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I have to plot a function of three varaibles $F(\theta,\beta,\gamma)$ with version 10.0 and I thought to follow the first advice of this answer, so my plot is given by:

xyz = Flatten[
   Table[{i, j, k}, {i, 0, Pi, 0.1}, {j, 0, 2 Pi, 0.1}, {k, 0, Pi, 
     0.1}], 2];

f[x_, y_, z_] := Cos[x] Sin[y] Cos[z];

Graphics3D[
 Point[xyz, VertexColors -> (Hue /@ Rescale[f[##] & @@@ xyz])], 
 Axes -> True, AxesLabel -> {\[Theta], \[Beta], \[Gamma]}]

I want to add a color legend to it how can I do it?

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The general way would be to use

Legended[
 Graphics3D[
  Point[xyz, VertexColors -> (Hue /@ Rescale[f[##] & @@@ xyz])], 
  Axes -> True, AxesLabel -> {\[Theta], \[Beta], \[Gamma]}],
 BarLegend[Hue]
 ]

Mathematica graphics

Now, you only need to scale the ticks of the legend, but I'm sure you find out yourself how this works by looking up the documentation of BarLegend.

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  • $\begingroup$ For clarification in this answer here, does the use of Rescale serve the same purpose as ColorFunctionScaling->False? $\endgroup$ – CA Trevillian Mar 3 '20 at 13:35
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    $\begingroup$ @CATrevillian I just copied the code from the OP. If anything, then the Rescale acts like ColorFunctionScaling -> True because it rescales the whole dataset of values in the range [0,1]. However, for VertexColors you need to rescale the values yourself opposed to things like Plot that do it for you. $\endgroup$ – halirutan♦ Mar 4 '20 at 6:59

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