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On Symmetry Detection
July 1985 (vol. 34 no. 7)
pp. 663-666
| ASCII Text | x | ||
| M.J. Atallah, "On Symmetry Detection," IEEE Transactions on Computers, vol. 34, no. 7, pp. 663-666, July, 1985. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1985.1676605, author = {M.J. Atallah}, title = {On Symmetry Detection}, journal ={IEEE Transactions on Computers}, volume = {34}, number = {7}, issn = {0018-9340}, year = {1985}, pages = {663-666}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1985.1676605}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - On Symmetry Detection IS - 7 SN - 0018-9340 SP663 EP666 EPD - 663-666 A1 - M.J. Atallah, PY - 1985 KW - string pattern matching KW - Analysis of algorithms KW - axis of symmetry KW - centroid KW - computational geometry VL - 34 JA - IEEE Transactions on Computers ER - | |||
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. 7, pp. 663-666, July 1985, doi:10.1109/TC.1985.1676605
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