Path: utzoo!mnetor!uunet!husc6!mit-eddie!bbn!uwmcsd1!ig!agate!saturn!skinner
From: skinner@saturn.ucsc.edu (Robert Skinner)
Newsgroups: comp.graphics
Subject: Defining a sphere with Bezier patches
Message-ID: <2390@saturn.ucsc.edu>
Date: 16 Mar 88 16:32:48 GMT
Organization: U.C. Santa Cruz, CIS/CE.
Lines: 22
Keywords: sphere, Bezier, REYES

In the 1987 Siggraph article on the REYES architecture, Cook, Carpenter
& Catmull state that a sphere can be defined by 32 patches.  They give
Computational Geometry for Design and Manufacture, by Faux and Pratt,
as the reference.  For some reason, I can't find anything in F&P that
says how to do this.  

The closest I get is a formula for a Bezier CURVE that is very close
to a circular arc of 90 degrees.  Starting with that, I can define 3
of the Bezier boundaries as great arcs on the sphere and the fourth is
a point at the pole.  This still leaves the center 4 points of patch
undefined.  Besides that, this would only use 8 patches.  So I suspect
that this has more error than using 32 patches.  

Can someone point out where in F&P this info is encoded?  
Better yet, if you've worked it out already, can you post the patch
definition of the sphere?  (Only 4 patches need to be defined from
symetry (sp))

aTdHvAaNnKcSe
-------------
Robert Skinner
skinner%saturn.ucsc.edu@ucscc.ucsc.edu