Torus parametrization and inverse

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SUMMARY

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), where a > 0 and r ∈ (0, a). The user seeks assistance in inverting this map to derive a chart map for the torus. A proposed starting point for the inversion is u = arcsin(z/r), indicating a direction towards solving the inverse parametrization problem.

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  • Understanding of toroidal geometry and its properties
  • Familiarity with trigonometric functions and their inverses
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Mathematicians, computer graphics developers, and students studying differential geometry who are interested in surface parametrization and inversion techniques.

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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