基于几何代数的矢量时空数据表达与建模方法

Spatio-Temporal Vector Data Modeling Based on Geometric Algebra

针对现有矢量时空数据建模时空分离所导致的时空表达不一致、不统一的问题,运用几何代数理论和统一时空观,对时间、空间与属性进行一体化的表达与建模。构建了时空统一表达的层次体系,并基于面向对象技术和UML方法,探讨了时间、空间与属性等组件的逻辑关系。提出了矢量时空数据时空统一建模流程,定义了相应的数据组织结构与存储结构,实现了对几何代数空间的对象表达与存储,以及常见矢量数据的集成与预处理方法。对上述成果进行整合,建立了相应的原型系统。实验以中国东南地区级行政区演化序列数据为例,实验结果验证了本文提出方法在时空数据的统一建模与表达方面的可行性,能够有效支撑变化检测等时空分析方法的构建与实现,为时空GIS的发展提供理论参考与方法借鉴。

Spatio-temporal modeling is one of the most important topics in the field of GIS.Unified representation of space and time can be seen as a new potential for temporal GIS,though practical advices on it in real world are still lack.The geometric algebra linking expression and computation of elements at different dimensions provides potations to express space and time in a unified framework.This paper proposes geometric algebra to overcome the drawbacks of existing vector spatio-temporal data modeling methods in representing time and space individually,which will lead to express inconsistent and not uniform issue.Based on the coding of coordinates with geometric algebra elements,the unified spatio-temporal expression integrates the temporal and spatial parts as a whole,by linking the basic elements of geometric algebra of different grades.And then,time,space and attributes are expressed and modeled based on geometric algebra and unified spatial-temporal views.The heretical level structure of unified spatio-temporal expression is proposed and the logical relations of time,space and attributes are discussed based on the UML technology in an object-oriented way.The process flow of unified vector spatio-temporal data model was proposed.Based on the multivector structure of geometric algebra,data organization and storage structures were defined.Finally,a prototype system was implemented that integrates the above mentioned technologies.Changing data of administrative regions（at prefectural level） of southeast China was used to evaluate the method.The results suggest that the method proposed in this paper can support unified spatio-temporal modeling and expression,which can also support the construction and implementation of spatio-temporal analysis methods,e.g.change detection.It seems that our work can provide theoretical foundation and method implementation reference for the development of temporal and spatial GIS.