On Symmetry Detection

A straight line is an axis ofsymmetry of a planar figure if the figure is invariant to reflection with respect to that line. The purpose of this correspondence is to describe an O( n log n) time algorithm for enumerating all the axes of symmetry of a planar figure which is made up of (possibly intersecting) segments, circles, points, etc. The solution involves a reduction of the problem to a combinatorial question on words. Our algorithm is optimal since we can establish an Ω(n log n) time lower bound for this problem.