Torus parametrization and inverse

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The discussion focuses on the parametrization of a torus using the equation φ(u,v) = ((r cos u + a) cos v, (r cos u + a) sin v, r sin u) with constraints a > 0 and r in (0, a). The user seeks assistance in inverting this map to obtain a chart map for the torus. A suggestion is made that u can be expressed as arcsin(z/r), which may serve as a starting point for the inversion process. The conversation revolves around the mathematical complexities of this inversion. Overall, the thread highlights the need for collaboration in solving the torus parametrization challenge.
Jess_l
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I've been looking at the torus parametrization
\begin{equation}
\phi(u,v)=((r\cos u+a)\cos v, (r\cos u +a)\sin v, r\sin u)
\end{equation}
with \begin{equation}a>0, r\in(0,a)\end{equation}. I want to invert this map to get a chart map for the torus.
Can anyone give me a hand with this?
Thanks!
 
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well, u seems to equal arcsin(z/r). how's that for a start?
 

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