Re: covering a sphere with patches

On 2012-4-17 10:12, Joe Heafner wrote:
> Can someone direct me to an algorithm for covering a sphere with
> patches of equal area for the purposes of illustrating the surface
> integral in Gauss's law? I've tried three so far and can't get
> good results. The problem is mostly with the poles and in the
> foreshortening of the patches near the poles. Is there a standard
> algorithm for this somewhere? Rectangular surfaces are easy.

The key thing to remember is that equally spaced parallel planes cut the 
sphere into bands of equal area.

http://maths.anu.edu.au/~leopardi/Leopardi-Sphere-PhD-Thesis.pdf (5.8MB) 
gives a partition of the sphere into relatively compact "rectangles" of 
equal area.  I think it even covers spheres of higher dimension.

-- 
Anton Sherwood *\\* www.bendwavy.org *\\* www.zazzle.com/tamfang

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