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On Symmetry Detection
July 1985 (vol. 34 no. 7)
pp. 663-666
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.
Index Terms:
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
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