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From: rick@hanauma.stanford.edu (Richard Ottolini)
Newsgroups: comp.graphics
Subject: Re: Tesselating the sphere
Message-ID: <509@med.Stanford.EDU>
Date: 25 Feb 90 17:17:07 GMT
References: <155@tacitus.tfic.bc.ca> <77100013@p.cs.uiuc.edu>
Sender: news@med.stanford.edu (USENET News System)
Reply-To: rick@hanauma.UUCP (Richard Ottolini)
Organization: Stanford University, Dept. of Geophysics
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In article <77100013@p.cs.uiuc.edu> moran@p.cs.uiuc.edu writes:
>
>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.

Some mathematician proved that was impossible, but you can get very close.
If you subtriangulate the triangles of a polyhedron most vertices will have
six edges except some of those of the original polyhedron.

A collegue of mine, chuck@hanauma.stanford.edu, propagated seismic waves on
a spherical mesh derived from a subtriangulated icosahedron.  The asymmetries
of the original twelve vertices still caused numerical artifacts in the
wave equation even when triangulated to 160K triangles.  He significatly
attenuated artifacts by equalizing triangular areas as a least squares problem
even though the resulting movement of the vertices was miniscule.