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Hypotrochoid

Both

R = 7 (slider from 1 to 7, step 1)
r = 3 (slider from 1 to 7, step 1)
d = 5.3 (slider from 0 to 7, step 0.1)
tmax = 18.84955592153876 (slider from 0 to 37.69911184307752, step π)
Hypotrocoid = CurveCartesian(((R - r) * cos(t)) + (d * cos(((R / r - 1) * t))), ((R - r) * sin(t)) - (d * sin(((R / r - 1) * t))), t, 0, tmax)
tpoint = 10.241592050702726 (slider from 0 to (6 * π), step π / 100)
CR = Circle((0, 0), R)
A: ((R * cos(tpoint)), (R * sin(tpoint)))
l = Ray((0, 0), A)
Caux = Circle(A, r)
B = Intersect(Caux, l, 1)
Cr = Circle(B, r)
P1: Hypotrocoid(tpoint + (((1 - 1) * 2) * π))
P2: Hypotrocoid(tpoint + (((2 - 1) * 2) * π))
P3: Hypotrocoid(tpoint + (((3 - 1) * 2) * π))
P4: Hypotrocoid(tpoint + (((4 - 1) * 2) * π) + π / 2)
P5: Hypotrocoid(tpoint + (((5 - 1) * 2) * π) + π / 2)
P6: Hypotrocoid(tpoint + (((6 - 1) * 2) * π) + π / 2)
P7: Hypotrocoid(tpoint + (((7 - 1) * 2) * π) + π)
P8: Hypotrocoid(tpoint + (((8 - 1) * 2) * π) + π)
P9: Hypotrocoid(tpoint + (((9 - 1) * 2) * π) + π)
P10: Hypotrocoid(tpoint + (((10 - 1) * 2) * π) + (3 * π / 2))
P11: Hypotrocoid(tpoint + (((11 - 1) * 2) * π) + (3 * π / 2))
P12: Hypotrocoid(tpoint + (((12 - 1) * 2) * π) + (3 * π / 2))
Pol1, p3, p1, p2 = Polygon(P1, P2, P3)
Pol2, p6, p4, p5 = Polygon(P4, P5, P6)
Pol3, p9, p7, p8 = Polygon(P7, P8, P9)
Pol4, p12, p10, p11 = Polygon(P10, P11, P12)
Pol5, f, g, h, i, C, D = Polygon(P11, P2, 4)
Pol6, j, k, m, n, E, F = Polygon(P5, P7, 4)
Pol7, p, q, s, t, G, H = Polygon(P1, P6, 4)
a = true
b = true
c = true
e = true
speed: 0.15
Op = 0.14 (slider from 0 to 0.5, step 0.01)
o = true
temp = 0 (slider from 0 to (12 * π), step π)
Segd = Segment(B, P1)
CP: P1