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Grid warping, rotating frame

Matthen May 14th, 2013 111 Never
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  1. n = 8;
  2. \[Omega] = 1/2;
  3. p1s = Table[{-Sqrt[1 - y^2], y}, {y, -1, 1, 2/n}][[2 ;; -2]];
  4. p1s2 = Table[{x, -Sqrt[1 - x^2]}, {x, -1, 1, 2/n}][[2 ;; -2]];
  5. frame[\[Omega]_] :=
  6.   Show[
  7.    Graphics[Circle[], PlotRange -> 1.1],
  8.    Table[
  9.     ParametricPlot[
  10.      RotationMatrix[\[Omega] (\[Tau] - 2 Pi)].(
  11.        p1 Max[0, (1 - (\[Tau]/(2 Pi))/(-p1[[1]]))] + {-p1[[1]],
  12.           p1[[2]]} Min[1, (\[Tau]/(2 Pi))/(-p1[[1]])]
  13.        )
  14.      , {\[Tau], -0.001, 2 Pi}, PlotStyle -> Thick, Axes -> None]
  15.     , {p1, p1s}
  16.     ],
  17.    Table[
  18.     ParametricPlot[
  19.      RotationMatrix[\[Omega] (\[Tau] - 2 Pi)].(
  20.        p1 Max[
  21.           0, (1 - (\[Tau]/(2 Pi))/(-p1[[2]]))] + {p1[[
  22.            1]], -p1[[2]]} Min[1, (\[Tau]/(2 Pi))/(-p1[[2]])]
  23.        )
  24.      , {\[Tau], -0.001, 2 Pi}, PlotStyle -> Thick]
  25.     , {p1, p1s2}
  26.     ]
  27.    ];
  28.  
  29. Manipulate[frame[\[Omega]], {\[Omega], -0.5, 0.5}]
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