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# Grid warping, rotating frame

Matthen May 14th, 2013 112 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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