Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!uunet!dg!mpogue
From: mpogue@dg.dg.com (Mike Pogue)
Newsgroups: comp.graphics
Subject: Re: Tesselating the sphere
Message-ID: <271@dg.dg.com>
Date: 19 Feb 90 20:17:32 GMT
References: <155@tacitus.tfic.bc.ca>
Reply-To: uunet!dg!mpogue (Mike Pogue)
Organization: Data General, Westboro, MA.
Lines: 24

In article <155@tacitus.tfic.bc.ca> clh@tfic.bc.ca (Chris Hermansen) writes:
> Tessellating the sphere discussion....


  It so happens that I am working on this right now (in my copious spare time).
The geometry is well-known, and has been used by good ole Bucky Fuller for quite
a few years.

  The method you suggest is basically correct.  Take an octahedron, and subdivide 
into triangles.  Project each intersection point out to a sphere (or spheroid, 
ellipsoid, or other superquadric).  Convert back to Cartesian coordinates, and
voila!

  You can also start with an icosahedron, and you get a better approximation, but
structurally it acts quite different (I'm interested from the geodesic dome
point of view).

  I have ray traced a 4-frequency octahedron, which looks quite nice....The code to
generate is quite simple (I'm writing a paper on it right now for publication).  Icosahedron
is a bit more complex, having a more complicated arrangement of sides.

Mike Pogue

I speak for myself, not my company....