郭薇, 陈军. 基于流形拓扑的三维空间实体形式化描述[J]. 武汉大学学报 ( 信息科学版), 1997, 22(3): 201-206.
引用本文: 郭薇, 陈军. 基于流形拓扑的三维空间实体形式化描述[J]. 武汉大学学报 ( 信息科学版), 1997, 22(3): 201-206.
Guo Wei, Chen Jun. Formal Framework of 3D Spatial Features and Topological Property Based on Manifold Topology[J]. Geomatics and Information Science of Wuhan University, 1997, 22(3): 201-206.
Citation: Guo Wei, Chen Jun. Formal Framework of 3D Spatial Features and Topological Property Based on Manifold Topology[J]. Geomatics and Information Science of Wuhan University, 1997, 22(3): 201-206.

基于流形拓扑的三维空间实体形式化描述

Formal Framework of 3D Spatial Features and Topological Property Based on Manifold Topology

  • 摘要: 阐述了三维空间实体语义概念及空间实体之间拓扑性质形式化描述的意义,以组合及点集拓扑理论为基础,给出了基于k-维伪流形的三维空间实体的语义定义。将单纯同调理论用于流形,通过单纯形和单纯复形间的几何构造关系,揭示出三维空间实体的拓扑性质并给出三维空间实体的形式化描述方法。

     

    Abstract: The lack of compressive theory and formal description methods about 3D spatial features and their topological properties have been a major impediment to practical 3D spatial data model implementation. This paper focused on the research of a topological model based on space partition for 3D GIS. In terms of point-set topology and combination topology, the formal definition of 3D spatial features are described as orientable n-pseudomanifolds(0≤n≤3),and it can be represented by complexes which is the union of same or lower simplexes. From the number of important topological properties of n-pseudomanifolds and continuous map about homeomorphism and homotopy, the topological properties such as space partition, orientability, connectivity and Euler characteristic are determined. According to the formal description of simplexes and complexes, the formal framework of 3D spatial features is presented.

     

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