Extended model of topological relations between spatial objects in geographic information systems

This paper presents an extended model for describing topological relations between two sets (objects) in geographic information systems (GIS). First, based on the definition of the topological relations between two objects, we uncover a sequence of topological relations between two convex sets. Second, an extended model for topological relations between two sets is proposed based on the new definition. The topological relations between two convex sets are expressed as a sequence of 4 × 4 matrices, which are the topological properties of A(o) ∩ B(o), A(o)\B, B(o)\A, ∂A ∩ ∂B. The model is also extended for handling the properties of the topological relations between two non-convex sets, where the factor of first fundamental group is added to A ∪ B to handle these complex relations. The results show that the number of topological relations between the two sets is not as simple as finite but infinite and can be approximated by a sequence of matrices.