understanding (and plotting) a surface (from implicit to parametric?) 
Possible Duplicate:
Automation of 3D Paper Modeling 

i am a programmer and not a mathematician, and my math knowledge are a little bit rusty. i have found this nice picture surfing on the net:

and i want to replicate it.
as i remember there is written an implicit function, and for plotting i need to transform it in a parametric one. is this right? how can i do?
then, once i have the parametric surface i can iterate over an axis and obtain the slices for replicate this nice paper-work.
i am code agnostic and i can use every opensource tool for mathematical computation (octave/matlab, wolfram alpha, python, java/c/etc).
 A: 
what about transformation of implicit to parametric? is it possible?

Sometimes, but not always. Here is one example of a case where it works. Suppose you have an implicit equation $g(x,y,z)=0$. If you're lucky, then, through each point $(x,y)$ in the $xy$-plane, you can fire a vertical "ray" (parallel to the $z$-axis), and it will hit the surface once. In other words, for each given $(x,y)$, you can find a value of $z$ for which $g(x,y,z)=0$. For complicated functions, you'll have to use numerical methods to find $z$ given $x$ and $y$. Anyway, numerical or not, this process maps a given $(x,y)$ to a point on the surface -- in other words, it gives you a parametric equation of a portion of the surface.
This is a fairly narrow scenario, but broad enough to cover your paper model, I think.
Also, you should note that parameterisation is helpful, but it's not absolutely necessary. There are methods of drawing surfaces given by implicit equations. Mathematica has functions to do this, or you can write your own code http://www.unchainedgeometry.com/jbloom/pdf/impencyc.pdf 
