GIS空间线目标间拓扑关系形式化描述模型

Formal Model Describing Topological Relations Between Spatial Linear Objects in GIS

针对现有拓扑关系描述模型的不足,首先以点集拓扑学基本理论为基础,定义了空间线目标的端点、内部、边界等概念,在此基础上提出了一种描述空间线目标间拓扑关系完善的形式化模型——New 9交模型。根据线目标的物理意义,提出了5条取值规则以排除模型描述的拓扑关系中没有意义的类型,并在此基础上总结出了空间线目标间拓扑关系的最小集,定义了6种线目标间的基本拓扑关系,并且证明了此最小集的互斥性与完备性。

Aiming at the deficiency of the current models describing topological relations, the concepts of the endpoint, inner and boundary of spatial linear object were defined on the basis of basic theory of point-set topology at first; and a formal perfect model describing topological relations between spatial linear objects was proposed based on that. Five rules were put forward to exclude the impossible topological relations which were de- scribed by the model according to the physical meaning of spatial linear objects. Based on that the smallest set of topological relations between spatial line objects was proposed, and the exclusivity and perfectibility of the smallest set were proved.