Spatial relations, minimum bounding rectangles, and spatial data structures

Spatial relations are important in numerous domains, such as Spatial Query Languages, Image and Multimedia Databases, Reasoning and Geographic Applications. This paper is concerned with the retrieval of topological and direction relations using spatial data structures based on Minimum Bounding Rectangles. We describe topological and direction relations between region objects and we study the spatial information that Minimum Bounding Rectangles convey about the actual objects they enclose. Then we apply the results in R-trees and their variations, R-trees and R*-trees, in order to minimize the number of disk accesses for queries involving topological and direction relations. We also investigate queries that express complex conditions in the form of disjunctions and conjunctions, and discuss possible extensions.