I'm trying to curve a set of lemnisate/infinity sign curves, such that the circles overlap along the z axis. Ie.
The equation for this curve is:
$x = a\cdot\sin(t)\cdot\cos(t)\\$
$y = a\cdot\sin(t)\cdot\sin(t)\\$
$z = b\cdot \sin(t)\\$
The problem I'm having is with the more complicated "double infinity" and "triple infinity" curves:
I expected the equations for these folded curves to be pretty simple, I can't seem to find anything that actually describes them well. Does anyone know what equations would describe these topologies?