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A PROVABLE ALGORITHM TO DETECT WEAK SYMMETRY IN A POLYGON

Laboratoire de Mathématiques Informatique et Applications, Université Haute Alsace, 4 Rue des Frères, Lumière 68093, Mulhouse, France

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FREDERIC CORDIER

Laboratoire de Mathématiques Informatique et Applications, Université Haute Alsace, 4 Rue des Frères, Lumière 68093, Mulhouse, France

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NICKOLAS S. SAPIDIS

Department of Mechanical Engineering, University of Western Macedonia, Bakola and Sialvera Street, Kozani GR-50100, Greece

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https://doi.org/10.1142/S0219467813500022Cited by:0 (Source: Crossref)

Abstract

This paper deals with the problem of detecting "weak symmetry" in a polygon, which is a special bijective and continuous mapping between the vertices of the given polygon. An application of this work is the automatic reconstruction of 3D polygons symmetric with respect to a plane from free-hand sketches of weakly-symmetric 2D polygons. We formalize the weak-symmetry notion and highlight its many properties which lead to an algorithm detecting it. The closest research work to the proposed approach is the detection of skewed symmetry. Skewed symmetry detection deals only with reconstruction of planar mirror-symmetric 3D polygons while our method is able to identify symmetry in projections of planar as well as nonplanar mirror-symmetric 3D polygons.

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