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3D LISSAJOUS CURVE

Curve studied by Bogle, Hearst, Jones et Stoilov in 1993. |

Cartesian parametrization: . |

The 3D Lissajous curves are the trajectories of a point in space the rectangular components of which have a sinusoidal motion.

The projections on the 3 coordinate planes are the classic 2D Lissajous curves.

For *n* = 1 or *n* = *m*, we get a cylindrical sine wave.

We get a closed curve if and only if *n* and *m* are rational.

When the curve does not have double points, nor a cusp, it forms a knot in space, called *Lissajous knot*, equivalent to a cubic billiard knot.

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© Robert FERRÉOL 2018