Working on a vector field, I'd like to use a ColorFunction dependent on both the vector direction and its norm. According to the documentation of ListVectorDensityPlot, one has access to ColorFunction -> Function[{x, y, vx, vy, s},.... However, in the codes below with two equivalent plottings, errors occur as if one can not use vx,vy. Same for both data0 and data1.
On the other hand, it does work when we delete the s entry in data0 or data1. However, I need explicit s for another reason: without explicit s, it will automatically plot a little beyond the supplied data range, which may cause trouble in certain cases.
Is there a way to access vx,vy?
f = {-y, x};
s = Norm[f];
data0 = Table[{f, s}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}];
data1 = Table[{{x, y}, {f, s}}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}];
ListVectorDensityPlot[data1, PlotRange -> Full,
PlotRangeClipping -> False, VectorColorFunction -> None,
VectorRange -> All, VectorStyle -> Black,
ColorFunctionScaling -> {False, False, False, False, True},
ColorFunction ->
Function[{x, y, vx, vy, s}, Hue[ArcTan[vx, vy]/(2 \[Pi]), s]]]
ListVectorDensityPlot[data1, PlotRange -> Full,
PlotRangeClipping -> False, VectorColorFunction -> None,
VectorRange -> All, VectorStyle -> Black,
ColorFunctionScaling -> {False, False, False, False, True},
ColorFunction -> (Hue[ArcTan[#3, #4]/(2 \[Pi]), #5] &)]
