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.