A System Handling RCC-8 Queries on 2D Regions Representable in the Closure algebra of Half-Planes

Brandon Bennett, Amar Isli, Anthony G. Cohn

Abstract: The paper describes an algebraic framework for representing and reasoning about 2D spatial regions. The formalism is based on a Closure Algebra (CA) of half-plaries -i.e., a Boolean Algebra augmented with a closure operator. The CA provides a flexible representation for polygonal regions and for expressing topological constraints among such regions. The paper relates these constraints to relations defined in the 1st-order Region Connection Calculus (RCC). This theory allows the definition of a set of eight topological relations (RCC-8) which forms a partition of all possible relations between two regions. We describe an implemented algorithm for determining which of the RCC-8 relations holds between any two regions representable in the CA. One application of such a system is in Geographical Information Systems (GIS), where often the data is represented quantitatively, but it would be desirable for queries to be expressed qualitatively in a high level language such as that of the RCC theory.