# Color vector according to angle

One can use the function VectorColorFunction in VectorPlot3D to color vectors according to their norms. How to color vectors according to the angle they are pointing along, say, in the x-y plane? Thanks!

VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
VectorColorFunction -> (Hue@Rescale[Arg[#4 + I #5], {0, 2 Pi}] &),
VectorColorFunctionScaling -> False]


• Arg[]'s range is $(-\pi,\pi]$. ;) Commented Nov 5, 2015 at 15:17
• @J.M. And the Plots are quite different, I see :) Commented Nov 5, 2015 at 15:25

There are a lot of arguments in VectorColorFunction. In your particular case you can write the following

VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
VectorColorFunction ->
Function[{x, y, z, vx, vy, vz, v}, Hue[ArcTan[vx, vy]/2/π]],
VectorColorFunctionScaling -> False]


• I was a bit slow... However, I believe this explicit function is more clear for OP. Commented Nov 5, 2015 at 15:25
• Thanks a lot, ybeltukov, I will upvote your answer! Much appreciated.
– jarm
Commented Nov 6, 2015 at 7:16