An Efficient Algorithm for Generating Composition Tables for Qualitative Spatial Relations

Qualitative Spatial Reasoning (QSR) is useful for deriving logical inferences when quantitative spatial information is not pertinent or not available. The automated derivation of such logical inferences becomes a binary constraint satisfaction problem; binary relations can be formulated as a region-based qualitative reasoning problem involving disjunctive constraints. It has been proved [1] that composition-based reasoning is complete for deriving inferences in various calculi; hence a composition table is a central part of QSR and consistency-checking. Previously developed algorithms to construct such tables have required manual or, at best, semi-automatic analysis. Herein we present a new divideand-conquer algorithm to automatically construct a composition table for spatial relations, and apply it to the 3D region connection calculus, VRCC3D+. This validates the hypothesis that consistency-checking, entailment checking, and occlusion can be supported in 3D.