[help-3dldf] Polyhedra and ellipses

[Laurence Finston]

Hello Martijn et al,

I've taken another look at what you've written.
I can see there's a lot to say about the Platonic polyhedra, and I shouldn't
be in such a hurry to get to the more "exciting" ones.  However, I'd still
like to know whether it's possible to find the vertices of the Archimedean
polyhedra, their duals, and the Kepler-Poinsot polyhedra the way you do for
the Platonic ones.

Someone recommended the book _An Introduction to Solid Modeling_ by Martti
Maentylae, and I ordered it through inter-library loan. 
It came today, and while it discusses polyhedra in general, it doesn't go into
these kinds of polyhedra.  I'm not really surprised, because _none_ of the
books on computer graphics I've looked at do (and I've looked at quite a few
and even bought a couple).  The people who program screen savers seem to know
how to do it, though, unless they just fold up virtual cardboard models, too. 


I may actually try to implement your method for finding ellipse intersections
for the coming release.  The math doesn't seem too difficult, and if you can
give me a formula I can just go ahead and program it without learning linear
algebra and analytic geometry first.  I don't mind if the formula's a bit
complicated. 
It would certainly be worth the effort.

I think it should be possible to pretest whether the ellipses are tangent.  
For this, however, it will make a difference whether the axes of the ellipses
are parallel and perpendicular, since this case will be easy to test.  I think
it might be possible to test whether they're too far apart to be tangent, or
whether one lies completely inside another with no tangents, even if their
axes are non-parallel and non-perpendicular.  Do you know whether there's a
way of finding the point on an ellipse that's closest to another ellipse, or
would this be just as hard as finding the tangent points?

Thanks again for all your help.

Laurence