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BrianWeinstein/Curves of Constant Width and Odd-Sided Reuleaux Polygons

Created October 18, 2014 04:33
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Curves of Constant Width and Odd-Sided Reuleaux Polygons
x[n_, \[Theta]_] := 2*Cos[Pi/(2*n)]*Cos[(1/2)*(\[Theta] + (Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1))] - Cos[(Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1)]
y[n_, \[Theta]_] := 2*Cos[Pi/(2*n)]*Sin[(1/2)*(\[Theta] + (Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1))] - Sin[(Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1)]
reuRotate[n_, \[Phi]_] :=
{pts[n, \[Phi]] = Table[RotationMatrix[\[Phi]] . {x[n, \[Theta]], y[n, \[Theta]]}, {\[Theta], 0, 2*Pi, (2*Pi)/100}];
xmin = Min[pts[n, \[Phi]][[All,1]]];
ymin = Min[pts[n, \[Phi]][[All,2]]];
xmax = Max[pts[n, \[Phi]][[All,1]]];
ymax = Max[pts[n, \[Phi]][[All,2]]];
ParametricPlot[
RotationMatrix[\[Phi]] . {x[n, \[Theta]], y[n, \[Theta]]},
{\[Theta], 0, 2*Pi},
PlotStyle -> Thickness[0.009],
PlotRange -> {{xmin, xmax}, {ymin, ymax}}, Axes -> False,
Background -> Darker[Gray, 0.75],
PlotRangePadding -> None
]
}[[1]]
Manipulate[reuRotate[n, \[Phi]], {n, 3, 15, 2}, {\[Phi], 0, 2*Pi}]
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