Path: utzoo!attcan!uunet!lll-winken!csd4.milw.wisc.edu!mailrus!tut.cis.ohio-state.edu!rutgers!columbia!cs!beshers From: beshers@cs.cs.columbia.edu (Clifford Beshers) Newsgroups: comp.graphics Subject: Re: Polygon Representation of a Sphere's Surface Message-ID: Date: 23 Mar 89 01:57:47 GMT References: <270@ai.etl.army.mil> <2908@kalliope.rice.edu> Sender: news@cs.columbia.edu Organization: Columbia University Computer Science Lines: 35 In-reply-to: foo@titan.rice.edu's message of 22 Mar 89 23:26:26 GMT In article <2908@kalliope.rice.edu> foo@titan.rice.edu (Mark Hall) writes: Summary: you may have do discover a new "Platonic" solid Lines: 31 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. >Richard Rosenthal Internet: richr@ai.etl.army.mil I think you are going to have a problem. As I remember the argument from a class a few years ago: Not at all. Start with an icosahedron. You now have a polygonal approximation to a sphere where each face is a triangle. Inscribe a triangle inside each face with its vertices at the midpoints of the edges, dividing each face into four triangular regions. Project the three new points onto the surface of the sphere. You now have a a polygonal approximation to a sphere where each face is a triangle. Inscribe a triangle... If you use Gouraud shading, you really don't have to recurse very far to get something that looks very nice. -- ----------------------------------------------- Cliff Beshers Columbia University Computer Science Department beshers@cs.columbia.edu