"Timothy R. Cook" wrote:
> I remember my HS chemistry book that had a small portion of
> Heisenberg's uncertainty formula, and an image of the solution
> to the whole thing...if THAT can be done, I'm sure a complex
> isosurface with noise and an atanh julia fractal could be done ;)

Well, you know, of course, that there is no general analytical solution to
find the roots of a polynome of sufficient degres (sufficient being more
than 4, IIRC). Nevertheless, it is possible to make an image of any polynome.

And some integration are impossible to perform mathematically, whereas computing
the value is done more easily. And some other, when using Mapple, take a very long
time and are really very long.

To go with the suggested method, you would have to stay as much as possible
analytic, avoiding all numerisations. I believe you would need to cross
the code of Mapple with a renderer. The interesting possible result would
be a RGBA formula for each pixel, this formula being dependent on all the
scene setting (objects, positions, textures, ior and so on).
The good thing is: you render once, and unless you remove/add an object or
replace a texture to drastically, you get 'instant-rendering' of multiple
variant (animation without #if/#switch, test of various mapping, variation
of IOR...)
The bad thing is: their is one enormous formula per pixel, and the time to 
evaluate it is also enormous.

The problem of anti-aliasing vs moire is badly answered with only a method
which use a discret ray.
If every object had a method to which a container ray(*) could be tested and
the answer was not the intersection point, but the amount of section intersected,
then it would be easier.

But there is a big gotcha: transforming a line in object space always result in
a line. But transforming a container ray, you might end up with very strange figure,
and the math are not easy.

(*): imagine a semi-infinite box (limited by only 5 perpendicular planes)

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