中文摘要：

本文提出了基于9 交矩阵的拓扑关系计算方法,将复杂区域分解有限个简单区域,采用正则表 达式描述其多部分和洞构成,通过定义两个9 交关系矩阵操作算子,利用分解区域间的拓扑关系直接计 算复杂区域间的9 交关系矩阵.详细证明和分析了两个操作算子的不成立条件以及消除不成立条件的 方法.结合关系矩阵表法拓扑关系的推导和推理过程,操作算子可用于推导已知结构复杂区域间的所 有可能 9 交拓扑关系.同时, 9 交关系矩阵操作算子依赖复杂区域的定义,不适用于所有区域对象.

英文摘要：

A novel method was proposed for computing topological relations between complex regions based on 9-intersection （91） matrices. A complex region was composed of a finite set of simple regions and its configuration was represented as a regular expression. Two 91 Boolean matrix operators were defined and used for computing the binary topological relations between complex regions while the relations between the decomposed regions were known. The establishing conditions of the operators were proved and analyzed in detail and the method of eliminating the ambiguities was given to make the computation correct. The approach can be used as a useful computation tool to analysis topological relations between spatial objects with specific configurations. In addition, the operators are dependent on definitions of complex regions and not suitable for regions which violate our definitions.