Symmetry Sets of Piecewise-Circular Curves
by Thomas F. Banchoff and P. J. Giblin

A piecewise-circular curve is a curve composed of circular arcs and line segments joined in such a way that the direction of the tangent vector varies continuously. This paper examines the symmetry sets and one-parameter families of these curves. PC curves have been used in applications involving approximations of smooth curves, and symmetry sets have numerous applications in the area of shape recognition. It is shown that symmetry sets of general one-parameter families of plane curves and mirrored by symmetry sets of a small set of PC curves.