Archimedova spirála

n ... počet bodů na jednom závitu

r ... poloměr pro poslední bod 1. závitu

S = (3.2733333333333343, -0.74)
r = 3 (slider from 0 to 12, step 0.1)
n = 12 (slider from 1 to 30, step 1)
kr = Sequence(Circle[S, i * r / n], i, 1, n)
pol3 = Sequence(Ray[S, Vector[10 * (cos(i * 360 * ° / n), sin(i * 360 * ° / n))]], i, 1, n)
body = Sequence(Intersect[Element[kr, i], Element[pol3, i]], i, 1, n)
s = 15.3588974175501 (slider from 0 to 18.84955592153876, step 0.08726646259971647)
obl = Sequence(CircleArc[S, S + i * r / n * (cos((i - 1) * 360 * ° / n), sin((i - 1) * 360 * ° / n)), S + i * r / n * (cos((i + 1) * 360 * ° / n), sin((i + 1) * 360 * ° / n))], i, 1, n)
spir = CurveCartesian(x(S) + r * t / (2 * π) * cos(t), y(S) + r * t / (2 * π) * sin(t), t, 0, 18.84956)
M: (x(S) + r * s / (2 * π) * cos(s), y(S) + r * s / (2 * π) * sin(s))
o1 = CircleArc(S, S + r / n * (cos((1 - 1) * 360 * ° / n), sin((1 - 1) * 360 * ° / n)), S + r / n * (cos((1 + 1) * 360 * ° / n), sin((1 + 1) * 360 * ° / n)))
pol1 = Ray(S, Vector[10 * (cos(360 * ° / n), sin(360 * ° / n))])
A = Intersect(o1, pol1, 1)
o2 = CircleArc(S, S + 2 * r / n * (cos((2 - 1) * 360 * ° / n), sin((2 - 1) * 360 * ° / n)), S + 2 * r / n * (cos((2 + 1) * 360 * ° / n), sin((2 + 1) * 360 * ° / n)))
pol2 = Ray(S, Vector[10 * (cos(2 * 360 * ° / n), sin(2 * 360 * ° / n))])
B = Intersect(o2, pol2, 1)
o3 = CircleArc(S, S + 3 * r / n * (cos((3 - 1) * 360 * ° / n), sin((3 - 1) * 360 * ° / n)), S + 3 * r / n * (cos((3 + 1) * 360 * ° / n), sin((3 + 1) * 360 * ° / n)))
pol33 = Ray(S, Vector[10 * (cos(3 * 360 * ° / n), sin(3 * 360 * ° / n))])
C = Intersect(o3, pol33, 1)
o4 = CircleArc(S, S + 4 * r / n * (cos((4 - 1) * 360 * ° / n), sin((4 - 1) * 360 * ° / n)), S + 4 * r / n * (cos((4 + 1) * 360 * ° / n), sin((4 + 1) * 360 * ° / n)))
pol4 = Ray(S, Vector[10 * (cos(4 * 360 * ° / n), sin(4 * 360 * ° / n))])
D = Intersect(o4, pol4, 1)
o5 = CircleArc(S, S + 5 * r / n * (cos((5 - 1) * 360 * ° / n), sin((5 - 1) * 360 * ° / n)), S + 5 * r / n * (cos((5 + 1) * 360 * ° / n), sin((5 + 1) * 360 * ° / n)))
pol5 = Ray(S, Vector[10 * (cos(5 * 360 * ° / n), sin(5 * 360 * ° / n))])
E = Intersect(o5, pol5, 1)
o6 = CircleArc(S, S + 6 * r / n * (cos((6 - 1) * 360 * ° / n), sin((6 - 1) * 360 * ° / n)), S + 6 * r / n * (cos((6 + 1) * 360 * ° / n), sin((6 + 1) * 360 * ° / n)))
pol6 = Ray(S, Vector[10 * (cos(6 * 360 * ° / n), sin(6 * 360 * ° / n))])
F = Intersect(o6, pol6, 1)
sp = CurveCartesian(x(S) + r * t / (2 * π) * cos(t), y(S) + r * t / (2 * π) * sin(t), t, 0, 5.654866776461628)