基于布尔运算的三维拓扑关系分析

Because of the complex of computational geometry algorithms and the lack of three dimensional topological relationships computing framework, it is difficult to acquire the three dimensional topological relationships. Boolean operations work on two or more shapes to create more complicated shapes in combination with each other. Boolean operations usually include intersection operation, union operation, and difference operation. By determining whether the intersection is empty or not, many topological relationship formal models are established. Boolean operations and topological relationship formal models are consistent in some aspects. In this project, boolean operations are introduced to solve three dimensional topological relationships analysis. Firstly, in order to describe the geospatial objects and their relationships, the unified spatial data model will be proposed. Secondly, the related three dimensional computational geometry algorithms and boolean operation framework will be designed to support the implementation of intersection operation, union operation, and difference operation. Thirdly, the formalized and semantic representation of the three dimensional topological relationships will be studied base on point set topology theory. Fourthly, three dimensional topological relationships technical framework based on boolean operations will be put forward to support the acquisition of topological relations semantic information from the original data structure. Lastly, three dimensional topological relationships operation tools will be designed to study three dimensional topological relationships analysis. In this project, boolean operations being introduced to the topic of three dimensional topological relationships analysis will expand the research of three dimensional topological relations and promote the development of three dimensional GIS.

三维拓扑关系获取涉及到复杂的计算几何算法，且缺乏系统的三维拓扑关系计算框架，由此导致三维拓扑关系分析比较困难。交、并和差等布尔算子的设计理念与三维拓扑关系表达方法的设计思路具有一致性。因此，本课题拟基于布尔运算的理论和方法实现三维拓扑关系分析。以三维空间数据构模理论为基础，研究各种维度的空间对象的统一表达；研究三维计算几何算法的实现和基于计算几何算法的布尔运算框架，实现交、并和差等布尔算子；以点集拓扑学理论为基础，研究三维拓扑关系形式化和三维拓扑关系语义表达方法；研究基于布尔运算的三维拓扑关系计算技术框架，实现直接从底层的数据结构获取高层次的拓扑关系语义信息；构建三维拓扑关系操作工具，实现三维拓扑关系分析。本课题将计算机领域的三维布尔运算理论和方法引入到三维拓扑关系分析中，拓展了三维拓扑关系研究的思路，有望在三维拓扑关系分析研究上取得创新性的研究成果，推动3D GIS的发展。

拓扑关系是指在拓扑变换下保持不变的空间关系，即拓扑不变量。三维拓扑关系的计算是三维GIS领域研究的热点。本项目定义了一种集成对象和域的面向对象的空间数据模型，实现了三维空间实体及其关系的表达；基于OGC简单要素规范，扩展对三维空间对象的表达，实现了零维、一维、二维、三维和混合维空间对象的统一表达。设计了三维空间对象之间的计算几何算法，并且基于计算几何算法，实现了空间对象的交、并和差布尔运算。基于9交集模型，实现了三维空间对象之间拓扑关系的表达；扩展了OpenGIS SQL实施规范的拓扑关系定义，定义点、线、面、体以及集合对象之间的八种拓扑关系：Disjoint、Touches、Within、Overlaps、Contains、Equal、Covers、CoveredBy；针对三维拓扑关系形式化模型和三维拓扑关系语义表达模型之间映射问题，建立点、线、面、体以及集合对象之间存在的拓扑关系的形式化表达模型，从而实现形式化表达模型和拓扑关系语义表达之间的对应。建立了拓扑关系决策树，并沿着拓扑关系决策树进行拓扑关系判别，从而计算出空间对象之间的拓扑关系。本课题的研究对于三维GIS的研究具有一定的促进作用。