多个空间区域间拓扑关系模型的研究

Spatial reasoning has important applications in geographic information systems, but with the human existence and activity space continues to expand, description and analysis of multiple spatial regions become more complex, massive and diverse. At present, the research on multiple spatial objects is usually based on the models of binary topological relation, through which the global topological relations between multiple spatial objects are derived from the local binary topological relations between each pairwise objects. This binary topological relation models is not efficient to deal with the topological relation of multiple spatial objects, cannot meet the description and analysis of multiple spatial regions in GIS. In order to solve this kind of problem, the region of space research will be extended, and the representation and reasoning model of topological relations between multiple spatial objects is established based on representation and reasoning model between the three regions and between the four regions (ie, 8-intersection cube model and 16-intersection model) . Further, the.theory of the representation and reasoning model of topological relations between multiple spatial objects is applied to simulate the typhoon-affected areas in precipitation. Disaster impact between all levels of typhoon and designated areas can be inferred and expressed, and helps improve typhoon warning and disaster assessment mechanism, to reduce casualties and economic losses are important.

空间推理在地理信息系统中有着重要的应用，然而随着人类生存与活动空间不断拓展，多个空间区域间的描述与分析变得更加复杂、海量与多样化。目前对多个（两个以上）空间对象的拓扑关系研究，都是基于二元拓扑关系模型，通过判断局部两两对象间的拓扑关系推导出全局多个对象间的拓扑关系。这种二元拓扑关系模型已不能有效处理多个空间对象的拓扑关系，即不能适应GIS中多个空间区域间的描述与分析。针对这一问题，本项目基于三个区域间和四个区域间拓扑关系的表示及推理模型（即8-交集体模型和16-交集模型），将研究的空间区域进行扩展，建立多个空间区域间拓扑关系的表示及推理模型。进一步，将多个空间区域间拓扑关系的表示及推理理论应用于台风对地区降水影响的模拟中，可对各个级别的台风与指定地区的受灾影响进行推理和表示，有助于完善台风预警和灾害评估机制，对减少人员伤亡和经济损失有重要意义。

空间推理在地理信息系统中有着越来越多的应用，对多个空间区域间的拓扑关系研究成为地理信息领域一个重要基础性研究方向。目前拓扑关系表达多基于两个区域间的空间关系，表达能力相对有限。为了建立适合更复杂区域的拓扑关系表达模型，本项目基于三个区域和四个区域间拓扑关系的表示及推理模型，引入张量概念，提出五个简单区域间的拓扑关系表达及推理模型。依据推理规则推导出推理复合表，实现拓扑关系的自动表示和推理，建立32-交集模型，并完成其给出拓扑关系互斥完备性的理论证明。构建能够表达n个简单区域间关系的拓扑关系模型，实现了多个简单区域拓扑关系表达与推理的结构化统一。抽象化台风对目标区域的降雨影响问题，研究一个带洞的简单区域与简单区域的拓扑关系推理，基于RCC8关系建立适合台风区域与目标区域表达的27-交集模型，并进一步完善其模型理论，建立两个不相交区域和一个简单区域之间拓扑关系的模型及推理。本项目研究成果应用于台风受灾评估中的多目标间复杂空间关系表述相关问题研究，有助于完善台风预警和灾害评估机制，为后续路径规划、更复杂三维空间推理模型的研究进行了有意义的探索。