基于点集拓扑学的三维拓扑空间关系形式化描述

THE FORMAL DESCRIPTION OF TOPOLOGICAL SPATIAL RELATIONSHIP IN 3D BASED ON POINT SET TOPOLOGY

本文阐明了研究空间关系理论的必要性，分析了拓扑空间关系描述方法的研究进展及存在问题，以点集拓扑理论为基础，运用维数扩展的方法，提出了三维拓扑空间关系完善和形式化的描述框架，在此基础上，对三维空间目标中存在着的拓扑空间关系进行了分类，定义了五种基本的拓扑空间关系。

Practical need in GIS have let to the investigation of formal method of describing spatial relationships. After an introduction to the basic ideas and notions of topological relationship, an extension of geometric point set approach by taking the dimension of the intersections into account is presented. This results in a very large number of different topological relationships in 3D for Point, Line, Surface, and Body features. Then we propose to group all possible case into a few meaningful topological relationships and discuss their exclusiveness and completeness with respect to the point set approach.