Ubuntu Manpage: Planimeter -- compute the area of geodesic polygons

Provided by: geographiclib-tools_2.3-1build1_amd64

NAME

       Planimeter -- compute the area of geodesic polygons

SYNOPSIS

       Planimeter [ -r ] [ -s ] [ -l ] [ -e a f ] [ -w ] [ -p prec ] [ -G | -Q | -R ] [ -E ] [
       --geoconvert-input ] [ --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 are be given as latitude and longitude.  By default latitude precedes longitude, however this
       convention is reversed with the -w flag and a hemisphere designator (N, S, E, W) can be used to
       disambiguate the coordinates.  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 (or rhumb line) between consecutive vertices.
       In certain cases, there may be two or many such shortest path, and in that case, the polygon is not
       uniquely specified by its vertices.  For geodesics, 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.

       Arbitrarily complex polygons are allowed.  In the case of self-intersecting polygons the area is
       accumulated "algebraically", e.g., the areas of the 2 loops in a figure-8 polygon will partially cancel.
       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 a f
specify the ellipsoid via the equatorial radius, a and the flattening, 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 toggle the longitude first flag (it starts off); if the flag is on, then when reading geographic
coordinates, longitude precedes latitude (this can be overridden by a hemisphere designator, N, S, E,
W).

-p prec
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 the edges joining the vertices are geodesics. This is the default option and is recommended for
terrestrial applications. This option, -G, and the following two options, -Q and -R, are mutually
exclusive.

-Q map the points to the authalic sphere and compute the area of the resulting spherical polygon. The
area will be reasonable accurate provided that the edges are sufficiently short. The perimeter
calculation is not accurate.

-R the edges joining the vertices are rhumb lines instead of geodesics.

-E use the exact equations for the geodesic -G, authalic -Q, and rhumb -R calculations instead of series
expansions. For the geodesic and rhumb methods, the area is computed by applying discrete sine
transforms to the integrand in the expression for the area. These are more accurate, albeit slower,
than the (default) series expansions for |f| > 0.02 and will give high accuracy for -99 < f < 0.99.
It is not necessary to specify this option for terrestrial applications.

--geoconvert-input
The input lines are interpreted in the same way as GeoConvert(1) allowing the coordinates for the
vertices to be given as UTM/UPS or MGRS coordinates, as well as latitude and longitude. CAUTION:
GeoConvert assumes the coordinates refer to the WGS84 ellipsoid (disregarding the -e flag) and MGRS
coordinates signify the center of the corresponding MGRS square.

--comment-delimiter commentdelim
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 infile
read input from the file infile instead of from standard input; a file name of "-" stands for
standard input.

--input-string instring
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 linesep
set the line separator character to linesep. By default this is a semicolon.

--output-file outfile
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 --geoconvert-input <<EOF
          18n 500000 4400000
          18n 600000 4400000
          18n 600000 4500000
          18n 500000 4500000
          EOF
          => 4 400139.532959 10007388597.2

       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
          grep -E '^((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' '

ACCURACY

       Using the -G option (the default), the accuracy was estimated by computing the error in the area for 10^7
       approximately regular polygons on the WGS84 ellipsoid.  The centers and the orientations of the  polygons
       were  uniformly  distributed,  the  number of vertices was log-uniformly distributed in [3, 300], and the
       center to vertex distance log-uniformly distributed in [0.1 m, 9000 km].

       The maximum error in the perimeter was 200 nm, and the maximum error in the area was

          0.0013 m^2 for perimeter < 10 km
          0.0070 m^2 for perimeter < 100 km
          0.070 m^2 for perimeter < 1000 km
          0.11 m^2 for all perimeters

AUTHOR

       Planimeter was written by Charles Karney.

HISTORY

       Planimeter was added to GeographicLib, <https://geographiclib.sourceforge.io>, in version 1.4.

GeographicLib 2.3                                  2023-07-25                                      PLANIMETER(1)