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From: moran@p.cs.uiuc.edu
Newsgroups: comp.graphics
Subject: Re: Tesselating the sphere
Message-ID: <77100013@p.cs.uiuc.edu>
Date: 25 Feb 90 01:31:14 GMT
References: <155@tacitus.tfic.bc.ca>
Lines: 21
Nf-ID: #R:tacitus.tfic.bc.ca:155:p.cs.uiuc.edu:77100013:000:1073
Nf-From: p.cs.uiuc.edu!moran    Feb 23 20:58:00 1990


A few months ago, I was looking for a way to generate a set of points
which would be perfectly distributed on the face of a unit sphere.
(Perfectly distributed meaning that all the solid angles between each point
and its neighbors would be equal).  The quantity needed to be in
the range 1000 to about 4000.  I came up with an idea similar to
that described previously, starting with a tetrahedron, subdividing
each face into four triangles, then normalizing all the new vertices
so they are on the sphere.  It was only after implementing this that
I learned about Platonic solids and the fact that there is no perfect
distribution for such a number of points.

Anyhow, I have C code which takes one argument n and outputs 4**n
points in spherical coordinates using the algorithm above.  Interally,
the program represents each face as the three cartesian points in
three space.  This isn't a very memory efficient to do it, but it makes
for a simpler program.  If anyone wants a copy, send me e-mail.

Pat Moran
University of Illinois at Urbana-Champaign
moran@cs.uiuc.edu