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Re: area enclosed by a polygon on a sphere
- 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: <firstname.lastname@example.org> <email@example.com>
- Xref: news.doit.wisc.edu comp.lang.idl-pvwave:15964
In article <firstname.lastname@example.org>,
Struan Gray <email@example.com> 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
> 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 :-).
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 Kling Consulting
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