Parametric Equations of Hypocycloid
Parametric Equations
If the smaller circle has radius r, and the larger circle has radius R = kr
x = (R-r)*cos(theta) + r*cos((R-r)/r*theta)
y = (R-r)*sin(theta) - r*sin((R-r)/r*theta)
If k is an integer, then the curve is closed and has k cusps.
If k is a rational number, say k = p/q expressed in simplest terms, then the curve has p cusps.