interpolate r depedent polar result to cartesian

Hi, I'm sure the answer is somewhere on the forum but I can't seem to find it. Bassically, I'm searching for this:

CartesianResult(z,x,y) = CylindricResult(z,r)

Where I have CylindricResult and the results have a symetry axis along the center of the cylinder.

I have the results of a simulation which a 2D matrix representing the slice on the cylinder. I have a symetry axis in the center so the value of the simulation are only dependent to z and r. Now I need to express those results in 3D Cartesian coordinates.

I already associated all x,y coordonates to a r coordonates. What I would like to do is when I don't have a round r coordonates, I'd like to interpolate the results I have. (linear is good enough) Since the results tends to 0 toward the extremities of the radius, any coordonates too far from the center in cartesian can be assume to have a value of 0.

Am I being clear? Thanks for the help.