Re: area enclosed by a poylgon on a sphere

[Craig Markwardt <craigmnet(at)cow.physics.wisc.edu>]

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
--------------------------------------------------------------------------