PLANIMETER(1)						      GeographicLib Utilities						     PLANIMETER(1)

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 '(),
	' ' ' | 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
%s
%s
%s

", 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)