From: steve@hcrlgw (Steven Collins)
Subject: Re: Sphere from 4 points?
Organization: Central Research Lab. Hitachi, Ltd.
Lines: 27
Nntp-Posting-Host: hcrlgw

In article <1qkgbuINNs9n@shelley.u.washington.edu> bolson@carson.u.washington.edu (Edward Bolson) writes:
>Boy, this will be embarassing if it is trivial or an FAQ:
>
>Given 4 points (non coplanar), how does one find the sphere, that is,
>center and radius, exactly fitting those points?  I know how to do it
>for a circle (from 3 points), but do not immediately see a 
>straightforward way to do it in 3-D.  I have checked some
>geometry books, Graphics Gems, and Farin, but am still at a loss?
>Please have mercy on me and provide the solution?  

Wouldn't this require a hyper-sphere.  In 3-space, 4 points over specifies
a sphere as far as I can see.  Unless that is you can prove that a point
exists in 3-space that is equi-distant from the 4 points, and this may not
necessarily happen.

Correct me if I'm wrong (which I quite possibly am!)

steve
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| Steven Collins			| email: steve@crl.hitachi.co.jp |
| Visiting Computer Graphics Researcher	| phone: (0423)-23-1111 	 |
| Hitachi Central Research Lab. Tokyo.	| fax:   (0423)-27-7742		 |
