Spring around torus 2
- Author:
- Thijs
- Topic:
- Curve Sketching
It seems to me that the contraction of Yugemaku's string alternates from left to right.
I've tried to imitate this, but I haven't quite succeeded.
History: post - Juan Carlos' Spring Around Torus
Setup:
R = 7
r_{Torus} = 1
r_{Spring} = 2
A = 0.33
ω = 1
n = 12
t = Slider(0, 2 pi, 0.01, 1, 160, true, true, false, false)
Tx(φ,θ) = (R + r_{Torus}*cos(θ)) * cos(φ)
Ty(φ,θ) = (R + r_{Torus}*cos(θ)) * sin(φ)
Tz(φ,θ) = r_{Torus} * sin(θ)
Torus = Surface((Tx(φ,θ), Ty(φ,θ), Tz(φ,θ)), φ,0,2π, θ,0,2π)
f(t) = (1 - A*cos(ω*t))^8 + 2
F = Integral(f)
F2π(t) = F(t) * 2π/F(2π)
Sx(φ) = (R + r_{Spring}*cos(n*φ)) * cos(F2π(φ+2t) - F2π(2t) + t)
Sy(φ) = (R + r_{Spring}*cos(n*φ)) * sin(F2π(φ+2t) - F2π(2t) + t)
Sz(φ) = r_{Spring}*sin(n*φ)
Spring= Curve((Sx(φ), Sy(φ), Sz(φ)), φ,0,2π)