yesbird wrote:

> > Why do you need a parametric?  Are you trying to create a mesh to decrease
> > render time?
>
> Yes, my latest project - online editor for math surfaces and curves
> assumes equations in parametric forms. MathView now in stable beta stage
> and ready to be filled with a content, I am already have a large list
> of candidates to this collection, fortunately they are free :).

Hmmm.
Parameterizing is usually difficult - if not impossible for complex implicit
equations.
I'd try a variety of software packages / approaches:  Maple, etc.

Also just try to search and see what you can find.
Sometimes I find very recent solutions to projects/problems that I put to the
side only a year or two before.
Also post what you're trying to do on StackExchange/Overflow, etc. and see if
any of the people over there have any ideas, references, or solutions.
Track down anyone who has ever played with these things and see if they have any
ideas. (Jos Leys, Paul Nylander, Etienne Ghys, math professors, etc)

And then maybe just try some crazy stuff - just to see what happens.
Express everything in terms of complex numbers, or invert them through a unit
sphere and see what pops out the other end.
See if there's some 4th dimensional way to approach it.  <x, y, z, w>
Sometimes you can do what seems to make things more complex, but get a result
that is easier to process in that other "space".
So if you're able to do something like that, you might be able to parameterize
the transformed equation, and then transform it back.


One thing that you CAN do in order to speed things up is take advantage of the
symmetry of these surfaces and only calculate a part of it - then just transform
the result to cover the other areas.
So, for those surfaces that have a dodecahedron nested inside, that means there
are parts of it to match each of its 20 vertices.  So if you calculated only one
and "copied" the rest, that's 1/20th of the calculation needed.

- BW

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