##
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.