Topological feature vectors for exploring topological relationships

Topological relationships between spatial objects such as overlap, disjoint, and inside have for a long time been a focus of research in a number of disciplines like cognitive science, robotics, linguistics, artificial intelligence, and spatial reasoning. In particular as predicates, they support the design of suitable query languages for spatial data retrieval and analysis in spatial database systems and Geographic Information Systems. While conceptual aspects of topological predicates (like their definition and reasoning with them) as well as strategies for avoiding unnecessary or repetitive predicate evaluations (like predicate migration and spatial index structures) have been emphasized, the development of correct and efficient implementation techniques for them has been rather neglected. Recently, the design of topological predicates for different combinations of complex spatial data types has led to a large increase of their numbers and accentuated the need for their efficient implementation. The goal of this article is to develop efficient implementation techniques of topological predicates for all combinations of the complex spatial data types point2D, line2D, and region2D, as they have been specified by different authors and in different commercial and public domain software packages. Our solution is a two‐phase approach. In the exploration phase, for a given scene of two spatial objects, all topological events like intersection and meeting situations are recorded in two precisely defined topological feature vectors (one for each argument object of a topological predicate) whose specifications are characteristic and unique for each combination of spatial data types. These vectors serve as input for the evaluation phase which analyzes the topological events and determines the Boolean result of a topological predicate or the kind of topological predicate. This paper puts an emphasis on the exploration phase and the definition of the topological feature vectors. In addition, it presents a straightforward evaluation method.