Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!usc!apple!netcom!rodent
From: rodent@netcom.COM (Ben Discoe)
Newsgroups: comp.graphics
Subject: Re: recursive sphere tesselation from tetrahedral seed
Message-ID: <1991Apr18.015350.24184@netcom.COM>
Date: 18 Apr 91 01:53:50 GMT
References: <1991Apr15.171109.2625@rice.edu> <3221@borg.cs.unc.edu>
Organization: Netcom - Online Communication Services  UNIX System {408 241-9760 guest}
Lines: 44

leech@homer.cs.unc.edu (Jonathan Leech) writes:
> [Concerning tesselating a tetrahedron]
>    I think it's just a bit odd-looking for the first few levels due
>to the odd symmetry of a tetrahedron compared to an octahedron, which
>has 3 perpendicular symmetry planes.  It looks fine by the 3rd or 4th
>subdivision level.

>    While checking this out, I modified my sphereoid generator (the
>one mentioned in the FAQ) to start with either tetrahedrons or
>octahedrons (somebody was going to contribute an icosahedron but
>hasn't yet).  Interested parties can retrieve it by anonymous ftp from
>ftp.cs.unc.edu:~pub/sphere.c
>
>    Jon Leech (leech@cs.unc.edu)    __@/

  My small 3d editor has a "frequency" feature which will raise any collection
of triangular faces to a given frequency (this is Buckminster Fuller-speak
for tesselating all faces to an equivalent degree).  In fact, this is the
only really neat feature of the editor (it's written for the Amiga, in case
anyone wants a copy).  Allowing "square" faces to also be tesselated in the
same operation would be an improvement, but I was unable to establish
an analogous geometric operation for faces with more than 4 sides
(although it's fun trying).  You need to tesselate 4-sided faces in order
to do the vector equilibrium ("cuboctahedron"), a worthy polyhedron.

  It's fun and easy to make your own geodesic spheres:
A. pick your favorite regular or irregular polyhedron 
B. raise it to the desired frequency (using above mentioned code)
C. normalize points to equidistant from their center (trivial)

Presto!  If anyone wants the Amiga code, ask me.  Now, I have two favors to
ask:	1. Anyone have any keen ideas on how to tesselate n-gons
	   with n>4?
	2. Anyone know where I can find C code to a 3D convex hull
	   algorithm?  I got _Computational Geometry: an introduction_
	   but the algorithm is abstract and gnarly.  This would enable
	   the user to simply define a few 3D points, do a convex hull
	   wrap, then go to step (A.) above.

To be precise, the above method is only one way (and not the "true" way)
to generate a geodesic sphere.  The "true" method involves dividing the
spherical angles, but the method mentioned isn't too far off.
----------
Ben Discoe, radical ecologist, computer scientist, loony at large :)