Issue No. 07 - July (1985 vol. 34)

ISSN: 0018-9340

pp: 663-666

M.J. Atallah , Department of Computer Sciences, Purdue University

ABSTRACT

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.

INDEX TERMS

string pattern matching, Analysis of algorithms, axis of symmetry, centroid, computational geometry

CITATION

M.J. Atallah, "On Symmetry Detection",

*IEEE Transactions on Computers*, vol. 34, no. , pp. 663-666, July 1985, doi:10.1109/TC.1985.1676605