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Lossless representation of topological spatial data

  • Spatial Data Models
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 951))

Abstract

We present a data structure used to represent planar spatial databases in the topological data model. Conceptually, such databases consist of points, lines between these points, and areas formed by these lines. The data structure has the distinctive feature that it is geared toward supporting queries involving topological properties of the database only: two databases that are topologically equivalent have the same representation. Moreover, no information is lost in this way: two databases that are not topologically equivalent never have the same representation.

On leave from the University of Antwerp. Research assistant of the Belgian National Fund for Scientific Research.

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References

  1. J.P. Corbett. Topological Principles of Cartography. Technical Paper No. 48, US Bureau of the Census, Washington, DC, USA: US Government Printing Office, 1979.

    Google Scholar 

  2. M. Egenhofer. Reasoning about Binary Topological Relations. Advances in Spatial Databases, Lecture Notes in Computer Science, 525, (eds. O. Günther and H.-J. Schek), 143–160, Springer-Verlag, 1991.

    Google Scholar 

  3. M. Egenhofer. Topological Relations between Regions of R 2 and Z 2. Advances in Spatial Databases, Lecture Notes in Computer Science, 692, (eds. D. Abel and B.C. Ooi), 316–336, Springer-Verlag, 1993.

    Google Scholar 

  4. M. Egenhofer and R. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 523–542, 1994.

    Google Scholar 

  5. M. Egenhofer and J. Herring A mathematical framework for the definition of topological relationships. Proceedings of the Fourth International Symposium on Spatial Data Handling, Zurich, Switzerland (eds. K. Brassel and H. Kishimoto), 803–813, 1990.

    Google Scholar 

  6. S. Even. Graph Algorithms. Computer Science Press, 1979.

    Google Scholar 

  7. R.H. Güting. An Introduction to Spatial Database Systems. The VLDB Journal, 3(4), 1994.

    Google Scholar 

  8. J. Herring. TIGRIS: Topologically Integrated Geographic Information Systems. Proceedings of Auto Carto 8 Conference, Baltimore, MD, (ed. N.R. Chrisman), 1987.

    Google Scholar 

  9. J. Hidders. An Isotopic Invariant for Planar Drawings of Connected Planar Graphs. Computing Science Note, 95/04, Eindhoven University of Technology, 1995.

    Google Scholar 

  10. R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. The A.P.I.C. Series, 37, Academic Press, 1992.

    Google Scholar 

  11. E.E. Moise. Geometric Topology in Dimensions 2 and 3. Graduate Texts in Mathematics, 47, Springer-Verlag, 1977.

    Google Scholar 

  12. S. Morehouse. The architecture of ARC/INFO. Proceedings of the Auto Carto 9 Conference, Baltimore, MD, American Society for Photogrammetry and Remote Sensing/American Congress for Surveying and Mapping, 266–277, 1989.

    Google Scholar 

  13. J. Paredaens. Spatial Databases. The Final Frontier. Database Theory — ICDT '95, Lecture Notes in Computer Science, 893, 14–32, Springer-Verlag, 1995.

    Google Scholar 

  14. J. Paredaens, J. Van den Bussche and D. Van Gucht. Towards a Theory of Spatial Database Queries. Proceedings of the 13th ACM SIGACT-SIGMOD-SIGART Symposium on the Principles of Database Systems, 279–288, ACM Press, 1994.

    Google Scholar 

  15. P. Preparata and M.I. Shamos. Computational geometry. Springer-Verlag, 1985.

    Google Scholar 

  16. J. Stillwell. Classical Topology and Combinatorial Group Theory. Graduate Texts in Mathematics, 72, Springer-Verlag, 1980.

    Google Scholar 

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Max J. Egenhofer John R. Herring

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© 1995 Springer-Verlag Berlin Heidelberg

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Kuijpers, B., Paredaens, J., Van den Bussche, J. (1995). Lossless representation of topological spatial data. In: Egenhofer, M.J., Herring, J.R. (eds) Advances in Spatial Databases. SSD 1995. Lecture Notes in Computer Science, vol 951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60159-7_1

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  • DOI: https://doi.org/10.1007/3-540-60159-7_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60159-3

  • Online ISBN: 978-3-540-49536-9

  • eBook Packages: Springer Book Archive

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