Issue No.07 - July (1985 vol.34)
M.J. Atallah , Department of Computer Sciences, Purdue University
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 O(n log n) time lower bound for this problem.
string pattern matching, Analysis of algorithms, axis of symmetry, centroid, computational geometry
M.J. Atallah, "On Symmetry Detection", IEEE Transactions on Computers, vol.34, no. 7, pp. 663-666, July 1985, doi:10.1109/TC.1985.1676605