Topological Relations In The World Of Minimum Bounding Rectangles: A Study With R-trees

Abstract

Recent developments in spatial relations have led to their use in numerous applications involving spatial databases. This paper is concerned with the retrieval of topological relations in Minimum Bounding Rectangle-based data structures. We study the topological information that Minimum Bounding Rectangles convey about the actual objects they enclose, using the concept of projections. Then we apply the results to R-trees and their variations, R⁺-trees and R*-trees in order to minimise disk accesses for queries involving topological relations. We also investigate queries that involve complex spatial conditions in the form of disjunctions and conjunctions and we discuss possible extensions.