共形几何代数框架下时空拓扑关系的统一表达与计算方法研究

项目名称： 共形几何代数框架下时空拓扑关系的统一表达与计算方法研究

项目编号： No.41471313

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 张丰

作者单位： 浙江大学

项目金额： 80万元

中文摘要： 时空拓扑分析是地理信息科学中一个重要的基础研究方向。目前时空拓扑关系表达普遍采用定性的方法以符合人们的认知习惯，无法直接对时空拓扑关系进行定量计算。针对不同类型、不同维度的地理对象往往需要构建相对独立的时空拓扑分析算法，缺乏空间结构与计算结构的统一性。本项目拟基于具有多维统一表达与几何计算能力的共形几何代数理论，实现复杂地理时空与几何代数空间的相互转换，构造基于多重向量的多维时空对象统一表达模型；通过时空对象与时空拓扑关系之间的映射，构建多维统一、语义明确的时空拓扑关系形式化表达与描述方法；设计并实现时空拓扑关系统一计算框架，包括完备的时空拓扑关系算子、算法集以及时空拓扑计算引擎与运算接口；最后结合土地利用时空拓扑分析实例，对所提出模型、方法的可行性与有效性进行验证。

中文关键词： 时空拓扑；共形几何代数；形式化表达；决策树

英文摘要： Spatio-temporal topological analysis is an important fundamental issue of the research topics in geographic information science. Currently, the temporal topological relationship is expressed with qualitative methods to meet with the people's cognitive habits, it's difficult to metric analysis the spatio-temporal topology. It's need design relatively independent topological analysis algorithms to response different types and dimensions of geographic objects, lack of uniformity of spatial structure and computation framework. The project intends to introduce conformal geometric algebra which integrate representation and computation of objects at different dimensions provides potations to express space and time in an unified framework. Achieving mutual conversion of complex geo-object between Euclidean space and conformal space, providing mapping method between spatio-temporal objects and spatio-temporal topological relation, to construct a new type of spatio-temporal data model supporting the representation and computation of unified multi-dimensional geographical objects based on multidimensional vector. Design and implement an unified spatio-temporal topology computing framework, including spatio-temporal topology operator, as well as spatio-temporal topology computing algorithms and engines. Finally, test and verify the feasibility and effectiveness of the proposed method with the examples of land use temporal topological analysis.

英文关键词： spatio-temporal topology;conformal geometric algebra;formal expression;dicision tree