Plotting 3D Regions in Mathematica 7

[n00dle0]

Hi!

I am plotting the following in Mathematica 7.

RegionPlot3D[(x^2 + y^2 + z^2 <= 1) && (x < 0 || y > 0 || 
    z < 0), {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
 ColorFunction -> 
  Function[{x, y, z}, ColorData["TemperatureMap"][x^2 + y^2 + z^2]], 
 PlotPoints -> 50, Mesh -> False, 
 Lighting -> {{"Directional", 
    RGBColor[1, 1, 1], {{-1, 1, -1}, {0, 0, 0}}}}, 
 AxesLabel -> {X, Y, Z}, {ViewPoint -> {2, -0.5, 0.5}}]

I need the plot to look such that the color on the cut out surface of the sphere should be a gradient in a radial fashion. Assume that there is a point heat source at the center of the sphere and colors represent the temperature profile within the sphere. Any ideas?

Thanks in advance,
- N

 

[Dale]

Add the option ColorFunctionScaling -> False

I don't know why, but it seems that the scaling is the problem.

 

[n00dle0]

Add the option ColorFunctionScaling -> False

I don't know why, but it seems that the scaling is the problem.

Thanks a lot Dale. I had been struggling with it since a week. Now does anyone have idea as to why. Is this behavior a feature or a bug?

- N

 

[n00dle0]

Thanks a lot Dale. I had been struggling with it since a week. Now does anyone have idea as to why. Is this behavior a feature or a bug?

- N

Well this seems to be the feature, as the help specifies,

Parameters to ColorFunction are normally scaled to be between 0 and 1:
__________________________(by default)_________________________

So, the parameters are scaled, not the results.

- N

 

[Dale]

Well this seems to be the feature, as the help specifies,

Parameters to ColorFunction are normally scaled to be between 0 and 1:
__________________________(by default)_________________________

So, the parameters are scaled, not the results.

- N

That explains it. So it takes x which ranges from -1 to 1 and rescales it to range from 0 to 1, similarly with y and z. Then when you calculate the norm you essentially get a scaled distance from the point (-1,-1,-1)