# Mathematica plotting

1. Feb 11, 2010

### n00dle0

Hi!

I am plotting the following in Mathematica 7.

Code (Text):

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?

- N

2. Feb 11, 2010

### Staff: Mentor

Add the option ColorFunctionScaling -> False

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

3. Feb 11, 2010

### 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

4. Feb 11, 2010

### n00dle0

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

5. Feb 11, 2010

### Staff: Mentor

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)