Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!eecae!cps3xx!flynn
From: flynn@pixel.cps.msu.edu (Patrick J. Flynn)
Newsgroups: comp.graphics
Subject: Re: Polygon Representation of a Sphere's Surface
Message-ID: <2264@cps3xx.UUCP>
Date: 23 Mar 89 12:35:41 GMT
References: <270@ai.etl.army.mil> <2908@kalliope.rice.edu>
Sender: usenet@cps3xx.UUCP
Reply-To: flynn@pixel.cps.msu.edu (Patrick J. Flynn)
Organization: Pattern Rec. & Img. Processing Lab, CS, Michigan State Univ.
Lines: 34

In article <2908@kalliope.rice.edu> foo@titan.rice.edu (Mark Hall) writes:
>In article <270@ai.etl.army.mil> richr@ai.etl.army.mil. (Richard Rosenthal) writes:
>>I want to have in 3-D space (x, y, z) a polygon near-representation
>>of the surface of a sphere where each polygon is identical
>>and regular (if that's the word). Is an icosahedron the right place to start?
>>I would like to be able to generate the representation with
>>increasing numbers of polygons, say first 20, and then
>>say 80.
>
>  I think you are going to have a problem. As I remember the argument 
> from a class a few years ago: 
>  One way to tile a sphere with regular (all sides/angles equal) polyhedra 
> is to take a regular solid centered at the sphere's center. Project 
> the edges of the solid onto the sphere. Works just fine. 
>  The kicker is that there are only 5 known regular solids.

Actually, one popular method of constructing a tesselation of the sphere
*starts* with a regular polyhedron (usually the icosahedron) and repeatedly
subdivides each facet into triangles.  The common method is to divide each
edge of a facet into k equal-length segments and construct k**2 equilateral
triangles from the original.  Each of these triangles can then be subdivided
to the desired resolution.

Ballard and Brown, "Computer Vision", p. 492 has a recipe for constructing
the icosahedron.

Also see

C. Brown, "Fast Display of well-tesselated surfaces", Computers and Graphics,
v. 4, p. 77-85, 1979.
--
Pat Flynn, CS, Mich. State U. | "What kind of chump do you take me for?" -Nick
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