '`"
DIST12="`echo $OUTPUT | cut -f7 -d' '`"
a12="`echo $OUTPUT | cut -f8 -d' '`"
m12="`echo $OUTPUT | cut -f9 -d' '`"
M1221="`echo $OUTPUT | cut -f10-11 -d' '`"
S12="`echo $OUTPUT | cut -f12 -d' '`"
if test "$TYPE" = D; then
POSITION1=$(geohack $POSG1 $POS1 Black)\ $(convertdeg "$AZI1")
POSITION2=$F$(geohack $POSG2 $POS2 Blue)\ $(convertdeg "$AZI2")$G
DIST12=$(encodevalue "$DIST12")
else
POSITION1=$(geohack $POSG1 $POS1 Black)\ $F$(convertdeg "$AZI1")$G
POSITION2=$(geohack $POSG2 $POS2 Black)\ $F$(convertdeg "$AZI2")$G
DIST12=$F$(encodevalue "$DIST12")$G
fi
else
STATUS="$OUTPUT"
fi
fi
echo Content-type: text/html
echo
cat <<EOF
<html>
<head>
<title>
Online geodesic calculator
</title>
<meta name="description" content="Online geodesic calculator" />
<meta name="author" content="Charles F. F. Karney" />
<meta name="keywords"
content="geodesics,
geodesic distance,
geographic distance,
shortest path,
direct geodesic problem,
inverse geodesic problem,
distance and azimuth,
distance and heading,
range and bearing,
spheroidal triangle,
latitude and longitude,
online calculator,
WGS84 ellipsoid,
GeographicLib" />
</head>
<body>
<h3>
Online geodesic calculations using the
<a href="https://geographiclib.sourceforge.io/C++/doc/GeodSolve.1.html">
GeodSolve</a> utility
</h3>
<form action="/cgi-bin/GeodSolve" method="get">
<p>
Geodesic calculation:
<table>
<tr>
<td valign='baseline'>
<label for='I'>
<input type="radio" name="type" value="I" id='I'
`test "$TYPE" = I && echo CHECKED`>
Inverse:
</label>
</td>
<td valign='baseline'>
<em>lat1 lon1 lat2 lon2</em>
</td>
<td valign='baseline'>
→ <em>azi1 azi2 s12</em>
</td>
</tr>
<tr>
<td valign='baseline'>
<label for='D'>
<input type="radio" name="type" value="D" id='D'
`test "$TYPE" = D && echo CHECKED`>
Direct:
</label>
</td>
<td valign='baseline'>
<em>lat1 lon1 azi1 s12</em>
</td>
<td valign='baseline'>
→ <em>lat2 lon2 azi2</em>
</td>
</tr>
</table>
</p>
<p>
Input (ex. «<tt>40.6 -73.8 49°01'N 2°33'E</tt>»
[inverse],
«<tt>40d38'23"N 073d46'44"W 53d30' 5850e3</tt>»
[direct]):
<br>
<input type=text name="input" size=72 value="$INPUTENC">
</p>
<p>
<table>
<tr>
<td>
Output format:
</td>
EOF
while read c desc; do
CHECKED=
test "$c" = "$FORMAT" && CHECKED=CHECKED
echo "<td> <label for='$c'>"
echo "<input type='radio' name='format' value='$c' id='$c' $CHECKED>"
echo "$desc</label></td>"
done <<EOF
g decimal degrees
d degrees minutes seconds
EOF
cat <<EOF
</tr>
<tr>
<td>
Heading at point 2:
</td>
EOF
while read c desc; do
CHECKED=
test "$c" = "$AZF2" && CHECKED=CHECKED
echo "<td> <label for='$c'>"
echo "<input type='radio' name='azi2' value='$c' id='$c' $CHECKED>"
echo "$desc</label></td>"
done <<EOF
f forward azimuth
b back azimuth
EOF
cat <<EOF
</tr>
<tr>
<td>
Longitude:
</td>
EOF
while read c desc; do
CHECKED=
test "$c" = "$UNROLL" && CHECKED=CHECKED
echo "<td> <label for='$c'>"
echo "<input type='radio' name='unroll' value='$c' id='$c' $CHECKED>"
echo "$desc</label></td>"
done <<EOF
r reduce to [−180°,180°]
u unroll
EOF
cat <<EOF
</tr>
<tr>
<td>
Output precision:
</td>
<td colspan="2">
<select name="prec" size=1>
EOF
while read p desc; do
SELECTED=
test "$p" = "$PREC" && SELECTED=SELECTED
echo "<option $SELECTED value='$p'> $desc</option>"
done <<EOF
0 1m 0.00001d 0.1"
1 100mm 0.01"
2 10mm 0.001"
3 1mm 0.0001"
4 100μm 0.00001"
5 10μm 0.000001"
6 1μm 0.0000001"
7 100nm 0.00000001"
8 10nm 0.000000001"
9 1nm 0.0000000001"
EOF
cat <<EOF
</select>
</td>
</tr>
<tr>
<td>Equatorial radius:</td>
<td>
<input type=text name="radius" size=20 value="$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>
Select action:<br>
<input type="submit" name="option" value="Submit">
<input type="submit" name="option" value="Reset">
</p>
<p>
Geodesic (input in black, output in ${F}blue${G}):<br>
<font size="4"><pre>
ellipsoid (a f)$S= `encodevalue "$RADIUS"` `encodevalue "$FLATTENING"`$TAG
status $S= `encodevalue "$STATUS"`
lat1 lon1 fazi1 (°) = $POSITION1
lat2 lon2 $AZIX (°) = $POSITION2
s12 (m) = $DIST12
a12 (°) = $F$a12$G
m12 (m) = $F$m12$G
M12 M21 = $F$M1221$G
S12 (m^2) = $F$S12$G</pre></font>
</p>
</form>
<hr>
<p>
<a href="https://geographiclib.sourceforge.io/C++/doc/GeodSolve.1.html">
GeodSolve (version $VERSION)</a>
performs geodesic calculations for an arbitrary ellipsoid of
revolution. 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 <em>geodesic</em>; 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.
There are two standard geodesic problems:
<ul>
<li> Direct: given [<em>lat1 lon1 azi1 s12</em>], find
[<em>lat2 lon2 azi2</em>];
<li> Inverse: given [<em>lat1 lon1 lat2 lon2</em>], find
[<em>azi1 azi2 s12</em>].
</ul>
Latitudes and longitudes can be given in various formats, 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>
Azimuths are given in degrees clockwise from north. The
distance <em>s12</em> is in meters.
</p>
<p>
The additional quantities computed are:
<ul>
<li> <em>a12</em>, the arc length on the auxiliary sphere (°),
<li> <em>m12</em>, the reduced length (m),
<li> <em>M12</em> and <em>M21</em>, the geodesic scales,
<li> <em>S12</em>, the area between the geodesic
and the equator (m<sup>2</sup>).
</ul>
</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>
GeodSolve is accurate to about 15 nanometers (for the WGS84
ellipsoid) and gives solutions for the inverse problem for any
pair of points.
</p>
<p>
<a href="https://geographiclib.sourceforge.io/C++/doc/GeodSolve.1.html">
GeodSolve</a>,
which is a simple wrapper of the
<a href="https://geographiclib.sourceforge.io/C++/doc/classGeographicLib_1_1Geodesic.html">
GeographicLib::Geodesic</a> class,
is one of the utilities provided
with <a href="https://geographiclib.sourceforge.io/">
GeographicLib</a>.
Geodesics can also be computed using JavaScript; see the
<a href="../scripts/geod-calc.html">JavaScript geodesic
calculator</a> and
<a href="../scripts/geod-google.html">geodesics on Google
maps</a>. If you wish to use GeodSolve 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>. See also the Wikipedia page,
<a href="https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid">
Geodesics on an ellipsoid</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