AN ALGEBRA FOR SLOPE-MONOTONE CLOSED CURVES
Kōkichi Sugihara, Toshiyuki Imai, Takeshi Hataguchi · International Journal of Shape Modeling · 1997
The paper proposes a new operation for a class of slope-monotone closed curves. This operation is closely related to the Minkowski sum in that the Minkowski sum can be considered as the binary operation for figures bounded by those closed curves. In this sense, the proposed algebra is a generalization of the Minkowski sum. Conventionally, the inverse of the Minkowski sum can be defined naturally for convex figures, but the generalization of the inverse to nonconvex figures results in a complicated algebraic structure. This paper, on the other hand, gives a natural definition of the inverse for nonconvex figures, and thus constructs a simple algebraic structure.