I have a function $f(r,\psi)$ and I would like to plot it on a circle such that the the radial direction indicates the change of the function as a function of $r$; the angular direction the change of the function as a function of $\psi$ and finally the height the actual value of the function.

Which plotting routine should I use for this?

• Probably ParametricPlot3D can you supply any function? Or more likely Plot3D, I'm not sure I got 'on a cricle'. Anyway you can make use of CoordinateTransform. – Kuba Jun 21 '17 at 8:43

Here's a quick mockup of Kuba's suggestion using a function I made up:

f[r_, θ_] := Sin[3*θ]^3/(r + 5);

ParametricPlot3D[
{x, y, f[Sequence @@ ToPolarCoordinates[{x, y}]]}
, {x, -1, 1}, {y, -1, 1}
, PlotRange -> All
, MeshFunctions -> {Abs[#1 + I #2] &, Arg[#1 + I #2] &}(*This produces the polar mesh.*)
, RegionFunction -> ((#1^2 + #2^2 < 1) &) (*You can eliminate this if you want the region to be rectangular.*)
]


This will produce the following plot: