id summary reporter owner description type status milestone component version severity resolution keywords cc 11931 spherical area wrong with pole encircling polygons, etc. Charles Karney Barend Gehrels "The following code illustrates a problem with handling of meridian crossing and pole encircling when computing spherical areas. It computes the area of a 4 identical diamond shaped areas at different positions on the sphere. Only the area of the last of these is computed correctly. The others are badly wrong. {{{#!c++ #include #include #include namespace bg = boost::geometry; typedef bg::model::point > pt; int main() { std::string polys[] = { "" 0 89, 90 89, 180 89, 270 89"", "" 0 -89, -90 -89, -180 -89, -270 -89"", ""-1 0, 0 -1, 1 0, 0 1"", ""89 0, 90 -1, 91 0, 90 1"" }; // Correct area for all these polygons is double area0 = 0.00060926577032113655; bg::model::polygon poly; std::cout << "" area relerr"" << ""\n""; for (int i = 0; i < 4; ++i) { bg::read_wkt(""POLYGON(("" + polys[i] + ""))"", poly); double area = bg::area(poly); std::cout << area << "" "" << (area - area0) / area0 << ""\n""; } } }}} Running this code gives {{{ area relerr 0.000304633 -0.5 -6.28288 -10313.2 0 -1 0.000609266 2.31338e-15 }}} Discussion: * I can't make out the handling of this issue in the current code at all. It seems to be irredeemably broken. * You need to do two things to handle these issues: 1. Make sure that the sign of lambda_2 - lambda_1 correctly corresponds to east and west going edges (with some consistent convention of edges which pass over the pole). 2. Count the number of times the polygon encircles a pole, e.g., by keeping track of when an edge crosses the prime meridian (again with some consistent treatment of cases when one or both ends of an edge lie on the prime meridian). * If this count is odd, then the total area needs to be adjusted by 2*pi, half the area of the sphere. * I believe I've handled these issues correctly in the PolygonAreaT class in [http://geographiclib.sourceforge.net/html/ GeographicLib]. " Bugs closed Boost 1.64.0 geometry Boost 1.58.0 Showstopper fixed area charles.karney@…