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Klein Bottle 3D Animation

By: Matthen on Jun 4th, 2011  |  syntax: None  |  size: 0.68 KB  |  hits: 232  |  expires: Never
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  1. r = 2; \[Theta] = Pi;
  2. Manipulate[
  3.  GraphicsGrid[{Table[ParametricPlot3D[{
  4.       (r + Cos[u/2] Sin[v] - Sin[u/2] Sin[2 v]) Cos[u],
  5.       (r + Cos[u/2] Sin[v] - Sin[u/2] Sin[2 v]) Sin[u],
  6.       Sin[u/2] Sin[v] + Cos[u/2] Sin[2 v]}, {u, 0,
  7.       Pi + If[t > 2, If[t < 2 + Pi, (t - 2), Pi], 0]}, {v, 0,
  8.       Pi/4 + If[t < 3 Pi/4, t,
  9.         If[t < 2 + Pi, 3 Pi/4,
  10.          If[t < 2 Pi + 2, 3 Pi/4 + t - 2 - Pi, 7 Pi/4]]]},
  11.      PlotRange -> {{-4, 4}, {-4, 4}, {-2, 2}}, Boxed -> False,
  12.      Axes -> None, PlotStyle -> Red,
  13.      ViewPoint ->
  14.       v], {v, {{10 Sin[\[Theta]], 10 Cos[\[Theta]],
  15.        3}, {10 Sin[\[Theta]], 10 Cos[\[Theta]], 3}}}]}]
  16.  , {t, 0, 2 Pi + 3}]
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