The Neighborhood Configuration Model: A Framework to Distinguish Topological Relationships between Complex Volumes

Abstract

Topological relationships between spatial objects are considered to be important for spatial databases. They lead to topological predicates, which can be embedded into spatial queries as join or selection conditions. Before rushing into the implementation of topological predicates, topological relationships between spatial objects must be first understood and clarified. This requires a detailed study of a vast number of possible spatial configurations at the abstract level, and as a result, methods that are able to classify and identify as many as possible different spatial configurations are needed. While a lot of research has already been carried out for topological relationships in the 2D space, the investigation in the 3D space is rather neglected. Developed modeling strategies are mostly extensions from the popular 9-intersection model which has been originally designed for simple 2D spatial objects. We observe that a large number of topological relationships, especially the ones between two complex 3D objects are still not distinguished in these models. Thus, we propose a new modeling strategy that is based on point set topology. We explore all possible neighborhood configurations of an arbitrary point in the Euclidean space where two volume objects are embedded, and define corresponding neighborhood configuration flags. Then, by composing the Boolean values of all flags, we uniquely identify a topological relationship between two complex volume objects.