基于代数拓扑的地理空间多特征表达与分析计算统一数据模型及方法研究

How to construct a three-dimensional spatial data model that supports both geospatial multi-features representation and analysis calculation, which is a key technology for the 3D GIS to support geo-analysis and computation. This project proposal takes advantage of the algebraic topology to do the research of the theory and method of 3D GIS, and tries to construct a unified data model of geospatial multi-features representation and analysis computations based on the algebraic topology, and then explore the implementation method of typical spatial analysis and computing operations of 3D GIS. Based on the cellular homology and cellular homotopy theory of the algebraic topology, the formal definition of geospatial objects is researched, and then the unified representation of multi-features information of geospatial objects such as geometry, topology, attributes and semantic is achieved. Through the research of abstracting analysis method of geospatial objects based on algebraic topology, the conceptual structure of the unified data model is designed. Making use of cellular complex chain and its operators of algebraic topology, the three-dimensional spatial data storage structure of the unified data model is realized, and then typical 3D GIS spatial analysis and computation operations method are achieved, such as three-dimensional spatial entities Boolean operations and three-dimensional space mesh discretization. This project has important significance in improving the theory and method of 3D GIS and its ability to solve practical geographic problems.

如何构建可以同时支持地理空间多特征表达与分析计算的三维空间数据模型，是三维GIS支持地学分析与计算的关键技术。本项目将代数拓扑引入到三维GIS理论与方法研究中，构建基于代数拓扑的地理空间多特征表达与分析计算统一数据模型，并探索典型三维GIS空间分析与计算操作的实现方法。以代数拓扑中胞腔同调和胞腔同伦理论为依据，研究基于代数拓扑的地理空间对象形式化定义方法，实现地理空间对象几何、拓扑、属性和语义等多特征信息的统一描述与表达；通过研究基于代数拓扑的地理空间对象抽象分析方法，实现统一数据模型的概念结构设计；利用代数拓扑中胞腔复形链及其操作算子，实现统一数据模型的三维空间数据存储结构，并探索基于代数拓扑的三维空间实体间布尔运算与三维空间网格离散等典型三维GIS空间分析与计算操作的实现方法。研究成果对完善三维GIS的理论与方法、提高其解决实际地理问题的能力等方面有重要意义。

为了增强三维GIS支持地学分析与计算的能力，项目组将代数拓扑引入到三维GIS理论与方法研究中，构建了基于代数拓扑的地理空间多特征表达与分析计算统一数据模型，并探索了典型三维GIS空间分析与计算操作的实现方法。项目组提出了基于代数拓扑的地理空间对象形式化定义方法，实现地理空间对象几何、拓扑、属性和语义等多特征信息的统一描述与表达；在此基础上，项目组利用代数拓扑中胞腔复形链及其操作算子，实现了统一数据模型的三维空间数据存储结构，并完成了基于代数拓扑的三维空间实体间布尔运算与三维空间网格离散等典型三维GIS空间分析与计算操作的实现方法。为了验证方法的正确性和有效性，进一步研究了基于能量算子的三维空间实体模型简化和细分方法，在此基础上,实现了顾及多结构特征约束的建筑物三维激光点云立面特征提取方法，取得了较好的科研成果。本项目的研究成果，对完善三维GIS的理论与方法、提高其解决实际地理问题的能力等方面有重要意义。