Hyperpolygons generated by the invertible Minkowski sum of polygons
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.
polygon minkowski sum inverse operation boundary representation angle-parametrized polygonal curve