Here we produce 2 elliptical epicycloid cusps.
We attempt to produce a cubic Bezier curve (yellow) to overlay the two paths exactly, using Control Points as indicated by yellow dots.
Similar to our earlier work with Bezier curves, we would like to know what (if any) relationship exists between the placement of the Control Points, and the various 'Original Conditions'. These being
The circle produces 2 cusps (it rotates twice).
This would indicate that the circumference of the ellipse is twice that of the circle.
The circle radius is 30, thus the circumference is 2𝝅r = 188.495559215387594
The ellipse radii is 120 and 90, making the ellipse circumference 663.1047648.
The lines from center to CP2 and CP4 indicate positions where the circle is in the same orientation as original - blue dot to the right.
Next we show the Elliptical Hypocycloid development.