Coloring surfaces in Mathematica

[Peaks Freak]

Hi, all,

I have a question about coloring a 3D parametric surface in Mathematica.

Setup:

Take as given a surface M in R^3 and a parameterization of that surface p:[a,b] x [c,d] -> R^3. Let f:M -> R be a function defined on M.

Question:

How can I plot this surface so that points p with f(p) >= 0 are colored white and points p with f(p) < 0 are colored gray?

Notes:

I'm using ParametricPlot3D and trying to work with the ColorFunction -> Function construct, but can't quite get it right.

Thanks in advance!

P

 

[Greg Bernhardt]

You can use the ColorFunction option when you are plotting parametric surfaces. For example, you can try something like this:

ParametricPlot3D[p[u,v], {u,a,b}, {v,c,d},
ColorFunction ->
Function[{x,y,z,u,v},
If[f[p[u,v]] >= 0, White, Gray]]]