Helix shape using Bezier Curve functions

Tom Cormack shared this question 5 months ago
Answered

I'm looking how to create a helix/spiral shape in the 3D calculator using cubic Bezier curves.


Ideas??

Comments (1)

photo
1

Enter the following commands:

n = 4
k = 0.25
r = 2
L = Sequence({(cos(2π / n (i - 1)) r, sin(2π / n (i - 1)) r, k (i - 1) * 2π / n), (cos(2π / n (i - 1)) r, sin(2π / n (i - 1)) r, k (i - 1) * 2π / n) + (-sin(2π / n (i - 1)), cos(2π / n (i - 1)), k / 2) r 4 / 3 tan(π / 2 / n), (cos(2π / n i) r, sin(2π / n i) r, k i 2π / n) + (sin(2π / n i), -cos(2π / n i), (-k) / 2) r 4 / 3 tan(π / 2 / n), (cos(2π / n i) r, sin(2π / n i) r, k i 2π / n)}, i, -n, n)
C = Zip(Curve(Element(LL, 1) (1 - t)³ + Element(LL, 2) * 3t (1 - t)² + Element(LL, 3) * 3t² (1 - t) + Element(LL, 4) t³, t, 0, 1), LL, L)
C_{analytic} = Curve(r cos(t), r sin(t), t k, t, -2π, 2π)
Note that Béziersplines only allow a approximation of circles.

Sources: [1] [2]

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