NAME¶

Planimeter -- compute the area of geodesic polygons

SYNOPSIS¶

Planimeter [ -r ] [ -s ] [ -l ] [ -e a f ] [ --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). 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 uses the WGS84 parameters.

--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 15 of C. F. F. Karney, Geodesics on an ellipsoid of revolution, Feb. 2011; preprint <http://arxiv.org/abs/1102.1215>. See also Section 6 of C. F. F. Karney, Algorithms for geodesics, Sept. 2011; preprint <http://arxiv.org/abs/1109.4448>.

AUTHOR¶

Planimeter was written by Charles Karney.

HISTORY¶

Planimeter was added to GeographicLib, <http://geographiclib.sf.net>, in version 1.4.