三个简单区域间的拓扑关系的表示模型

空间拓扑关系的研究多数集中在两个区域间的拓扑关系上,对两个以上区域间拓扑关系的研究则很少。本文通过扩展4-交集矩阵得到8-交集模型,对三个简单区域间空间关系进行表示,并给出了三个简单区域间的109种拓扑关系图。与分别表示出三个简单区域间两两拓扑关系的4-交集矩阵方法相比,本文提出的8-交集矩阵表示法能直接对三个简单区域间的拓扑关系进行表示,且新增了56种基本关系,表达力更强。证明了8-交集模型中基本关系的完备性和互斥性,给出算法并通过程序验证了三个简单区域间至多有109种可实现的拓扑关系,并给出了109种三元拓扑关系的概念领域图。

Representation model of topological relationship among three simple regions

There exist representative models for spatial topological relationships,such as the Region Connection Calculus(RCC) model and Intersection model.However,most of the models are suitable for the spatial relation between two regions,but few for three regions.In this paper,we extend the 4-intersection matrix model to 8-intersection model to represent the spatial relationship among three simple regions.Using this model we can obtain 109 topological relationships among three simple regions,which are 56 more than that can be obtained by the 4-intersection matrix model.We proved the exclusivity the completeness of the 109 topological relationships.We also present an algorithm to show that at most there are 109 feasible topological relationships among three simple regions.The conceptual neighborhood graph of 109 ternary topologiral relations is also given.