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Epitrochoid

An epitrochoid is a roulette traced by a point attached to a circle of radius b rolling around the outside of a fixed circle of radius a, where the point is a distance h from the center of the exteriour circle.

The parametric equations for an epitrochoid are:

x = (a + b)\cos\theta + h\cos({a + b \over b}\theta)
y = (a + b)\sin\theta + h\sin({a + b \over b}\theta)

Special cases include the limaçon with h = b and the epicycloid with h = b

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