Mathematica Question: Wrapping Density Plot on Sphere

[dewood88]

I am new to Mathematica and I am trying to make models of white dwarf spherical harmonics similar to the ones on this site: http://whitedwarf.org/education/vis/index.html. So far the closest thing I have is this:

SphericalPlot3D[3, {\[Theta], 0, \[Pi]}, {\[Phi], 0, 2 \[Pi]},
Mesh -> None,
ColorFunction ->
Function[{x, y, z, \[Theta], \[Phi], r},
Evaluate[
Hue@Rescale[
Arg@Re[SphericalHarmonicY[3,
1, \[Theta], \[Phi]]], {-\[Pi], \[Pi]}]]],
ColorFunctionScaling -> False, PlotPoints -> 35]

However, the color scaling does not allow a blending of the two colors, so instead I would like to wrap a density plot like this one:

Manipulate[
DensityPlot[
Re[SphericalHarmonicY[l, m, \[Theta], \[Phi]]], {\[Theta],
0, \[Pi]}, {\[Phi], 0, 2 \[Pi]},
FrameLabel -> {\[Theta], \[Phi]}], {l, 1, 10, 1}, {m, 0, 10, 1}]

over a sphere of radius 3 and be able to control the l and m values with sliders ("Manipulate"). Does anyone know a simple way to do this? Any helpful hints would be greatly appreciated! :)

 

[NoobixCube]

You might want to shift this post to 'programming' section. May get more responses there

 

[oswaler]

I can provide some insights and suggestions for your Mathematica question. First, it is great that you are using Mathematica for your models of white dwarf spherical harmonics. Mathematica is a powerful tool for scientific visualization and data analysis.

To wrap a density plot on a sphere, you can use the function SphericalPlot3D with the option ColorFunction. This will allow you to specify a color function that depends on the coordinates of the sphere, which you can use to map the density values from the density plot onto the sphere's surface.

Here is an example code that wraps a density plot on a sphere:

SphericalPlot3D[3, {\[Theta], 0, \[Pi]}, {\[Phi], 0, 2 \[Pi]},
Mesh -> None,
ColorFunction ->
Function[{x, y, z, \[Theta], \[Phi], r},
ColorData["TemperatureMap"][DensityPlot[
Re[SphericalHarmonicY[3, 1, \[Theta], \[Phi]]], {\[Theta],
0, \[Pi]}, {\[Phi], 0, 2 \[Pi]},
ColorFunctionScaling -> False,
PlotPoints -> 35][[1, 1, 3]]]],
ColorFunctionScaling -> False]

In this code, we use the ColorData function to specify a color map (in this case, the "TemperatureMap") and then we use the DensityPlot function to generate the density values for the spherical harmonics. The DensityPlot function returns a Graphics object, and we extract the color values from the Graphics object using Part ([[1,1,3]]). This allows us to map the density values onto the sphere's surface.

You can also use the Manipulate function to control the l and m values, as shown in your example code. Here is an example code that combines both the density plot and the spherical harmonics:

Manipulate[
SphericalPlot3D[3, {\[Theta], 0, \[Pi]}, {\[Phi], 0, 2 \[Pi]},
Mesh -> None,
ColorFunction ->
Function[{x, y, z, \[Theta], \[Phi], r},
ColorData["TemperatureMap"][DensityPlot[
Re[SphericalHarmonicY[l, m, \[Theta],