"Dan Johnson" <zap### [at] hotmailcom> wrote in message
news:3DF1C3CD.A9BA456F@hotmail.com...
> Warp wrote:
> >
> > Dan Johnson <zap### [at] hotmailcom> wrote:
> > > Anyone know if this approach
> > > is actually faster than plane intersections?
> >
> >   There was once a long thread in some group about the most efficient
way
> > of making a box with all six sides textured differently.
> >   Several approaches were made and their rendering times measured. For
> > example it was done with the intersection of six planes, the union of
> > six 2-dimensional boxes, six polygons and a mesh. (Also using a single
> > box with a clever pattern was suggested, but that's irrelevant in this
case).
> >   Perhaps a bit surprisingly, with such a low triangle count the mesh
was
> > not the fastest option. I don't remember which one was, but it might
have
> > been the union of polygons. (The problem with it is that it's not usable
> > in CSG.)
>
> Interesting..
>
> >   In your case the intersection of planes might be just ok. You simply
have
> > to manually bound the tetrahedron eg. with a sphere.
>
> If my thinking is correct that can be done such that each vertex is
> exactly on the surface of the sphere.

I bet the Graphics Gems books have code that will allow you to determine a
sphere tangential to 4 points in 3-space.  The code for those books can be
found on-line.

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