I don't think there is any "standard" algorithm.
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.
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...
OK, I know, I forgot the octahedron...
Then, the subdivision of the faces you obtain into smaller ones
should not be too difficult.
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...