1PLANIMETER(1) GeographicLib Utilities PLANIMETER(1)
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6 Planimeter -- compute the area of geodesic polygons
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9 Planimeter [ -r ] [ -s ] [ -l ] [ -e a f ] [ -w ] [ -p prec ] [ -G | -E
10 | -Q | -R ] [ --comment-delimiter commentdelim ] [ --version | -h |
11 --help ] [ --input-file infile | --input-string instring ] [
12 --line-separator linesep ] [ --output-file outfile ]
13
15 Measure the area of a geodesic polygon. Reads polygon vertices from
16 standard input, one per line. Vertices may be given as latitude and
17 longitude, UTM/UPS, or MGRS coordinates, interpreted in the same way as
18 GeoConvert(1). (MGRS coordinates signify the center of the
19 corresponding MGRS square.) The end of input, a blank line, or a line
20 which can't be interpreted as a vertex signals the end of one polygon
21 and the start of the next. For each polygon print a summary line with
22 the number of points, the perimeter (in meters), and the area (in
23 meters^2).
24 The edges of the polygon are given by the shortest geodesic between
26 consecutive vertices. In certain cases, there may be two or many such
27 shortest geodesics, and in that case, the polygon is not uniquely
28 specified by its vertices. This only happens with very long edges (for
29 the WGS84 ellipsoid, any edge shorter than 19970 km is uniquely
30 specified by its end points). In such cases, insert an additional
31 vertex near the middle of the long edge to define the boundary of the
32 polygon.
33 By default, polygons traversed in a counter-clockwise direction return
35 a positive area and those traversed in a clockwise direction return a
36 negative area. This sign convention is reversed if the -r option is
37 given.
38 Of course, encircling an area in the clockwise direction is equivalent
40 to encircling the rest of the ellipsoid in the counter-clockwise
41 direction. The default interpretation used by Planimeter is the one
42 that results in a smaller magnitude of area; i.e., the magnitude of the
43 area is less than or equal to one half the total area of the ellipsoid.
44 If the -s option is given, then the interpretation used is the one that
45 results in a positive area; i.e., the area is positive and less than
46 the total area of the ellipsoid.
47 Arbitrarily complex polygons are allowed. In the case of self-
49 intersecting polygons the area is accumulated "algebraically", e.g.,
50 the areas of the 2 loops in a figure-8 polygon will partially cancel.
51 Polygons may include one or both poles. There is no need to close the
52 polygon.
53
55 -r toggle whether counter-clockwise traversal of the polygon returns a
56 positive (the default) or negative result.
57 -s toggle whether to return a signed result (the default) or not.
59 -l toggle whether the vertices represent a polygon (the default) or a
61 polyline. For a polyline, the number of points and the length of
62 the path joining them is returned; the path is not closed and the
63 area is not reported.
64 -e a f
66 specify the ellipsoid via the equatorial radius, a and the
67 flattening, f. Setting f = 0 results in a sphere. Specify f < 0
68 for a prolate ellipsoid. A simple fraction, e.g., 1/297, is
69 allowed for f. By default, the WGS84 ellipsoid is used, a =
70 6378137 m, f = 1/298.257223563. If entering vertices as UTM/UPS or
71 MGRS coordinates, use the default ellipsoid, since the conversion
72 of these coordinates to latitude and longitude always uses the
73 WGS84 parameters.
74 -w toggle the longitude first flag (it starts off); if the flag is on,
76 then when reading geographic coordinates, longitude precedes
77 latitude (this can be overridden by a hemisphere designator, N, S,
78 E, W).
79 -p prec
81 set the output precision to prec (default 6); the perimeter is
82 given (in meters) with prec digits after the decimal point; the
83 area is given (in meters^2) with (prec - 5) digits after the
84 decimal point.
85 -G use the series formulation for the geodesics. This is the default
87 option and is recommended for terrestrial applications. This
88 option, -G, and the following three options, -E, -Q, and -R, are
89 mutually exclusive.
90 -E use "exact" algorithms (based on elliptic integrals) for the
92 geodesic calculations. These are more accurate than the (default)
93 series expansions for |f| > 0.02. (But note that the
94 implementation of areas in GeodesicExact uses a high order series
95 and this is only accurate for modest flattenings.)
96 -Q perform the calculation on the authalic sphere. The area
98 calculation is accurate even if the flattening is large, provided
99 the edges are sufficiently short. The perimeter calculation is not
100 accurate.
101 -R The lines joining the vertices are rhumb lines instead of
103 geodesics.
104 --comment-delimiter commentdelim
106 set the comment delimiter to commentdelim (e.g., "#" or "//"). If
107 set, the input lines will be scanned for this delimiter and, if
108 found, the delimiter and the rest of the line will be removed prior
109 to processing. For a given polygon, the last such string found
110 will be appended to the output line (separated by a space).
111 --version
113 print version and exit.
114 -h print usage and exit.
116 --help
118 print full documentation and exit.
119 --input-file infile
121 read input from the file infile instead of from standard input; a
122 file name of "-" stands for standard input.
123 --input-string instring
125 read input from the string instring instead of from standard input.
126 All occurrences of the line separator character (default is a
127 semicolon) in instring are converted to newlines before the reading
128 begins.
129 --line-separator linesep
131 set the line separator character to linesep. By default this is a
132 semicolon.
133 --output-file outfile
135 write output to the file outfile instead of to standard output; a
136 file name of "-" stands for standard output.
137
139 Example (the area of the 100km MGRS square 18SWK)
140 Planimeter <<EOF
142 18n 500000 4400000
143 18n 600000 4400000
144 18n 600000 4500000
145 18n 500000 4500000
146 EOF
147 => 4 400139.53295860 10007388597.1913
148 The following code takes the output from gdalinfo and reports the area
150 covered by the data (assuming the edges of the image are geodesics).
151 #! /bin/sh
153 egrep '^((Upper|Lower) (Left|Right)|Center) ' |
154 sed -e 's/d /d/g' -e "s/' /'/g" | tr -s '(),\r\t' ' ' | awk '{
155 if ($1 $2 == "UpperLeft")
156 ul = $6 " " $5;
157 else if ($1 $2 == "LowerLeft")
158 ll = $6 " " $5;
159 else if ($1 $2 == "UpperRight")
160 ur = $6 " " $5;
161 else if ($1 $2 == "LowerRight")
162 lr = $6 " " $5;
163 else if ($1 == "Center") {
164 printf "%s\n%s\n%s\n%s\n\n", ul, ll, lr, ur;
165 ul = ll = ur = lr = "";
166 }
167 }
168 ' | Planimeter | cut -f3 -d' '
169
171 GeoConvert(1), GeodSolve(1).
172 An online version of this utility is availbable at
174 <https://geographiclib.sourceforge.io/cgi-bin/Planimeter>.
175 The algorithm for the area of geodesic polygon is given in Section 6 of
177 C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43-55 (2013);
178 DOI <https://doi.org/10.1007/s00190-012-0578-z>; addenda:
179 <https://geographiclib.sourceforge.io/geod-addenda.html>.
180
182 Planimeter was written by Charles Karney.
183
185 Planimeter was added to GeographicLib,
186 <https://geographiclib.sourceforge.io>, in version 1.4.
187GeographicLib 1.51 2020-11-22 PLANIMETER(1)