Efficient determination of spatial relations using composition tables and decision trees

In order for Qualitative Spatial Reasoning applications to be both useful and usable, the information feedback loop between the computational engine and the user must be as seamless as possible. Inherently, computational geometry can be quite expensive, and every effort must be made to avoid inefficient or unnecessary calculations. Within the field of Region Connection Calculi, the 9-Intersection model often is used to determine the spatial relation between two regions. Consequently, optimization efforts typically focus on calculations involving the intersections between the interiors, boundaries, and exteriors of the regions, or the use of composition tables to narrow down the possibilities for the relations that can hold between two regions. The few implementations of spatial reasoners that have been attempted have been simply proofs-of-concept and/or have been limited to two dimensions. Herein we present a novel approach that combines the use of composition tables and decision trees to efficiently determine the spatial relation between two objects in 3D considering both connectivity and obscuration. This approach has been fully implemented for the VRCC-3D+ spatial reasoning system, and benchmarks are included to corroborate our claims of efficiency.