Topological relations in spatial databases

Various models for the representation of topological relations have been developed. The aim of this chapter is to propose a comprehensive view of state-of-the-art models for topological relations in spatial databases. A prominent role is assumed by the CBM (calculus-based method), which offers a small set of topological relations with high expressiveness and suitability to be embedded as operators of a spatial query language. The CBM is applicable to all kinds of complex geometric features and constitutes the user-oriented level (top level) of a hierarchy of topological operators. At lower levels (with more geometric details), other models are proposed, which are also applicable to geometric features with a broad boundary (features that are able to model spatial uncertainty). Eventually, a classification of all topological invariants of a spatial relation between two features offers the tools to describe the finest topological details.