This is adapted from the code provided for me by Mike Williams in p.a-u 
(thread "arbitrary remapping").  In the left sphere, the -z pole is in 
the bigger of the two tiny red triangles.  The pigment of that sphere is 
conformally mapped twice around the right sphere, resulting in 
distortions of size but preservation of local angle; you can see two 
copies of everything that surrounds that polar spot (which is much 
magnified, and now has six corners instead of three).

-- 
Anton Sherwood, http://www.ogre.nu/

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