Abstract
Exact algorithms for detecting all rotational and involutional symmetries in point sets, polygons and polyhedra are described. The time complexities of the algorithms are shown to be θ (n) for polygons and θ (n logn) for two- and three-dimensional point sets. θ (n logn) time is also required for general polyhedra, but for polyhedra with connected, planar surface graphs θ (n) time can be achieved. All algorithms are optimal in time complexity, within constants.
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Wolter, J.D., Woo, T.C. & Volz, R.A. Optimal algorithms for symmetry detection in two and three dimensions. The Visual Computer 1, 37–48 (1985). https://doi.org/10.1007/BF01901268
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DOI: https://doi.org/10.1007/BF01901268