基于几何代数的矢量时空数据表达与建模方法

doi:10.3724/SP.J.1047.2012.00067

地球信息科学学报 ›› 2012, Vol. 14 ›› Issue (1): 67-73.doi: 10.3724/SP.J.1047.2012.00067

• 地球信息科学理论方法 • 上一篇下一篇

基于几何代数的矢量时空数据表达与建模方法

俞肇元¹, 袁林旺^1*, 胡勇², 李玉¹, 宗真¹

1. 南京师范大学虚拟地理环境教育部重点实验室, 南京 210046;
2. 南京师范大学计算机科学与技术学院, 南京 210046

收稿日期:2011-08-08 修回日期:2012-02-03 出版日期:2012-02-25 发布日期:2012-02-24
通讯作者: 袁林旺(1973-),男,博士,教授,主要研究领域为地理信息系统。E-mail:yuanlinwang@163.com E-mail:yuanlinwang@163.com
作者简介:俞肇元(1984-), 男,博士, 讲师,主要研究领域为地理信息系统。E-mail:yuzhaoyuan@163.com
基金资助:
国家自然科学基金项目(41171300)和国家高技术研究发展计划专项"863"课题(2009AA12Z205)资助。

Spatio-Temporal Vector Data Modeling Based on Geometric Algebra

YU Zhaoyuan¹, YUAN Linwang^1*, HU Yong², LI Yu¹, ZONG Zhen¹

1. Key Laboratory of Virtual Geographical Environment, Ministry of Education, Nanjing Normal University, Nanjing 210046, China;
2. Department of Computer and Ttechnology, Nanjing Normal University, Nanjing 210046, China

Received:2011-08-08 Revised:2012-02-03 Online:2012-02-25 Published:2012-02-24

摘要/Abstract

摘要： 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。

关键词: 矢量时空数据建模, 几何代数, 数据结构, 时空分析

Abstract: 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.

Key words: vector spatio-temporal data modeling, geometric algebra, data structure, spatio-temporal analysis

俞肇元, 袁林旺, 胡勇, 李玉, 宗真. 基于几何代数的矢量时空数据表达与建模方法[J]. 地球信息科学学报, 2012, 14(1): 67-73.DOI:10.3724/SP.J.1047.2012.00067

YU Zhaoyuan, YUAN Linwang, HU Yong, LI Yu, ZONG Zhen. Spatio-Temporal Vector Data Modeling Based on Geometric Algebra[J]. , 2012, 14(1): 67-73.DOI:10.3724/SP.J.1047.2012.00067

参考文献

[1] Longley P A, Goodchild M F, Maguire D J, et al. Geographic information systems and science (Second Edition)[J]. New York: Wiley, 2005.

[2] Karssenberg D, Jong D K. Dynamic environmental modelling in GIS: 1.Modelling in three spatial dimensions[J]. International Journal of Geographical Information Science, 2005, 19 (5): 559-579.

[3] Mcintosh J, Yuan M. A framework to enhance semantic flexibility for analysis of distributed phenomena[J]. International Journal of Geographic Information Science, 2005, 19(10): 999-1018.

[4] Galton A P. Desiderata for a spatio-temporal geo-ontology[J].COSIT, 2003, 2825:1-12.

[5] Goodchild M F, Yuan M, Cova T J. Towards a general theory of geographic representation in GIS[J]. International Journal of Geographical Information Science, 2007, 21(3): 239-260.

[6] Liu Y, Goodchild M F, Guo Q, et al. Towards a general field model and its order in GIS[J]. International Journal of Geographical Information Science, 2008, 22(6): 623-643.

[7] Carroll J E. Complex signals can be real[J]. European Journal of Physics, 2007,28(6): 1151-1160.

[8] Pavši? M. Clifford space as a generalization of spacetime: Prospects for QFT of point particles and strings[J]. Foundations of Physics, 2005, 35: 1617-1642.

[9] Yuan L, Yu Z, Chen S, et al. CAUSTA: Clifford algebra based unified spatio-temporal analysis[J]. Transactions in GIS. 2010,14(s1):59-83.

[10] 复旦大学历史地理研究中心.CHGIS Datasets V4. http://yugong.fudan.edu.cn/Chgisii/chgis_Data_Download/index.asp[2011-07-12].

[11] Hestenes D. Space-time algebra[M] New York: Gordon and Breach, 1966.

[12] Doran C, Lasenby A. Geometric algebra for physicists[J]. Cambridge: Cambridge University Press, 2003: 228-264.

[13] 李武明. N维时空单位球面的若干性质及应用[J]. 哈尔滨师范大学自然科学学报,2003(4):35-38.

[14] 袁林旺, 俞肇元, 罗文, 等. 基于共形几何代数的GIS 三维空间数据模型[J]. 中国科学:地球科学, 2010, 40(12): 1740-1751.

[15] 俞肇元.基于几何代数的多维统一GIS数据模型研究[D].南京师范大学,2011.

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

PDF (PC)

赞

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	贾涛, 杨仕浩, 李欣, 鄢鹏高, 喻雪松, 罗希, 陈凯. 武汉居民建筑物碳排放反演计算和时空分析[J]. 地球信息科学学报, 2020, 22(5): 1063-1072.
[2]	秦昆, 林珲, 胡迪, 许刚, 张晓祥, 卢宾宾, 叶信岳. 空间综合人文学与社会科学研究综述[J]. 地球信息科学学报, 2020, 22(5): 912-928.
[3]	袁林旺, 俞肇元, 罗文, 袁帅, 周春烨. PIR传感网数据的几何代数建模与行为分析[J]. 地球信息科学学报, 2020, 22(1): 21-29.
[4]	邓敏, 蔡建南, 杨文涛, 唐建波, 杨学习, 刘启亮, 石岩. 多模态地理大数据时空分析方法[J]. 地球信息科学学报, 2020, 22(1): 41-56.
[5]	康朝贵, 刘璇, 许欣悦, 秦昆. 天气因素对武汉市出租车出行活动的影响[J]. 地球信息科学学报, 2019, 21(1): 118-127.
[6]	王楠, 杜云艳, 易嘉伟, 刘张, 王会蒙. 基于手机信令数据的北京市空间品质时空动态分析[J]. 地球信息科学学报, 2019, 21(1): 86-96.
[7]	萧声隽, 宗真, 项丽燕, 胡勇. 多粒度时空对象空间关系的统一表达与计算[J]. 地球信息科学学报, 2017, 19(9): 1178-1184.
[8]	刘鹏华, 姚尧, 梁昊, 梁兆堂, 张亚涛, 王昊松. 耦合卡尔曼滤波和多层次聚类的中国PM_2.5时空分布分析[J]. 地球信息科学学报, 2017, 19(4): 475-485.
[9]	张宁旭, 廖一兰, 刘小驰, 陈会宴. “山东疫苗事件”应急反应能力时空分析[J]. 地球信息科学学报, 2017, 19(3): 346-354.
[10]	郝贵斌, 吴波, 张立福, 付东杰, 李瑶. ESTARFM模型在西藏色林错湖面积时空变化中的应用分析(1976-2014年)[J]. 地球信息科学学报, 2016, 18(6): 833-846.
[11]	史婷婷, 杨晓梅, 张涛, 刘李, 田文君. 基于TRMM数据的福建省降水时空格局BME插值分析[J]. 地球信息科学学报, 2014, 16(3): 470-481.
[12]	甘龙飞, 邹杰, 唐丽玉, 陈崇成, 黄洪宇. 高逼真度虚拟森林环境的半球成像方法模拟分析[J]. 地球信息科学学报, 2013, 15(3): 345-355.
[13]	江洪, 汪小钦, 孙为静. 福建省森林生态系统NPP的遥感模拟与分析[J]. 地球信息科学学报, 2010, 12(4): 580-586.
[14]	温永宁, 闾国年, 陈旻, 苏红军, 胡迪. 华夏家谱GIS的数据组织与系统架构[J]. 地球信息科学学报, 2010, 12(2): 235-241.
[15]	郭继发, 刘臻, 崔伟宏. 基于时空特征分析技术的烤烟GIS系统[J]. 地球信息科学学报, 2009, 11(3): 370-375.