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A New Shape Function Based Spatiotemporal Interpolation Method

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Constraint Databases (CDB 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3074))

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Abstract

In this paper we propose a new spatiotemporal interpolation method for 3-D space and 1-D time geographic data. Similarly to the existing ST (space-time) product and the tetrahedral spatiotemporal interpolation methods, this new method is also based on shape functions. However, instead of only manipulating the time dimension as in the ST product and the tetrahedral methods, our new method combines 2-D shape functions in the (x,y) domain with the (z,t) domain shape functions. This method yields data that can be represented and queried in constraint databases and we discuss how to represent this new method in constraint databases. We also show certain unique properties of the new shape function based spatiotemporal interpolation method.

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References

  1. Buchanan, G.R.: Finite Element Analysis. McGraw-Hill, New York (1995)

    Google Scholar 

  2. Cai, M., Keshwani, D., Revesz, P.: Parametric rectangles: A model for querying and animating spatiotemporal databases. In: Zaniolo, C., Grust, T., Scholl, M.H., Lockemann, P.C. (eds.) EDBT 2000. LNCS, vol. 1777, pp. 430–444. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Chang, K.-t.: Introduction to Geographic Information Systems, 2nd edn. McGraw-Hill, New York (2004)

    Google Scholar 

  4. Demers, M.N.: Fundamentals of Geographic Information Systems, 2nd edn. John Wiley & Sons, New York (2000)

    Google Scholar 

  5. Deutsch, C.V., Journel, A.G.: GSLIB: Geostatistical Software Library and User’s Guide, 2nd edn. Oxford University Press, New York (1998)

    Google Scholar 

  6. Forlizzi, L., Güting, R.H., Nardelli, E., Schneider, M.: A data model and data structure for moving object databases. In: Proc. ACM SIGMOD International Conference on Management of Data, pp. 319–330 (2000)

    Google Scholar 

  7. Freitag, L.A., Gooch, C.O.: Tetrahedral mesh improvement using swapping and smoothing. International Journal for Numerical Methods in Engineering 40, 3979–4002 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Geerts, F., Kuijpers, B.: Deciding termination of query evaluation in transitiveclosure logics for constraint databases. In: Proceedings of the 19th ACM SIGACTSIGMOD-SIGART Symposium on Principles of Database Systems, pp. 126–135. ACM Press, New York (2000)

    Google Scholar 

  9. Geerts, F., Kuijpers, B.: Linear approximation of planar spatial databases using transitive-closure logic. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 190–206. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Goodman, J.E., O’Rourke, J. (eds.): Handbook of Discrete and Computational Geometry. CRC Press, Boca Raton (1997)

    MATH  Google Scholar 

  11. Grumbach, S., Rigaux, P., Segoufin, L.: Manipulating interpolated data is easier than you thought. In: Proc. IEEE International Conference on Very Large Databases, pp. 156–165 (2000)

    Google Scholar 

  12. Hang, F., Li, Y.: On applicability of sparse grid algorithms. Numerical Algorithms (submitted)

    Google Scholar 

  13. Harbaugh, J.W., Preston, F.W.: Fourier Analysis in Geology, pp. 218–238. Prentice-Hall, Englewood Cliffs (1968)

    Google Scholar 

  14. Jaffar, J., Michaylov, S., Stuckey, P.J., Yap, R.H.: The CLP(R) language and system. ACM Transactions on Programming Languages and Systems 14(3), 339–395 (1992)

    Article  Google Scholar 

  15. Kanellakis, P.C., Kuper, G.M., Revesz, P.: Constraint query languages. Journal of Computer and System Sciences 51(1), 26–52 (1995)

    Article  MathSciNet  Google Scholar 

  16. Kanjamala, P., Revesz, P., Wang, Y.: MLPQ/GIS: A GIS using linear constraint databases. In: Prabhu, C.S.R. (ed.) Proc. 9th COMAD International Conference on Management of Data, pp. 389–393 (1998)

    Google Scholar 

  17. Kuper, G.M., Libkin, L., Paredaens, J. (eds.): Constraint Databases. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  18. Lam, N.S.: Spatial interpolation methods: A review. The American Cartographer 10(2), 129–149 (1983)

    Article  Google Scholar 

  19. Langran, G.: Time in Geographic Information Systems. Taylor and Francis, London (1992)

    Google Scholar 

  20. Li, L., Revesz, P.: A comparison of spatio-temporal interpolation methods. In: Egenhofer, M.J., Mark, D.M. (eds.) GIScience 2002. LNCS, vol. 2478, pp. 145–160. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Li, L., Revesz, P.: The relationship among GIS-oriented spatiotemporal databases. In: Proc. of the Third National Conference on Digital Government Research, Boston (2003)

    Google Scholar 

  22. Li, L., Revesz, P.: Interpolation methods for spatio-temporal geographic data. Journal of Computers, Environment and Urban Systems (2003) (in press)

    Google Scholar 

  23. Li, Y.: Applicability of Smolyak’s algorithms to certain Banach spaces of multivariate functions. Journal of Complexity 18(2), 792–814 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  24. Longley, P.A., Goodchild, M.F., Maguire, D.J., Rhind, D.W.: Geographic Information Systems and Science. John Wiley, Chichester (2001)

    Google Scholar 

  25. Miller, E.J.: Towards a 4D GIS: Four-dimensional interpolation utilizing kriging. In: Kemp, Z. (ed.) Innovations in GIS 4: Selected Papers from the Fourth National Conference on GIS Research U.K. ch. 13, pp. 181–197. Taylor & Francis, London (1997)

    Google Scholar 

  26. Piltner, R.: Low order plate bending elements with enhanced strains. Computers & Structures 80, 849–856 (2002)

    Article  Google Scholar 

  27. Piltner, R., Taylor, R.L.: Triangular finite elements with rotational degrees of freedom and enhanced strain modes. Computers & Structures 75, 361–368 (2000)

    Article  Google Scholar 

  28. Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction. Springer, Heidelberg (1985)

    Google Scholar 

  29. Revesz, P.: Introduction to Constraint Databases. Springer, New York (2002)

    MATH  Google Scholar 

  30. Revesz, P., Chen, R., Kanjamala, P., Li, Y., Liu, Y., Wang, Y.: The MLPQ/GIS constraint database system. In: Proc. ACM SIGMOD International Conference on Management of Data (2000)

    Google Scholar 

  31. Revesz, P., Li, L.: Constraint-based visualization of spatial interpolation data. In: Proc. of the Sixth International Conference on Information Visualization, London, England, pp. 563–569. IEEE Press, Los Alamitos (2002)

    Chapter  Google Scholar 

  32. Revesz, P., Li, L.: Representation and querying of interpolation data in constraint databases. In: Proc. of the Second National Conference on Digital Government Research, Los Angeles, California, pp. 225–228 (2002)

    Google Scholar 

  33. Shepard, D.: A two-dimensional interpolation function for irregularly spaced data. In: Proc. 23nd National Conference ACM, pp. 517–524. ACM, New York (1968)

    Chapter  Google Scholar 

  34. Shewchuk, J.R.: Triangle: Engineering a 2D quality mesh generator and delaunay triangulator. In: Proc. First Workshop on Applied Computational Geometry, Philadelphia, Pennsylvania, pp. 124–133 (1996)

    Google Scholar 

  35. Shewchuk, J.R.: Tetrahedral mesh generation by delaunay refinement. In: Proc. 14th Annual ACM Symposium on Computational Geometry, Minneapolis, Minnesota, pp. 86–95 (1998)

    Google Scholar 

  36. Tossebro, E., Güting, R.H.: Creating representation for continuously moving regions from observations. In: Proc. 7th International Symposium on Spatial and Temporal Databases, Redondo Beach, CA, pp. 321–344 (2001)

    Google Scholar 

  37. Van den Bussche, J.: Constraint databases: A tutorial introduction. SIGMOD Record 29(3), 44–51 (2000)

    Article  Google Scholar 

  38. Watson, D.F.: Computing the n-dimensional delaunay tesselation with application to voronoi polytopes. The Computer Journal 24(2), 167–172 (1981)

    Article  MathSciNet  Google Scholar 

  39. Worboys, M.F.: GIS: A Computing Perspective. Taylor & Francis, Abington (1995)

    Google Scholar 

  40. Zienkiewics, O.C., Taylor, R.L.: Finite Element Method. The Basic Formulation and Linear Problems, vol. 1. McGraw-Hill, New York (1989)

    Google Scholar 

  41. Zienkiewics, O.C., Taylor, R.L.: Finite Element Method. The Basis, vol. 1. Butterworth Heinemann, London (2000)

    Google Scholar 

  42. Zurflueh, E.G.: Applications of two-dimensional linear wavelength filtering. Geophysics 32, 1015–1035 (1967)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Georgia Southern University, Statesboro, GA, 30460-7997, USA

    Lixin Li & Youming Li

  2. University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, USA

    Reinhard Piltner

Authors
  1. Lixin Li
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  2. Youming Li
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  3. Reinhard Piltner
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Editor information

Editors and Affiliations

  1. Theoretical Computer Science Group, Hasselt University & Transnational University of Limburg, Belgium

    Bart Kuijpers

  2. University of Nebraska - Lincoln, NE 68588, Lincoln, USA

    Peter Revesz

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Li, L., Li, Y., Piltner, R. (2004). A New Shape Function Based Spatiotemporal Interpolation Method. In: Kuijpers, B., Revesz, P. (eds) Constraint Databases. CDB 2004. Lecture Notes in Computer Science, vol 3074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25954-1_2

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  • DOI: https://doi.org/10.1007/978-3-540-25954-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22126-5

  • Online ISBN: 978-3-540-25954-1

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