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

Abstract

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.

A Complete Classification of Occlusion Observer’s Point of View for 3D Qualitative Spatial Reasoning

“…RCC8 spatial relation for 3D objects is incomplete without occlusion consideration. VRCC-3D+ is a region connection calculus that qualitatively determines the spatial relations between 3D objects, both in terms of connectivity and obscuration [6,8,9]. The VRCC-3D+ connectivity relations are named the same as in RCC8; however, the VRCC-3D+ connectivity relations are calculated in 3D rather than 2D.…”

“…The relative depth is denoted by tri-valent parameter InFront. Fifteen obscuration relations were defined in VRCC-3D+ [8,9]. Considered from a 2D projection, each VRCC-3D+ obscuration relation is a refinement of basic concepts of no obscuration, partial obscuration, and complete obscuration.…”

“…In Section 1, we mentioned that there are issues in the implementation of occlusion in VRCC-3D+ [9]. Let us first describe the problems and then we will present new formulation and new crisp occlusion relations in Section 5.…”

“…Also there are repeated occlusion ray tracing computations that can be eliminated. As it is, the occlusion computation is quite inefficient in [9]. Table 1.…”

“…However there were some issues that required resolution. Recently, Eloe et al attempted to resolve such issues and improve upon the computational aspects in 2014 [9]. In their attempt, they introduced two predicates for depth as discussed in Section 4, which turned out to be obscure and inefficient.…”