Abstract
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for the recognition of polygons in R 2 modulo the special Euclidean, Euclidean, equi-affine, skewed-affine, and similarity Lie groups. We also solve the case of polygons in the Poincar\'e half-plane under the action of SL(2) and explain a method applicable to Lie group actions in general. The time complexity of our algorithms is linear in the number of vertices and they are noise resistant. The signatures used allow the detection of partial, as well as approximate, equivalences.
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Communicated by Arieh Iserles
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Boutin, M. Polygon Recognition and Symmetry Detection. Found Comput Math 3, 227–271 (2003). https://doi.org/10.1007/s10208-001-0027-5
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DOI: https://doi.org/10.1007/s10208-001-0027-5