Modeling Cardinal Direction Relations in 3D for Qualitative Spatial Reasoning

Many fundamental geoscience concepts and tasks require advanced spatial knowledge about the topology, orientation, shape, and size of spatial objects. Besides topological and distance relations, cardinal directions also can play a prominent role in the determination of qualitative spatial relations; one of the facets of spatial objects is the determination of relative positioning of objects. In this paper, we present an efficient approach to representing and determining cardinal directions between free form regions. The development is mathematically sound and can be implemented more efficiently than the existing models. Our approach preserves converseness of direction relations between pairs of objects, while determining directional relations between gridded parts of the complex regions. All the essential details are in 2D. Yet the extension to 3D is seamless; it needs no additional formulation for transition from 2D to 3D. Furthermore, the extension to 3D and construction of a composition table has no adverse impact on the computational efficiency, as the technique is akin to 2D.