A formal model describing topological relations between spatial linear objects in GIS-T

Abstract

The importance of studying topological relations between spatial linear objects is expounded. The concepts endpoint, interior, exterior and boundary of spatial linear object are defined on the basis of basic theories of point-set topology, and a formal and perfect model describing topological relations between spatial linear objects is proposed based on that. Fifteen negative rules are putted forward to exclude the impossible topological relations which are described by the model according to the realistic physical meaning of spatial linear objects. The smallest set of topological relations between spatial line objects is proposed, and the exclusivity and perfectibility of the smallest set are proved.