Lissajous Curves

Lissajous (/ˈlɪsəʒuː/) curves or also Lissajous figures or even Bowditch curves are the family of curves described by the following parametric equations

$$ x(t) = A \cos{\left(\omega_x t - \delta_x\right)} \\ y(t) = B \cos{\left(\omega_y t - \delta_y\right)} $$

sometimes also written in the form

$$ x(t) = a \sin{\left(\omega t + \delta\right)} \\ y(t) = b \sin{t}. $$

Lissajous curves find applications in physics, astronomy, and other sciences.

Introduction

Connection between Lissajous Curves and Chebyshev Polynomials

Padua Points

Lissajous Knots

Spherical Lissajous Curves

Aerial Search Patterns

Planning Multi-Agent Trajectories

links

social