3D Curves

3D Parametric curves


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Thomas

Torus knot

Parameters:

$p, q$

Parametric equation:

$$\left\{ \begin{eqnarray*} x(t)&=&\cos(q t) \cos (p t)\\ y(t)&=&\cos(q t) \sin (p t)\\ z(t)&=&\sin (q t) \end{eqnarray*}\right. $$

Aizawa

Knots

Parameters:

$a, b, c, d, e, f$

Parametric equation:

\begin{eqnarray*} \phi(t)&=&c \pi \sin (d t)\\ r(t)&=&f+a\sin(6t+e)\\ \theta(t)&=&bt \end{eqnarray*}

$$\left\{ \begin{eqnarray*} x(t)&=&r(t)\cos(\phi (t)) \cos (\theta(t))\\ y(t)&=&r(t)\cos(\phi (t)) \sin (\theta(t))\\ z(t)&=&\sin (\phi (t)) \end{eqnarray*}\right. $$


Source

      

Live Code


Notes

Parametric curves in 3d using the p5.EasyCam library developed by Thomas Diewald.


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