Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!swrinde!elroy.jpl.nasa.gov!decwrl!sgi!shinobu!odin!texas.asd.sgi.com!robert
From: robert@texas.asd.sgi.com (Robert Skinner)
Newsgroups: comp.graphics
Subject: Re: recursive sphere tesselation from tetrahedral seed
Message-ID: <1991Apr17.154919.8090@odin.corp.sgi.com>
Date: 17 Apr 91 15:49:19 GMT
References: <1991Apr15.171109.2625@rice.edu>
Sender: news@odin.corp.sgi.com (Net News)
Reply-To: robert@1.com
Organization: Silicon Graphics Inc., Advanced Systems Division
Lines: 43

In article <1991Apr15.171109.2625@rice.edu>, fontenot@comet.rice.edu (Dwayne Jacques Fontenot) writes:
|> 
|> Hello,
|> 
|> I have been playing with recursive triangular sphere tessellations. Starting
|> with an octahedron works beautifully, but since each triangle is split into
|> four triangles at each iteration, the progression of numpolys looks like this:
|> 
|> 	8  32  128  512  2048  8192  ...
|> 
|> I want more flexibility in the number of polygons per sphere. So, I tried
|> starting with a tetrahedron, so that I could get:
|> 
|> 	4  16  64  256  1024  4096  ...
|> 
|> This, plus the above would give me any power of 2, which is probably enough
|> flexibility...
|> 

recursive triangular subdivision is elegant and simple to code, but its
not very flexible, as you point out.  For an M-sided polyhedra, you get
M*2^N polygons, where N is the level of subdivision.  A better choice
is to do non-recursive subdivision of the triangle by some integer
factor K.  You will get K*K smaller triangles from each original
triangle, so the progression of numpolys for an octahedron would be

	8 32 72 128 200 288  ...

and for a tetrahedron would be

	4 16 36 64 100 144  ...

Also, non-recursive subdivision should be (at least marginally)
faster.  You have a lot fewer function invocations, and doing the
subdivision incrementally might help too.

-- 
Robert Skinner
robert@sgi.com

	Is that a pistol in your pocket, or are you just glad to see me?

			-  Mae West