Suppose you have a vectorial wave described by a complicated function of time and cartesian coordinates $t$, $x$, $y$ $z$ (very simple example below) :
WaveField[t_, x_, y_, z_] := 0.5{1, 0, 0}Sin[2Pi(z - t) + Pi/3] + 0.75{0, 1, 0}Sin[2Pi(x - t) + Pi/2] + 0.25{0, 0, 1}Sin[2Pi(y - t) + 2Pi/3]
How would you represent its "density", defined as
WaveDensity[t_, x_, y_, z_] := WaveField[t, x, y, z].WaveField[t, x, y, z]
on the surface of the unit sphere ? Or maybe on the $x y$ plane ?
My problem is to create a kind of vizualisation of that wave, which is varying in time and space. Drawing a vectorial 3D representation over a cubic space would be extremely messy.
Manipulate
. See the edit to my answer. $\endgroup$