I'm looking for a method to transform a three dimensional geometry. This geometry has a rotational symmetry, so the $r$- and $z$-coordinates are all the same over $\phi$. I want to transform this cylindrical geometry in a linear geometry (something like $z\rightarrow x$, $r\rightarrow y$ and $\phi\rightarrow z$).
As you can see from this explanation I'm no mathematician. Can anybody help me find a conformal map that solves this problem or point me to some literature on this topic?
Thank you for your help!