The four intersection-and-difference model for line-line topological relations

Abstract

The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance. It is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR1 and IR2.