A More Efficient Representation of Obscuration for VRCC-3D+ Relations

VRCC-3D+ is an implementation of a region connection calculus that qualitatively determines the spatial relation between two 3D objects in terms of connectivity and obscuration. The eight connectivity relations are conceptually the same as RCC8, but calculated in 3D rather than 2D. The fifteen obscuration relations are calculated using the projection of the 3D objects on a particular 2D plane and the distance of the objects from the viewpoint. Herein we present a smaller, more precise set of VRCC-3D+ obscuration relations that retains the qualities of being jointly exhaustive and pairwise disjoint. However, this new set of relations overcomes two problems that existed in the previous set of fifteen relations: (1) lack of a precise mathematical definition for a key predicate, InFront, and (2) lack of an intuitive mapping of converse relations.