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?
Do it parametrically. Here's a generic implementation: