Modelling and Managing Topology in 3D Geoinformation Systems

  • Andreas Thomsen
  • Martin Breunig
  • Edgar Butwilowski
  • Björn Broscheit
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


Modelling and managing topology in 3D GIS is a non-trivial task. The traditional approaches for modelling topological data in 2D GIS cannot be easily extended into higher dimensions. In fact, the topology of real 3D models is much more complex than that of the 2D and 2.5D models used in classical GIS; in consequence there is a great number of different 3D spatial models ranging from constructive solid geometry to boundary representations. The choice of a particular representation is generally driven by the requirements of a given application. Nevertheless, from a data management point of view, it would be useful to provide a general topological model handling 2D, 2.5D and 3D models in a uniform way. In this paper we describe concepts and the realisation of a general approach to modelling and managing topology in a 3D GIS based on oriented d-Generalised Maps and the closely related cell-tuple structures. As an example of the applicability of the approach, the combination of a group of buildings from a 3D city model with the corresponding part of a 2D city is presented. Finally, an outlook to ongoing research is given in the context of topological abstraction for objects represented in multi-representation databases.


Simplicial Complex Topological Model City Model Triangle Element Constructive Solid Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Mäntylä, M.: An Introduction to Solid Modelling. Computer Science Press (1988)Google Scholar
  2. [2]
    Turner, A.K. (1992)(Ed.): Three-Dimensional Modelling with Geoscientific Information Systems, proc. NATO ASI 354, Kluwer, Dordrecht, 123–142.Google Scholar
  3. [3]
    Balovnev, O., Bode, T., Breunig, M., Cremers, A.B., Müller, W., Pogodaev, G., Shumilov, S., Siebeck, J., Siehl, A., Thomsen, A.: The Story of the GeoToolKit — An Object-Oriented Geodatabase Kernel System. GeoInformatica 8(1) (2004) 5–47.CrossRefGoogle Scholar
  4. [4]
    Egenhofer, M.J.: A formal definition of binary topological relationships. In: Proc. 3th Int. Conf. on foundation of data organisation and algorithms (1989) 457–472Google Scholar
  5. [5]
    Zlatanova, S.: 3D GIS for Urban Development. PhD dissertation, TU GRAZ, ITC Dissertation 69 (2000).Google Scholar
  6. [6]
    Egenhofer, M.J., Frank, A.U. and Jackson, J.P.: A topological data model for spatial databases. In: Buchmann, A. P., Günther, O., Smith, T. R. and Wang, Y.-F.(eds.): Design and Implementation of Large Spatial, LNCS 409, Springer, Berlin (1990) 271–286 Zlatanova, S.: 3D GIS for Urban Development. PhD dissertation, TU GRAZ, ITC Dissertation 69 (2000).Google Scholar
  7. [7]
    Pigot, S.: A topological model for a 3D spatial information system. 5th SDH, Charleston, (1992), 344–360.Google Scholar
  8. [8]
    Brisson, E.: Representing Geometric Structures in d Dimensions: Topology and Order. Discrete & Computational Geometry 9 (1993) 387–426.CrossRefGoogle Scholar
  9. [9]
    Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. Int. Journal Comp. Geometry and applications 4(3) (1994) 275–324.CrossRefGoogle Scholar
  10. [10]
    Mallet, J.L.: Geomodelling. Oxford University Press (2002)Google Scholar
  11. [11]
    Lévy, B.: Topologie Algorithmique — Combinatoire et Plongement. PhD Thesis, INPL Nancy (1999)Google Scholar
  12. [12]
    Fradin, D., Meneveaux, D. and Lienhardt, P.: Partition de l’espace et hiérarchie de cartes généralisées. AFIG 2002, Lyon, décembre (2002), 12p.Google Scholar
  13. [13]
    Raza, A., Kainz, W.: An Object-Oriented Approach for Modelling Urban Land-Use Changes. ACM-GIS (1999) 20–25.Google Scholar
  14. [14]
    Mallet, J.L.: GOCAD: A computer aided design programme for geological applications. In: Turner, A.K. (Ed.): Three-Dimensional Modelling with Geoscientific Information Systems, proc. NATO ASI 354, Kluwer, Dordrecht, 123–142.Google Scholar
  15. [15]
    MOKA: Modeleur de Cartes (2006).
  16. [16]
    van Oosterom, P., Stoter, J.E., Quak, C.W., Zlatanova, S., The Balance Between Geometry and Topology. In: Richardson, D. and van Oosterom, P. (eds.), Advances in Spatial Data Handling, 10th SDH, Springer, Berlin (2002).Google Scholar
  17. [17]
    Thompson, R.J.., van Oosterom, P.: Implementation issues in the storage of spatial data as regular polytopes. Information Systems for Sustainable Development-Part1 (2006) 2.33–2.46 (2006).Google Scholar
  18. [18]
    Penninga, F., van Oosterom, P. and Kazar, B. M.: A tetrahedronized irregular network based DBMS approach for 3D topographic data modeling. In: Riedl, Andreas, Kainz, W., Elmes and Gregory A. (eds.): Progress in Spatial Data Handling, 12th SDH 2006, Springer, Berlin (2006) 581–598CrossRefGoogle Scholar
  19. [19]
    Saadi Mesgari, M.: Topological Cell-Tuple Structures for Three-Dimensional Spatial Data. PhD thesis University of Twente. ITC Dissertation 74 (2000).Google Scholar
  20. [20]
    Thomsen, A., Breunig, M.: Some remarks on topological abstraction in multi representation databases. In: Popovich, V., Schrenk, M. and Korolenko, K. (eds.): 3rd workshop Inf. Fusion & GIS, Springer, Berlin (2007) 234–251.Google Scholar
  21. [21] (2006).
  22. [22]
  23. [23]
    Butwilowski, E.: Topologische Fragestellungen bei der Kombination von 3D-Stadtmodellen mit 2D-Karten in einer Räumlichen Datenbank. Diplomarbeit, Fachgebiet Geographie, Universität Osnabrück, (2007).Google Scholar
  24. [24]
    FRIDA: Free data from the city of Osnabrueck. (2007).
  25. [25]
    Breunig, M., Bär W. and Thomsen, A.: Usage of Spatial Data Stores for Geo-Services. 7th AGILE Conf. Geographic Information Science, (2004) 687–696.Google Scholar
  26. [26]
    Bär, W.: Verwaltung geowissenschaftlicher 3D Daten in mobilen Datenbanksystemen PhD Thesis, dept. of Mathematics/Computer Science, University of Osnabrück (2007).
  27. [27]

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andreas Thomsen
    • 1
  • Martin Breunig
    • 1
  • Edgar Butwilowski
    • 1
  • Björn Broscheit
    • 1
  1. 1.Institute for Geoinformatics and Remote SensingUniversity of OsnabrückOsnabrückGermany

Personalised recommendations