Tracing path of vector
Script
a = Slider(0, 2 pi, 0.01, 1, 170, false, true, false, false)
r = Slider(0, 5, 0.01, 1, 170, false, true, false, false)
fx(x) = r * cos(x * 10) * sin(x/2)
fy(x) = r * sin(x * 10) * sin(x/2)
fz(x) = r * cos(x/2)
c = Curve(fx(u), fy(u), fz(u), u, 0, a)
O = (0,0,0)
s = Sphere(O, r)
v = Vector(O, c(a))
Script using polar form
r = 3
rot = 10
α = Slider(0, 360°, 1°, 1, 170, true, true, false, false)
c = Curve((r; rot t; 90° + t / 2), t, 0, α)
O = (0,0,0)
B = (r; rot α; 90° + α / 2)
v = Vector(O, B)
s = Sphere(O, r)