Message Boards Message Boards

[GIF] Pushed Around (a geodesic in pentagon space)

GROUPS:

A geodesic in pentagon space

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}]
POSTED BY: Clayton Shonkwiler
Answer
1 year ago

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations !

We are happy to see you at the tops of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

POSTED BY: Moderation Team
Answer
1 year ago

Group Abstract Group Abstract