Pushed Around
Continuing with the theme ( 1 , 2 , 3 , 4 ), this is another closed geodesic in polygon space. For some reason, I’ve almost never used Dashing before, but it’s kind of fun to play around with.
Here’s the code:
ToReal[z_] := {Re[z], Im[z]};
ToComplex[{x_, y_}] := x + I y;
FrameToPol[{A_, B_}] := ToReal[ToComplex[#]^2] & /@ Transpose[{A, B}];
FrameToVertices[{A_, B_}] := Accumulate[FrameToPol[{A, B}]];
Manipulate[Module[{cols, fr, dfr, θ, verts},
cols = RGBColor /@ {"#00C3FF", "#3B475E"};
fr = Transpose[
ToReal[Sqrt[#]] & /@
Table[2/5 E^(I θ), {θ, π/5,
4 π + π/5 - 4 π/5, 4 π/5}]];
dfr = Transpose[
ToReal[Sqrt[#]] & /@
Table[2/5 E^(I θ), {θ, π/5,
2 π + π/5 - 2 π/5, 2 π/5}]];
θ = π (1/2 - 1/2 Cos[π s]);
Graphics[{FaceForm[None],
EdgeForm[
Directive[cols[[1]], JoinForm["Round"], CapForm["Round"],
Dashing[{.02, .04}], Thickness[.005]]], {
verts =
RotationMatrix[4 π/5].# & /@
FrameToVertices[Cos[θ] fr + Sin[θ] dfr];
Polygon[-Mean[verts] + # & /@ verts]}}, ImageSize -> 540,
PlotRange -> 1/Sqrt[2], Background -> cols[[2]]]], {s, 0., 1}]
