NAME¶
Planimeter -- compute the area of geodesic polygons
SYNOPSIS¶
Planimeter [
-r ] [
-s ] [
-l ] [
-e a
f ] [
-p prec ] [
-E ] [
-Q ] [
--comment-delimiter commentdelim ] [
--version |
-h |
--help ] [
--input-file infile |
--input-string instring ] [
--line-separator
linesep ] [
--output-file outfile ]
DESCRIPTION¶
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
GeoConvert(1).
(MGRS coordinates signify the center of the corresponding 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).
The edges of the polygon are given by the
shortest geodesic between
consecutive vertices. In certain cases, there may be two or many such shortest
geodesics, and in that case, the polygon is not uniquely specified by its
vertices. This only happens with very long edges (for the WGS84 ellipsoid, any
edge shorter than 19970 km is uniquely specified by its end points). In such
cases, insert an additional vertex near the middle of the long edge to define
the boundary of the polygon.
By default, polygons traversed in a counter-clockwise direction return a
positive area and those traversed in a clockwise direction return a negative
area. This sign convention is reversed if the
-r option is given.
Of course, encircling an area in the clockwise direction is equivalent to
encircling the rest of the ellipsoid in the counter-clockwise direction. The
default interpretation used by
Planimeter is the one that results in a
smaller magnitude of area; i.e., the magnitude of the area is less than or
equal to one half the total area of the ellipsoid. If the
-s option is
given, then the interpretation used is the one that results in a positive
area; i.e., the area is positive and less than the total area of the
ellipsoid.
Only simple polygons are supported for the area computation. Polygons may
include one or both poles. There is no need to close the polygon.
OPTIONS¶
- -r
- toggle whether counter-clockwise traversal of the polygon returns a
positive (the default) or negative result.
- -s
- toggle whether to return a signed result (the default) or not.
- -l
- toggle whether the vertices represent a polygon (the default) or a
polyline. For a polyline, the number of points and the length of the path
joining them is returned; the path is not closed and the area is not
reported.
- -e
- specify the ellipsoid via a f; the equatorial radius is
a and the flattening is f. Setting f = 0 results in a
sphere. Specify f < 0 for a prolate ellipsoid. A simple
fraction, e.g., 1/297, is allowed for f. (Also, if f > 1,
the flattening is set to 1/ f.) By default, the WGS84 ellipsoid is
used, a = 6378137 m, f = 1/298.257223563. If entering
vertices as UTM/UPS or MGRS coordinates, use the default ellipsoid, since
the conversion of these coordinates to latitude and longitude always uses
the WGS84 parameters.
- -p
- set the output precision to prec (default 6); the perimeter is
given (in meters) with prec digits after the decimal point; the
area is given (in meters^2) with ( prec - 5) digits after the
decimal point.
- -E
- use "exact" algorithms (based on elliptic integrals) for the
geodesic calculations. These are more accurate than the (default) series
expansions for | f| > 0.02. (But note that the implementation of
areas in GeodesicExact uses a high order series and this is only accurate
for modest flattenings.) -E and -Q are mutually
exclusive.
- -Q
- perform the calculation on the authalic sphere. The area calculation is
accurate even if the flattening is large, provided the edges are
sufficiently short. The perimeter calculation is not accurate. -E
and -Q are mutually exclusive.
- --comment-delimiter
- set the comment delimiter to commentdelim (e.g., "#" or
"//"). If set, the input lines will be scanned for this
delimiter and, if found, the delimiter and the rest of the line will be
removed prior to processing. For a given polygon, the last such string
found will be appended to the output line (separated by a space).
- --version
- print version and exit.
- -h
- print usage and exit.
- --help
- print full documentation and exit.
- --input-file
- read input from the file infile instead of from standard input; a
file name of "-" stands for standard input.
- --input-string
- read input from the string instring instead of from standard input.
All occurrences of the line separator character (default is a semicolon)
in instring are converted to newlines before the reading
begins.
- --line-separator
- set the line separator character to linesep. By default this is a
semicolon.
- --output-file
- write output to the file outfile instead of to standard output; a
file name of "-" stands for standard output.
EXAMPLES¶
Example (the area of the 100km MGRS square 18SWK)
Planimeter <<EOF
18n 500000 4400000
18n 600000 4400000
18n 600000 4500000
18n 500000 4500000
EOF
=> 4 400139.53295860 10007388597.1913
The following code takes the output from gdalinfo and reports the area covered
by the data (assuming the edges of the image are geodesics).
#! /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' '
SEE ALSO¶
GeoConvert(1). The algorithm for the area of geodesic polygon is given in
Section 6 of C. F. F. Karney,
Algorithms for geodesics, J. Geodesy 87,
43-55 (2013); DOI <
http://dx.doi.org/10.1007/s00190-012-0578-z>;
addenda: <
http://geographiclib.sf.net/geod-addenda.html>.
AUTHOR¶
Planimeter was written by Charles Karney.
HISTORY¶
Planimeter was added to GeographicLib,
<
http://geographiclib.sf.net>, in version 1.4.