[help-3dldf] Re: Rotations

[Laurence Finston]

On Tue, 17 Aug 2004, Hans Aberg wrote:

> My hunch is that this, finding exact intersections, is not a topic for a
> graphics program, but a wholly independent set of programs, belonging
> currently to the area of symbolic math and specialty programs for algebraic
> geometry.

I'll just have to do the best I can then, because I really want this
functionality in 3DLDF.  I thought it would be a fairly elementary topic,
but when I looked into it I discovered that intersection theory is
anything but trivial.

>
> I do not see why you get so many points: I just thing of the points
> defining the curves in say a NURBS model. These should be fairly few. These
> are ones want to agree. Then, once this geometric object has been modelled,
> the rendering only takes place within what is possible on the output device.
>

Imagine one of the fancier Archimedian polyhedra in a space with
multiple reflective surfaces, where the reflections can also be reflected.
While smooth curves can possibly be represented by spline curves
using a relatively small number of points, I will need a point
for each vertex of a polyhedron, and then a point for each reflection of
the original point.

Surface hiding can also cause the number of points to
increase rapidly, because one of the methods I will probably have
to use requires
objects to be broken down into smaller sub-objects.

Laurence