Hyperpolygons generated by the invertible Minkowski sum of polygons

Authors:
Kokichi Sugihara
Affiliations:
Department of Mathematical Informatics Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Venue:
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Year:
2004

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Abstract

The paper gives a new formulation of the Minkowski sum of polygons. In the conventional Minkowski sum, the inverse operation is not well defined unless the polygons are restricted to be convex. In the proposed formulation, on the other hand, the set of polygons is extended to the set of "hyperpolygons", in which the Minkowski sum forms a commutative group. Consequently, every polygon has its unique inverse, and the sum and the inverse operations can be taken freely. A relation between hyperpolygons and physical reality is also discussed.