Sign up ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

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?

share|improve this question
Have you tried RevolutionPlot3D? –  Cassini Feb 5 '13 at 14:59
@David That's a nice idea when $z$ is independent of $\theta$, but how do you propose using RevolutionPlot3D when $z$ does vary with $\theta$? –  whuber Feb 5 '13 at 16:26
@whuber: Of course you're right. I didn't read the question too carefully. –  Cassini Feb 5 '13 at 20:49
@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. –  J. M. is back. Feb 7 '13 at 3:12

2 Answers 2

up vote 9 down vote accepted

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]


share|improve this answer


RevolutionPlot3D[ f[r,t], {r, rmax, rmin}, {t, tmax, tmin}]
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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