From three-dimensional topological relations to contact relations

Abstract

Topological relations, which concern how two objects intersect, are one of the most fundamental and well-studied spatial relations. However, in reality, two physical objects can take only disjoint relation if they are solid. Thus, we propose an alternative of topological relations, called contact relations, which capture how two objects contact each other. Following the framework of the 9-intersection, this model distinguishes contact relations based on the presence or absence of contacts between several surface elements of two objects. Consequently, the contact relations have a strong correspondence to the 9-intersection-based topological relations. Making use of this correspondence, we derive the contact relations between various combinations of objects in a 3D Euclidean space (R3). For this purpose, we first review and analyze the topological relations in R3. Then, these topological relations are mapped to contact relations.