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Rotating square's points

Isaac Keith

Posted 3 years ago

Hi, I'm trying to make a function to rate a square within a square, thus the second square will form a diamond. I'm pretty new, so I think NestList is the way to go, however, I'm not sure how to rotate the coordinates of my polygon. squarePts = {{0, 0}, {1, 0}, {1, 1}, {0, 1}}; f7 = NestList[# ?? &, squarePts , 1] I tried to get the middle points of each side and then rotate by 45 degree, but after the second square the thing become messy. Thank you

POSTED BY: Isaac Keith

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Updating Name

Posted 3 years ago

Crossposted here.

POSTED BY: Updating Name

Eric Rimbey

Posted 3 years ago

For a more general solution, you might want to apply the transformation functions `ScalingTransform` and `RotationTransform`: SquareTunnel[angle_, count_] := With[ {vertices0 = {{1, 1}, {-1, 1}, {-1, -1}, {1, -1}}}, With[ {center = Mean[vertices0], scale = (1/(Cos[angle] + Sin[angle]))}, NestList[ ScalingTransform[{scale, scale}]@*RotationTransform[angle, center], vertices0, count]]]; Graphics[{FaceForm[None], EdgeForm[Black], Polygon[SquareTunnel[Pi/8, 4]]}]

For a more general solution, you might want to apply the transformation functions ScalingTransform and RotationTransform:

SquareTunnel[angle_, count_] :=
 With[
  {vertices0 = {{1, 1}, {-1, 1}, {-1, -1}, {1, -1}}},
  With[
   {center = Mean[vertices0], scale = (1/(Cos[angle] + Sin[angle]))},
   NestList[
    ScalingTransform[{scale, scale}]@*RotationTransform[angle, center], 
    vertices0, 
    count]]];

Graphics[{FaceForm[None], EdgeForm[Black], Polygon[SquareTunnel[Pi/8, 4]]}]

enter image description here

POSTED BY: Eric Rimbey

Eric Rimbey

Posted 3 years ago

POSTED BY: Eric Rimbey

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