Spatio-Temporal Vector Data Modeling Based on Geometric Algebra

  • 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 date: 2011-08-08

  Revised date: 2012-02-03

  Online published: 2012-02-24


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.

Cite this article

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


[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.[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.