I'm trying to plot a function of the form $z(r,\theta)$ where $r \in [0, R]$ for a finite R, $\theta \in [0,2\pi[$, and z is the third coordinate, a function of the first two. I couldn't find anything to do it natively, so I went back to Cartesian coordinates. But the result does not satisfy me, because the range of x is a function of y, a consequence of the constraint $ x^2+y^2 < R^2$. Is there already something in Mathematica to handle this kind of plot?

  • 2
    $\begingroup$ Have you tried RevolutionPlot3D? $\endgroup$
    – Cassini
    Commented Feb 5, 2013 at 14:59
  • $\begingroup$ @David That's a nice idea when $z$ is independent of $\theta$, but how do you propose using RevolutionPlot3D when $z$ does vary with $\theta$? $\endgroup$
    – whuber
    Commented Feb 5, 2013 at 16:26
  • $\begingroup$ @whuber: Of course you're right. I didn't read the question too carefully. $\endgroup$
    – Cassini
    Commented Feb 5, 2013 at 20:49
  • 1
    $\begingroup$ @whuber, you can still use RevolutionPlot[] for the purpose. Witness for instance RevolutionPlot3D[r^2 Cos[3 t], {r, 0, 1}, {t, 0, 3 π/2}]. Of course, it's more enlightening to use ParametricPlot3D[] instead, as in your answer. $\endgroup$ Commented Feb 7, 2013 at 3:12

2 Answers 2


Do it parametrically. Here's a generic implementation:

cylinderPlot3D[f_, {rMin_, rMax_}, {tMin_, tMax_}, opts___] := 
   ParametricPlot3D[{r Cos[t], r Sin[t], f[r, t]}, {r, rMin, rMax}, {t, tMin, tMax}, opts]

For example,

f[r_, t_] := r^2 Cos[3 t];
cylinderPlot3D[f, {0, 1}, {0, 2 Pi}, Mesh->None, Boxed->False]




RevolutionPlot3D[ f[r,t], {r, rmax, rmin}, {t, tmax, tmin}]

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.