From: watson@madvax.uwa.oz.au (David Watson)
Subject: Re: Sphere from 4 points?
Organization: Maths Dept UWA
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In article <1qkgbuINNs9n@shelley.u.washington.edu>, 
bolson@carson.u.washington.edu (Edward Bolson) writes:
 
|> Given 4 points (non coplanar), how does one find the sphere, that is,
|> center and radius, exactly fitting those points?  

Finding the circumcenter of a tetrahedron is discussed on page 33 in

CONTOURING: A guide to the analysis and display of spatial data,
by Dave Watson, Pergamon Press,  1992, ISBN 0 08 040286 0, 321p.

Each pair of tetrahedral vertices define a plane which is a 
perpendicular bisector of the line between that pair.  Express each
plane in the form Ax + By + Cz = D
and solve the set of simultaneous equations from any three of those
planes that have a vertex in common (all vertices are used).  
The solution is the circumcenter.

-- 
Dave Watson                          Internet: watson@maths.uwa.edu.au
Department of Mathematics            
The University of Western Australia               Tel: (61 9) 380 3359
Nedlands, WA 6009  Australia.                     FAX: (61 9) 380 1028