Lissajous curves are curves described by a set of parametric equations, more often than not in a 2D plane. It’s fairly trivial to extend this to three dimensions by adding another parametric equation.
Since these are time dependent, they are also easy to animate (animation to come once I figured out how to properly add UV’s to texture these).
These curves are a special case of a Harmonograph under simple harmonic motion – which would also be an interesting thing to try simulate. [note to self]
In the most general form, the equations for a lissajous curve are
x = Asin(a1t) * cos(a2t);
y = Bsin(b1t) * cos(b2t);
z = Csin(c1t) * cos(b2t)
Since these are time dependent, they are also easy to animate (animation to come once I figured out how to properly add UV’s to texture these).
These curves are a special case of a Harmonograph under simple harmonic motion – which would also be an interesting thing to try simulate. [note to self]
In the most general form, the equations for a lissajous curve are
y = Bsin(b1t) * cos(b2t);
z = Csin(c1t) * cos(b2t)
Houdini
Redshift
