Cycloids and Trochoids of an Elliptic Base Curve

Trochoids and cycloids are glisettes: curves generated when a closed curve rolls inside or outside a fixed base curve.
In this Demonstration, the rolling curve is a circle, which rolls without slipping on an elliptic base curve; the generated curve is called a hypotrochoid or an epitrochoid, according to whether the circle rolls on the inside or the outside of the ellipse. The generator point (or pole) that draws the curve is at a variable distance from the center of the rolling circle. If is equal to the circle radius, the trochoids become cycloids.
The circle radius is computed such that the circle performs an integer number of revolutions around itself while completing a loop around the ellipse. The number of cusps formed in the completed curve is for a hypotrochoid and for an epitrochoid.

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