Integrating Representation of Topological Relationships and Direction Relationships and Their Inter-restriction

An integrating representation method of the topological and direction relationships is proposed.Nine intersection model and direction relation matrix are used to depict the two relationships separately.Topological relationships and direct relationships are represented by 3×3 matrix respectively,so we proposed to use 3×6 matrix to depict topological and direct relationships in an unified framework.Based on the Goyal's research on direction relationships,additional 163 types of direction relationships are illustrated for linear object as source spatial object.In an uniform framework,seven theorems and their mathematical proofs for the inter-restriction of topological and direction relationships are set forth.This integration representation method can improve the representation effect of spatial relationships.