Fran & Melissa wrote:

> >is nonlinear transformations, but the reason that hasn't been done is nobody
> >knows how to do it.
>
> The last bit about the non-linear transformations....
> Don't have any idea how to do this but something like
> matrix {
>     <formula,formula,formula>
> etc
>
> Sorta like a translation matrix.
> So to get the new point, take old point and move( change) by formula amount.
> Just an idea. anyway


First of all, you really mean a transformation vector rather than a matrix.
Second, this sort of transformation is very easy to do if you want to plot a
number of points, but in ray-tracing, you cast rays and aim at finding out where
the objects intersect these rays, for this reason ray-tracing with a
transformation vector as you suggest is either extremely computer intensive
(many samples to have some sort of accuracy as to where the ray intersects an
object) or impossible if you really want exact intersections (as far as numeric
calculation allows) because for most of these mathematical equations it is
impossible to have a set of equations that describe the set of solutions. So you
have to give up this very nice fancy idea and restrict it to an easier
mathematical game, for example if you limit your functions to polynoms of degree
2, that makes it degree 6 as a whole, for this there exists powerful root
solvers. Such functions can be nice but you pretty quickly find lots of limits
to what you can do with them, you can only distort your objects in some set
patterns, nothing really weird. Another step is to look for more complex
equations for which we can find roots with a few iterations (not many), ... I'm
working on that sort of possibility but you'll have to wait a few years, unless
someone else comes up with it before I do.

Cheers,
Al.

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