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From: lambert@cheops.eecs.unsw.oz (Timothy Lambert)
Newsgroups: comp.graphics
Subject: Re: smallest sphere enclosing a set of
Message-ID: <1451@cheops.eecs.unsw.oz>
Date: 8 Dec 89 03:18:41 GMT
References: <207400043@s.cs.uiuc.edu>
Organization: EE & CS, Uni N.S.W., Sydney, Australia
Lines: 16

/* Written  9:18 pm  Nov 28, 1989 by rwang@caip.rutgers.edu in s.cs.uiuc.edu:comp.graphics */
I need the solution for the following problem:
find the smallest sphere that encloses a set of given points, in both
2-D and 3-D (or even n-D, if you like).
/* End of text from s.cs.uiuc.edu:comp.graphics */

 From article <207400043@s.cs.uiuc.edu>, by mcooper@s.cs.uiuc.edu:
> find the two points which are farthest away from one another.  1/2 the
> distance between them is the diameter of your enclosing circle/sphere.  Center
> your circle/sphere on the halfway point of the line between them.

I'm afraid this doesn't work.  Try the vertices of an equilateral triangle
for a counter-example.  See "Computational Geometry" by Preparata and Shamos
for an answer to the 2D case.

Tim