Torus parametrization and inverse

1. May 30, 2015

Jess_l

I've been looking at the torus parametrization

\phi(u,v)=((r\cos u+a)\cos v, (r\cos u +a)\sin v, r\sin u)

with $$a>0, r\in(0,a)$$. I want to invert this map to get a chart map for the torus.
Can anyone give me a hand with this?
Thanks!

2. May 30, 2015

mathwonk

well, u seems to equal arcsin(z/r). how's that for a start?