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]]]

 

[oswaler]

icking colors for surfaces in Mathematica can be done using the ColorFunction option in the ParametricPlot3D function. This option takes a function as an argument that maps values to colors. In this case, we want to map positive values of f(p) to white and negative values to gray. We can achieve this by defining a function like so: ColorFunction -> Function[{x,y,z}, If[f[p[x,y]] >= 0, White, Gray]]. This function takes the x,y,z coordinates of a point on the surface and uses the parameterization p to calculate the value of f at that point. If the value is greater than or equal to 0, it returns the color White, otherwise it returns Gray. This function can then be passed as the argument to ColorFunction in the ParametricPlot3D function to color the surface accordingly.