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1994 (Publication #75)

On the Geometry of Piecewise Circular Curves (with Peter Giblin)

American Mathematical Monthly 101 No. 5 (1994) 403-416.

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A piecewise circular (PC) curve consists of a finite number of circular arcs such that the endpoint of each in the starting point of the next. If the directed tangent line varies continuously along the PC curve, it is said to be smooth.

PC curves arise in a variety of applications in robotics, engineering, and mathematics, mainly because of the elegant properties that PC curves possess. For instance, since the outward parallel curve of a circle is a circle, the outward parallel curve of a PC is another PC curve. PC curves also arise as the solutions to various length and area optimization problems.