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Make a movie that shows creation of the torus in yet another manner. Namely, imagine a thin inflatable wire that runs inside the torus along the circle
$\qquad (x^2) + y^2 = (a^2), \quad z=0$

I was given the following as one way of animating a torus drawing.

torus[a_, b_, umin_, umax_, vmin_, vmax_] := 
  ParametricPlot3D[{(a + b Cos[u])*Cos[v], (a + b Cos[u])*Sin[v], b*Sin[u]}, 
    {u, umin, umax}, {v, vmin, vmax}, 
    PlotPoints -> 30]

creation2[FromU_, ToU_]:=
  Animate[
    Show[torus[2, 1, FromU, U, 0, 2*Pi],
    PlotRange->{{-3.5 , 3.5}, {-3.5, 3.5}, {-1.5, 1.5}}], {U, FromU + 0.01, ToU},
    AnimationRunning -> False];

I need another way, such as the 1st paragraph suggests by starting with a thin wire, then inflating it into a torus, and also a way of doing the inverse.

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  • $\begingroup$ OK Cool problem. What have you tried? $\endgroup$
    – MarcoB
    Dec 1, 2020 at 19:14
  • 1
    $\begingroup$ Ive tried switching u and v $\endgroup$ Dec 1, 2020 at 19:20
  • $\begingroup$ You haven't defined torus. Please advise. $\endgroup$
    – Jagra
    Dec 1, 2020 at 19:55
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    $\begingroup$ Is this a homework problem or something...? $\endgroup$
    – b3m2a1
    Dec 1, 2020 at 21:34
  • 1
    $\begingroup$ I meant to ask whether you meant: b*Cos[ ] $\endgroup$
    – Jagra
    Dec 1, 2020 at 22:08

1 Answer 1

1
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Animate[Show[torus[2, j, 0, 2 \[Pi], 0, 2 \[Pi]], 
  PlotRange -> {{-3.5, 3.5}, {-3.5, 3.5}, {-1.5, 1.5}}], {j, 0, 1}, 
 AnimationRunning -> False]

If I understood you correctly.

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