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.

GeographicLib 1.21                                 2012-04-24                                      PLANIMETER(1)