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Torus parametrization and inverse

  1. May 30, 2015 #1
    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!
     
  2. jcsd
  3. May 30, 2015 #2

    mathwonk

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