> I have a mesh, I want to find the smallest possible bounding sphere that
> encompasses all the points.

This is a really interesting problem.

After thinking about it a bit, the only solution I can come up with is that
if you find the two points which are farthest apart, and then center the
sphere right between them, with a radius of (their distance
apart)/2*sqrt(3), all of the points will be in that sphere. (The sqrt(3) is
necessary because there could be a third point forming an equilateral
triangle with the first two.)

However, I'm tempted to think that there's a possible solution that will
find it perfectly. Maybe something like starting with a tiny (r=0) sphere in
the midst of the points, and growing its radius and moving it around to make
it encompass one point after another... I dunno.

 - Slime
[ http://www.slimeland.com/ ]

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