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From: lambert@cheops.eecs.unsw.oz (Timothy Lambert)
Newsgroups: comp.graphics
Subject: Re: smallest sphere enclosing a set of points
Message-ID: <1452@cheops.eecs.unsw.oz>
Date: 11 Dec 89 12:19:01 GMT
References: <5497@nucleus.UUCP>
Organization: EE & CS, Uni N.S.W., Sydney, Australia
Lines: 18

From article <5497@nucleus.UUCP>, by mjb@nucleus.UUCP (Mark Bobak):
> Hmm....Could everyone be overlooking the obvious?  It seems to me, for a
> circle, sphere, hypersphere, (in 2D,3D,4D, or N-D for that matter) that will
> enclose a set of points, simply find the max x,y,z and min x,y,z.  Then, the
> center point should be:
> ( Average(maxx,minx),Average(maxy,miny),Average(maxz,minz) )
> Then, your radius would be longest of the distances from center point to any
> point.  I tried a couple examples, let's use (-1,0),(1,0),(0,2) here:
 [Calculation deleted]
> Therefore, we have C(0,1) and radius Sqrt(2).  

This encloses the points but we want the _smallest_ circle.  For three
points this is just the circumcircle which has centre (0,0.75) and radius
1.25.

(You can find the equation for the circumcircle in the CRC tables.)

Tim