Abstract
Two planar figures aresimilar if a scaled version of one of them can be moved so that it coincides with the second figure. The problem of checking whether two planar figures are similar is relevant to both computational geometry and pattern recognition. An efficient algorithm is known for checking whether two polygonsP andQ are similar(1) The purpose of this note is to give an efficient algorithm for checking whether two planar figuresP andQ are similar when the figures are no longer constrained to be polygons. We give anO(n logn) time algorithm for solving this problem when each figure consists of a collection of (possibly intersecting) straight line segments, circles, and ellipses. Our algorithm can easily be modified for figures which include other geometric patterns as well. We also prove that our algorithm is optimal.
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This work was partially supported by the Office of Naval Research under Contract N00014-84-K-0502.
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Atallah, M.J. Checking similarity of planar figures. International Journal of Computer and Information Sciences 13, 279–290 (1984). https://doi.org/10.1007/BF00977833
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DOI: https://doi.org/10.1007/BF00977833