Built-In Volumes

Use spheres with sectors of varying size removed as the surface slices for a contour plot.

In[1]:=

opts = {ColorFunction -> (ColorData["SunsetColors", Rescale[#, {-2.5, 2.5}]] &), ColorFunctionScaling -> False, ClippingStyle -> Automatic, Axes -> False, Boxed -> False, SphericalRegion -> True, ImageSize -> 250, PlotPoints -> 32, Method -> {"ShrinkWrap" -> True}};

In[2]:=

func = Simplify[ Sum[Cos[5 Norm[{x, y, z} - {Sin[\[Theta]], Cos[\[Theta]], 0}]], {\[Theta], 0., 2 \[Pi] - (2 \[Pi])/3, (2 \[Pi])/ 3}], (x | y | z) \[Element] Reals];

In[3]:=

Grid[Partition[ Table[SliceContourPlot3D[func, s, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Contours -> Subdivide[-2.5, 2.5, 2], Evaluate@opts], {s, {"CenterSphere", "CenterCutSphere", {"CenterCutSphere", 3 Pi/4}, {"CenterCutSphere", Pi}}}], 2], Spacings -> {2, 2}]

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