# understanding (and plotting) a surface (from implicit to parametric?) [duplicate]

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).

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## marked as duplicate by Raskolnikov, nkint, William, Rahul, J. M.Sep 19 '12 at 9:28

To me, it looks like what is "plotted" is $z=sin(\sqrt{x^2+y^2})/\sqrt{x^2+y^2}$ and not the equation written down on the paper. Or maybe the colors imply the third dimension? – Raskolnikov Sep 13 '12 at 13:35
yeah it seems a duplicate question – nkint Sep 13 '12 at 13:52
buy the way, what about transformation to implicit to parametric? does it make sense? is it possible? – nkint Sep 13 '12 at 13:53

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.