IMPROVING 9-INTERSECTION MODEL BY REPLACING THE COMPLEMENT WITH VORONOI REGION

摘要

9-intersection model is the most popular framework used for formalizing the rnspatial relations between two spatial objects A and B. It transforms the topological relationrnships between two simple spatial objects A and B into point-set topology problem in terms of rnthe intersections of A's boundary ( A), interior (A0) and exterior (A - ) with B's boundrnary ( B),interior (B0) and exterior (B-). It is shown in this paper that there exist some rnlimitations of the original 9-intersection model due to its definition of an object's exterior as rnits complement,and it is difficult to distinguish different disjoint relations and relations berntween complex objects with holes, difficult or even impossible to compute the intersections rnwith the two object' s complements ( A ∩ B -, A0 ∩ B -, A - ∩ B, A- ∩ B0 and A - ∩rnB - )since the complements are infinitive. The authors suggest to re-define the exterior of sparntial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-in-rntersection (VNI) is proposed and used for formalizing topological relations between spatial rnobjects. By improving the 9-interscetion model, it is now possible to distinguish disjoint relarntions and to deal with objects with boles. Also it is possible to compute the exterior-based inrntersections and manipulate spatial relations with the VNI.