PLANIMETER(1) GeographicLib Utilities PLANIMETER(1)NAMEPlanimeter-- compute the area of geodesic polygons
SYNOPSISPlanimeter [ -r ] [ -s ] [ -l ] [ -e a f ] [ -w ] [ -p prec ] [ -G | -E
| -Q | -R ] [ --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 (i.e., non-self-intersecting) 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. 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.
-w when reading geographic coordinates, longitude precedes latitude
(this can be overridden by a hemisphere designator, N, S, E, W).
-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.
-G use the series formulation for the geodesics. This is the default
option and is recommended for terrestrial applications. This
option, -G, and the following three options, -E, -Q, and -R, are
mutually exclusive.
-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.)
-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.
-R The lines joining the vertices are rhumb lines instead of
geodesics.
--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 ALSOGeoConvert(1), GeodSolve(1).
An online version of this utility is availbable at
<http://geographiclib.sourceforge.net/cgi-bin/Planimeter>.
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 <https://dx.doi.org/10.1007/s00190-012-0578-z>; addenda:
<http://geographiclib.sf.net/geod-addenda.html>.
AUTHORPlanimeter was written by Charles Karney.
HISTORYPlanimeter was added to GeographicLib, <http://geographiclib.sf.net>,
in version 1.4.
GeographicLib 1.45 2015-09-30 PLANIMETER(1)
