Mathematically, the Lissajous curve (also known as Lissajous figure or Bardis curve) is a synthetic trajectory of two sinusoidal vibrations along mutually perpendicular directions.

The Lissajous curve is defined by the following parametric equation:

x=asint

y=bsin(nt+φ)

Where 0≤φ≤π/2 and n≥ 1.

N is called the parameter of the curve and is the frequency ratio of two sinusoidal vibrations. If the ratio is rational, then n=p/q, and the parameter equation can be written as:

x=asin(pt)

y=bcos(qt+φ)

0≤t≤2π，

Where 0≤φ≤π/2p.