3D digital topological relationship analysis for spatial entity with fuzzy boundary

This paper discusses the topological relations between 3D spatial entities with fuzzy boundaries, and introduces a regular block model-based computable topological analysis approaches. Based on 3D digital topology theory, a regular block is defined with 6-connectiviity and the interior, the fuzzy boundary and the k-order 6 neighborhoods of a spatial entity with fuzzy boundary are defined. Furthermore, a new topological relationship analysis model improved from 9-intersection model is presented and named as k-order six neighborhoods 9-Intersection model (K6N9-I model). In this model, the original interior, boundary and exterior of 9-I model are respectively replaced with newly defined components for spatial entities with fuzzy boundaries. SQL is introduced to compute the count and content of each intersection element of the new model. The mapping regulation from quantitative model matrix to qualitative topological relations is discussed in details and several refined topological relations such as deeply/shallowly intersect, far/nearly disjoint etc are identified.