基于结点度和欧拉数的拓扑关系一般化描述

The General Description of Topological Relations based on Node Degree and Euler-number

拓扑关系是GIS中空间目标间最基本、最重要的关系之一,然而目前的拓扑关系模型在描述两目标间的详细拓扑关系方面存在不足。针对二元目标间任意交的情况,提出了基于结点度和欧拉数的拓扑关系模型的一般化描述形式,使用目标整体间交(∩)、差(\)两个集合算子的结果来区分目标间的拓扑关系,结果的取值包括内容、维数、结点度、欧拉数4个拓扑不变量。重点讨论了线/线、线/面和面/面拓扑关系一般化描述表达式。

Topological relationship is one of the most basic and the most important relations between two spatial objects in GIS.However,current topological models have deficiencies when they are used to describe detailed topological relations.In this paper,one general descriptive form of topological relation model was proposed based on the node degree and the euler-number aiming at random two objects.In this model,all parts of one spatial object were treated as a whole object,and intersection difference operators were selected from several set operators to distinguish the topological relations,and four types of topological invariants were used for the computational results of contents,dimension,node degree,and euler-number.The topological description form of line-line,line-area,area-area were discussed emphatically.