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From: robert@victoria.esd.sgi.com (Robert Skinner)
Newsgroups: comp.graphics
Subject: Re: Tesselating the sphere
Message-ID: <4437@odin.SGI.COM>
Date: 22 Feb 90 17:58:43 GMT
References: <271@dg.dg.com> <155@tacitus.tfic.bc.ca>
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Reply-To: robert@sgi.com
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In article <271@dg.dg.com>, mpogue@dg.dg.com (Mike Pogue) writes:
> In article <155@tacitus.tfic.bc.ca> clh@tfic.bc.ca (Chris Hermansen) writes:
> > Tessellating the sphere discussion....

There is an article that talks about these things in the most
recent issue of IEEE Computer Graphics and Applications:
"Visualizing Functions Over a Sphere", by Foley, Lane, and Nielson.
Jan, 1990.

About the only differences are that they do the triangle tesselation
on the unit sphere, after projection.  That ensures that the triangles
are closer to the same size.  They also point out that recursively 
tesselating each triangle into four results in an exponential
explosion of triangles:  4**k, starting w/ a tetrahedron (4), and
doing k subdivisions.  They found that 1000-8000 triangles were
sufficiently dense for sampling their functions, but for k=5 you get
1024, k=6 yields 4096, and k=7 gives 16K triangles.  

In contrast, you can divide the tetrahedral triangles into k segments 
along each edge, then you get 4*k**2 triangles total.  This grows much
more slowly than the previous method.


Robert Skinner
robert@sgi.com

		Which is worse, ignorance or apathy?
		Who knows?  Who cares?