Epicycloids and Hypocycloids
Positive frequencies let the circle role outside
Modify the curve
frequency, -12 ... +12:
stick, 0 ... 5:
The curves are defined by these equations:
c(t) = [ RR * cos(t), RR * sin(t) ] +
[ sticklength*cos(frequency*t), sticklength*sin(frequency*t)];
The curve and ists tangents are obtained
from a rolling construction.
If sticklength = RR/|frequency| (stick = 1), the curves are
called epicycloids - which roll outside - and hypocycloids - which roll inside.
For other sticklengths these curves are called epitrochoids resp. hypotrochoids.