Tor Olav Kristensen wrote:
> It will in some cases be possible to
> find spheres with smaller radii, that
> encloses the tetrahedron.
> 
> And in these cases only 2 or 3 of the
> 4 points (vertices) will be on the surface
> of the sphere. The other 2 or 1 will be
> inside it.
> 
> The problem is now to find the bounding
> sphere with the smallest radius.

I seem to remember the sequence goes something like this:

Find the two points furthest apart and set a sphere so that they are on 
the diameter. If both other points are inside the sphere you are done.

If one or two points are outside the sphere find the point furthest 
outside the sphere. Produce the sphere that has the circumcircle of the 
three points as its great-circle. If the fourth point is inside this 
sphere you are done.

Otherwise find the sphere with all four points on the surface.

I think this is right ...

Mike Andrews.

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