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Stereographic Projection for general surfaces

  1. Stereographic Projection for "general" surfaces

    First off, sorry if this is in the wrong forum. I came across this while studying computer vision, but it's of a somewhat mathematical nature. Please move it if it's in the wrong place.

    In the book I'm reading*, stereographic projection is used to generate a reflectance map of an illuminated surface. A similar approach can be found here: http://books.google.com/books?id=XEOsAAAAIAAJ&pg=PA117&source=gbs_toc_r&cad=0_0#PPA154,M1 (that link should get you to page 154 of a book called "Computer Vision" by Michael Brady and H. G. Barrow)

    My problem is this: the stereograpic projection is put forward for a sphere, then (apparently) generalised to more general surfaces. However this generalisation isn't made explicit. What is it? Am I missing something really simple? EDIT: From further reading, I've come across the Gaussian sphere, which seems to play a role here...but the details are still a little hazy to me.

    Many thanks in advance!

    *"Artificial Intelligence" 2 ed. by Patrick Henry Wilson, picked up at a local charity shop for £2.99 :-)
     
    Last edited: Dec 22, 2008
  2. jcsd
  3. Re: Stereographic Projection for "general" surfaces

    Um, it looks like the book you linked to was just using the projection to parameterize the sphere, and thus the set of surface orientations. Of course, this parameterization will induce local coordinate systems for most places on suitably well-behaved surfaces (is this the ultimate goal? Google wouldn't let me read very far). What did the other book say that makes you think that you need to generalize directly.
     
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