拓扑关系形式化描述的Euler示性数模型  

Modeling Topological Relations Based on Euler Characteristics

作　　者：邓敏[1] 张雪松[2] 林宗坚[3] 

机构地区：[1]南京大学城市与资源学系,南京市汉口路22号210093 [2]武汉大学空间信息与数字工程研究中心,武汉市珞喻路129号430079 [3]中国测绘科学研究院

出　　处：《武汉大学学报（信息科学版）》2004年第10期872-876,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(40101022);国家教育部高校博士点基金资助项目(20010284011)。

摘　　要：给出了空间目标的一般表达式,并利用代数运算和集合运算相结合的方法计算出空间目标的拓扑边界和内部。针对空间目标点集拓扑运算所得集合的非闭性,提出了一种适合于Euler示性数计算的方法,建立了一种形式化描述拓扑关系的Euler示性数模型。实例证明了所提方法和形式化模型的正确性。The criteria on the description and determination of topological relations are topological invariants, which may be dimension, separations, Euler characteristics etc. This paper is concentrated on some basic issues of modeling topological relations using Euler characteristics. Geometricaly, a detailed investigation on the relations among simplex, complex and spatial object is made. With the introduction of the concept of pure complex, a generic representation of spatial object in the GIS field is given. Topological components of simplex, i.e. boundary and interior, are then defined through the algebraic topology. A suitable and sound pre-processing approach is put forward prior to calculation of Euler characteristics. Compared with the classic 4/9-intersection model, the model based on Euler characteristics can distinguish more details in topological aspect.

关 键 词：单纯剖分 拓扑关系 形式化方法 分离数 

分 类 号：P208[天文地球—地图制图学与地理信息工程]