Re: covering a sphere with patches

Joe Heafner:
> 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.
>
> Joe Heafner
I don't think there is any "standard" algorithm.
Perhaps you should have written what DID you try...
And, what are your restrictions concerning patches?

There are of course some trivial ways. Map into your sphere through the 
central projection one of the following:
1. A tetrahedron
2. A cube (this is known as the Cobe Sky Cube...)
3. A dodecahedron.
Voilà. May I suggest one more? Thanks...
4. An icosahedron...   (http://space.mit.edu/home/tegmark/icosahedron.gif)

OK, I know, I forgot the octahedron...
Then, the subdivision of the faces you obtain into smaller ones should 
not be too difficult.

Jerzy Karczmarczuk

PS. People who want always have one nice mathematical formula for some 
spherical problems too often forget that it is not necessary to have two 
singularities at the poles, just one is possible with the stereographic 
projection. But the distortions are awful...

**

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