Representation and Reasoning of Three-Dimensional Spatial Relationships Based on R5DOS-Intersection Model Representation and Reasoning Based on R5DOS Model

Abstract

This paper aims to disclose the compound topological and directional relationships of three simple regions in the three-dimensional (3D) space. For this purpose, the directional model and the 8-intersection model were coupled into an R5DOS-intersection model and used to represent three simple regions in the 3D space. The matrices represented by the model were found to be complete and mutually exclusive. Then, a self-designed algorithm was adopted to solve the model, yielding 11,038 achievable topological and directional relationships. Compared with the minimum bounding rectangle (MBR) model, the proposed model boasts strong expressive power. Finally, our model was applied to derive the topological and directional relationships between simple regions A and C from the known relationships between simple regions A and B and those between B and C. Based on the results, a compound relationship reasoning table was established for A and C. The research results shed new light on the representation and reasoning of 3D spatial relationships.