In polygon mode, Planimeter (version 2.4) calculates the perimeter and area of a polygon whose edges are either geodesics or rhumb lines on the WGS84 ellipsoid. In polyline mode, it calculates the length of the geodesic or rhumb line path joining the points.
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 paths, and in that case, the polygon is not uniquely specified by its vertices. In such cases, insert an additional vertex near the middle of the long edge to define the boundary of the polygon.
Counter-clockwise traversal of a polygon results in a positive area. Arbitrarily complex polygons are allowed. In the case of self-intersecting polygons the area is accumulated "algebraically", i.e., the areas of the 2 loops in a figure-8 polygon will partially cancel. There is no need to close the polygon. Polygons may include one or both poles.
Give the vertices in terms of latitude and longitude, for example (these all refer to the position of Timbuktu):
16.776 -3.009
16d47' -3d1'
W3°0'34" N16°46'33"
3:0:34W 16:46:33N
A blank line or a coordinate which cannot be understood
causes the reading of vertices to be stopped.
The ellipsoid is specified by its equatorial radius, a, and its flattening, f = (a − b)/a, where b is the polar semi-axis. The default values for these parameters correspond to the WGS84 ellipsoid. The method is accurate for −99 ≤ f ≤ 0.99 (corresponding to 0.01 ≤ b/a ≤ 100). Note that f is negative for a prolate ellipsoid (b > a) and that it can be entered as a fraction, e.g., 1/297.
For moderately complex polygons, the perimeter is accurate to about 200 nm and the area is accurate to about 0.1 m2.
Planimeter, which is a simple wrapper of the GeographicLib::PolygonAreaT class, is one of the utilities provided with GeographicLib. Geodesic areas can also be computed using JavaScript; see the JavaScript geodesic calculator. If you wish to use Planimeter directly, download and compile GeographicLib. The algorithms are described in C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43–55 (2013); DOI: 10.1007/s00190-012-0578-z; addenda: geod-addenda.html and C. F. F. Karney, The area of rhumb polygons, Stud. Geophys. Geod. (2024); DOI: 10.1007/s11200-024-0709-z.