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*Subject*: Re: area enclosed by a poylgon on a sphere*From*: Craig Markwardt <craigmnet(at)cow.physics.wisc.edu>*Date*: 03 Aug 1999 11:02:35 -0500*Newsgroups*: comp.lang.idl-pvwave*Organization*: U. Wisc. Madison Physics -- Compact Objects*References*: <7o4m5g$uvv$1@nnrp1.deja.com> <37A707EA.3C237551@ssec.wisc.edu>*Reply-To*: craigmnet(at)cow.physics.wisc.edu*Xref*: news.doit.wisc.edu comp.lang.idl-pvwave:15958

Nick Bower <nick.bower@ssec.wisc.edu> writes: > > > > I need to be able to find the area enclosed by an arbitrarily shaped > > series of lat/lon points on the surface of the Earth. I have been told > > that I can solve this using Green's Theorem, but before I gut through > > the math I was hoping that someone would have solved this and be willing > > to share the code. If it is already in IDL that would be great, but any > > language will do. > > What does area in lat's and lon's mean? Since there is no unique > "square lat/lon" area unit, you'd have to use a projection at some point > I would guess. Don't have any code then for the area - always used > ArcView for this type of thing. But maybe it's possible to project, > pick a point inside a *convex* polygon, connect it with each vertex and > find the summed area of triangles. You'd end up with an area, but it's > specific to your spheroid/projection pair. Sorry if it's not what > you're after, as there's a real chance you won't have a convex shape. My guess is that he's after the area of the surface defined by the lat/lon points on the sphere (I assume boundary lines joining the points would be great circles). This is equivalent to finding the solid angle enclosed by the points. There is a relatively simple formula involving a sum of vector cross products which compute the area of any planar polygon, so there must be an analogous form on the surface of a sphere. Unfortunately, it doesn't come to mind immediately. Craig -- -------------------------------------------------------------------------- Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response --------------------------------------------------------------------------

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

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