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An Unified CGA-Based Formal Expression of Spatio-Temporal Topological Relations for Computation and Analysis of Geographic Objects

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Abstract

Geographic objects usually change their locations, shape and characteristics over time. Change in one object can trigger a series of changes in the adjacent objects and their topological relationships. The spatio-temporal topological relations analysis of geographic objects is an important issue in the development of a more temporally aware geographical information science. Research on, and applications of spatial topology are mature, yet the methods to exploit spatio-temporal topology are still far from the reach of GIS users. Such research has probed the definition of time, and explored the formalization of spatio-temporal topology from different perspectives. However, almost all methods and representations are mathematical or logical methods represented in qualitative ways. Conformal geometric algebra (CGA) is a new tool for unified multidimensional representation and geometric computation, from a unified perspective of multidimensional space-time. In this research, we pursue a logic based on the concept of a unified representational model based on CGA for spatio-temporal objects and their spatio-temporal topological relations formally expressed by a multi-branch decision tree, which is not only qualitative but also quantitative. The research provides theoretical and methodological support for expressing and computing the spatio-temporal topological relations among any set of geographic objects. This ability effectively promotes the expression of spatio-temporal topological relationships and enhances the analytical capabilities of GIS for dealing with both space and time.

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References

  1. Allen, J.F.: Maintaining knowledge about temporal intervals. Commun. ACM 26(11), 12 (1983)

    Article  Google Scholar 

  2. Bittner, T.: Qualitative spatio-temporal relations. In: Proceedings of the 8th International Conference on Principles of Knowledge Representation and Reasoning, edited. Toulouse, France (2002)

  3. Bruce, B.: A model for temporal references and its application in a question answering program. Artif. Intell. 4, 25 (1972)

    Google Scholar 

  4. Cameron, J., Lasenby, J.: Oriented conformal geometric algebra [J]. Adv. Appl. Clifford Algebras 18(3–4), 523–538 (2008)

    Article  MathSciNet  Google Scholar 

  5. Claramunt, C., Jiang, B.: An integrated representation of spatial and temporal relationships between evolving regions. J. Geogr. Syst. 3(4), 18 (2001)

    Article  Google Scholar 

  6. Clementini, E., Di, F. P., and Oosterom, P.: A small set of formal topological relationships suitable for end-user interaction. In: Proceedings of the 3rd International Symposium on Advances in Spatial Databases, Edited, pp. 277-295 (1993)

  7. Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. Int. J. Geogr. Inf. Syst. 5(2), 13 (1991)

    Google Scholar 

  8. Egenhofer, M. J., and Herring, J. R.: Categorizing binary topological relationships between regions, lines and points in geographic database. Report. University of Maine, Orono (1991)

  9. Egenhofer, M.J., Mark, D.M.: Modelling conceptual neighbourhoods of topological line-region relations[J]. Int. J. Geogr. Inf. Sys. 9(5), 555–565 (1995)

    Article  Google Scholar 

  10. Erwig, M., Schneider, M.: Spatio-temporal predicates. IEEE Trans. Knowl. Data Eng. 14(4), 21 (2002)

    Article  Google Scholar 

  11. Hitzer, E.M.S.: Conic sections and meet intersections in geometric algebra. Int Conf Comput Algebra Geom Algebra Appl 3519, 350–362 (2004)

    MATH  Google Scholar 

  12. Huang, B., Yao, L.: Spatiotemporal object database approach to dynamic segmentation. Transp Res Rec J Transp Res Board 1836(1), 118–125 (2003)

    Article  Google Scholar 

  13. Ladkin, P. B., Maddux, R. D.: The algebra of convex intervals[R]. Technical Report, KES-U-87-2. Krestel Institute, Palo Alto, pp 1–5 (1987)

  14. Langran, G.: Time in Geographic Information System. Taylor & Francis, London (1992)

    Book  Google Scholar 

  15. Leong, H.U., Mouratidis, K., Mamoulis, N.: Continuous spatial assignment of moving users. VLDB J 19(2), 19 (2010)

    Google Scholar 

  16. Li, H., Hestenes, D., Rockwood, A.: A universal model for conformal geometries of euclidean, spherical and double-hyperbolic spaces. In: Geometric Computing with Clifford Algebra, Edited, pp. 77–104. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. McDermott, D.: A temporal logic for reasoning about processes and plans. Cogn. Sci. 6(2), 55 (1982)

    Article  Google Scholar 

  18. Muller, P.: Topological spatio-temporal reasoning and representation. Comput. Intell. 18(3), 31 (2002)

    Article  MathSciNet  Google Scholar 

  19. Peuquet, D.J., Duan, N.: An event-based spatio-temporal data model (ESTDM) for temporal analysis of geographical data. Int. J. Geogr. Inf. Syst. 9(1), 18 (1995)

    Google Scholar 

  20. Raafat, H., Yang, Z., Gauthier, D.: Relational spatial topologies for historical geographical information. Int. J. Geogr. Inf. Syst. 8(2), 11 (1994)

    Google Scholar 

  21. Shen, J.W., Wen, Y.N., LV, G.N., Wu, M.G.: Representation and reasoning about spatial temporal topological relationships. Geogr. Geo-Inf. Sci. 26(6), 5 (2010)

    Google Scholar 

  22. Shen, J.W., Wen, Y.N., LV, G.N., Wu, M.G.: Calculation of topological relationships between bodies. Sci Surv Mapp. 37(4), 3 (2012)

    Google Scholar 

  23. Van, B.J.: The Logic of Time. D. Reidel Publishing Company, Dordrecht (1983)

    Google Scholar 

  24. Yu, Z., Luo, W., Yuan, L., et al.: Geometric algebra model for geometry-oriented topological relation computation. Trans. GIS 20(2), 259–279 (2016)

    Article  Google Scholar 

  25. Yu, Z., Luo, W., Yuan, L., et al.: Change detection for 3D vector data: a CGA-based Delaunay–TIN intersection approach. Int. J. Geogr. Inf. Sci. 29(12), 2328–2347 (2015)

    Article  Google Scholar 

  26. Yuan, L., Yu, Z., Chen, S.: CAUSTA: Clifford algebra-based unified spatio-temporal analysis. Trans. GIS 14(S1), 25 (2010)

    Google Scholar 

  27. Yuan, L., Yu, Z., Luo, W., et al.: Multidimensional-unified spatial relation computation model based on geometric algebra. Int. J. Geogr. Inf. Sci. 28(12), 2435–2455 (2014)

    Article  Google Scholar 

  28. Zhang, F., Jiang, X., Zhang, X., Wang, Y., Du, Z., Liu, R.: Unified spatial intersection algorithms based on conformal geometric algebra. In: Mathematical Problems in Engineering, 2016 (2016-11-16), vol. 4, pp. 1–10 (2016)

  29. Zong, Z., Yuan, L., Luo, W., Yu, Z., Hu, Y.: Triangulation intersection algorithm based on conformal geometric algebra. Acta Geod. Cartogr. Sin. 43(2), 8 (2014)

    Google Scholar 

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Acknowledgements

This research was funded by the National Natural Science Foundation of China (41471313). We thank M. Chen, X. Jiang, and Q. Wang, three graduated graduate students, for their research results, which provided a good foundation for this study.

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Authors and Affiliations

  1. Department of Public Order, Zhejiang Police College, 555 Binwen Road, Hangzhou, 310053, China

    Yingzhi Wang

  2. School of Earth Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, China

    Feng Zhang

  3. Zhejiang Provincial Key Laboratory of Geographic Information Science, 148 Tianmushan Road, Hangzhou, 310028, China

    Feng Zhang

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  1. Yingzhi Wang
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  2. Feng Zhang
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Correspondence to Feng Zhang.

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This article is part of the Topical Collection on Geometric Algebra for Computing, Graphics and Engineering edited by Yu Zhaoyuan, Dietmar Hildenbrand, Kit Ian Kou, and Eckhard Hitzer.

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Wang, Y., Zhang, F. An Unified CGA-Based Formal Expression of Spatio-Temporal Topological Relations for Computation and Analysis of Geographic Objects. Adv. Appl. Clifford Algebras 29, 59 (2019). https://doi.org/10.1007/s00006-019-0971-2

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