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*Subject*: Re: area enclosed by a polygon on a sphere*From*: Ronn Kling <ronn(at)rlkling.com>*Date*: Wed, 04 Aug 1999 00:58:00 GMT*Newsgroups*: comp.lang.idl-pvwave*Organization*: Deja.com - Share what you know. Learn what you don't.*References*: <7o4m5g$uvv$1@nnrp1.deja.com> <7o74n7$aa7$1@news.lth.se>*Xref*: news.doit.wisc.edu comp.lang.idl-pvwave:15964

In article <7o74n7$aa7$1@news.lth.se>, Struan Gray <struan.gray@sljus.lu.se> wrote: > No code, but an idea which essentially uses Green's Theorem. > > 1) convert lat/lon to cartesian coords > 2) use them to make an IDLgrPolygon object > 3) use the IDLgrTessellator object to turn that > into a set of triangles > 4) for each triangle work out the solid angle it > subtends from the centre of the earth > 5) add up the solid angles and convert to an > area. > > Working out the solid angle subtended by an arbitrary > triangle of points on the surface of a sphere is left as an > exercise for the reader (watch out for triplets of points on > the same great circle :-). > > Struan > I found out how to do this today. For a spherical triangle the solid angle subtended is the sum (in radians) of the interior angles - Pi. This can be generalized to any polygon as Area = (sum of all interior angles) - (n-2)*Pi Where n is the number of points. -Ronn -- Ronn Kling Ronn Kling Consulting www.rlkling.com Sent via Deja.com http://www.deja.com/ Share what you know. Learn what you don't.

**Follow-Ups**:**Re: area enclosed by a poylgon on a sphere***From:*Struan Gray

**References**:**area enclosed by a poylgon on a sphere***From:*Ronn Kling

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