Path: utzoo!attcan!uunet!husc6!rutgers!tut.cis.ohio-state.edu!n8emr!uncle!oink!jep
From: jep@oink.UUCP (James E. Prior)
Newsgroups: comp.graphics
Subject: Re: Ray Traced Bounding Spheres
Keywords: Ray trace, bounding volumes, intersection
Message-ID: <22@oink.UUCP>
Date: 11 May 89 19:06:53 GMT
References: <17241@versatc.UUCP>
Reply-To: jep@oink.UUCP (James E. Prior)
Organization: Random Prime Research Institute  Columbus, Ohio
Lines: 25

In article <17241@versatc.UUCP> ritter@versatc.UUCP (Jack Ritter) writes:
>Given a cluster of points in 3 space, is there
>a good method for finding the minumum radius
>sphere which encloses all the points?

I'll try my hand at it:
1) Figure out which pair of points are furthest away from each other.
	(This need not be unique, i.e. this algorithm will work even
	if 2 or 3 of the points are at the same location.)

2) Define Sphere A as having its center halfway between the furthest points,
	and its radius as half the distance between the furthest points.

If the other point lies inside or on Sphere A, then Sphere A is the solution.

Otherwise, the other point lies outside Sphere A, 
and the solution is Sphere B defined as follows:

Sphere B has the same center and radius as the circle defined by the
three points.

It feels right, but I don't guarantee it.  This is the result of my
own mental hacking, and not a reference book.  
-- 
Jim Prior    jep@oink    osu-cis!n8emr!oink!jep    N8KSM