# How to make a 3D plot using polar coordinates radius and angle dependence

I want to create a polar plot like this:

Which can not be made with the RevolutionPlot3D comand like here, it is because my function is dependent of the radius r and the angle Theta. I already tried with this code:

b = 0.042
m = 1
a = 0.1075
Gamma1 = 27.656142169163004496112989727407693862915039062550.
B1 = 10.872115877119069793366179510485380887985229492187550.
C1 = 1.008385426862300926487137076037470251321792602539062550.
D1 = 12.75578769379862009714088344480842351913452148437550.
ParametricPlot3D[{(BesselJ[m, Gamma1*r] +
B1*BesselY[m, Gamma1*r] + C1*BesselI[m,Gamma1*r] +
D1*BesselK[m,Gamma1*r])*
(Sin[m*Theta]+Cos[m*Theta])}, {Theta, 0, 2*Pi}, {r, b, a}]


I do not know why my code does not work.

• Your function should be a vector-valued function to use ParameticPlot3D. – L.Yu May 23 at 17:16
• @L.Yu What do you mean by vector-valued function?. – Alfredo May 23 at 19:05
• maybe ParametricPlot3D[{r Cos[ Theta], r Sin[Theta], (BesselJ[m, Gamma1*r] + B1*BesselY[m, Gamma1*r] + C1*BesselI[m, Gamma1*r] + D1*BesselK[m, Gamma1*r])*(Sin[m*Theta] + Cos[m*Theta])}, {Theta, 0, 2*Pi}, {r, b, a}, BoxRatios -> {1, 1, 1}]? – kglr May 23 at 19:10
• Comment: an interesting surface, which appears to be topologically a cylinder. – murray May 24 at 14:11

ParametricPlot3D[{r Sin[Theta], r Cos[Theta],
(BesselJ[m, Gamma1 r] + B1 BesselY[m, Gamma1 r] +
C1 BesselI[m, Gamma1 r] + D1 BesselK[m, Gamma1 r])*(Sin[m Theta] + Cos[m Theta])},
{Theta, 0, 2 Pi}, {r, b, a}, Mesh -> {Range[0, 2 Pi, 2 Pi/20], 10},
PlotStyle -> None, Boxed -> False, Axes -> False, BoxRatios -> 1,
BoundaryStyle -> Black]