The Neighborhood Configuration Model: A Framework to Distinguish Topological Relationships between Complex Volumes

  • Tao Chen
  • Markus Schneider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6999)

Abstract

Topological relationships between spatial objects are considered to be important for spatial databases. They lead to topological predicates, which can be embedded into spatial queries as join or selection conditions. Before rushing into the implementation of topological predicates, topological relationships between spatial objects must be first understood and clarified. This requires a detailed study of a vast number of possible spatial configurations at the abstract level, and as a result, methods that are able to classify and identify as many as possible different spatial configurations are needed. While a lot of research has already been carried out for topological relationships in the 2D space, the investigation in the 3D space is rather neglected. Developed modeling strategies are mostly extensions from the popular 9-intersection model which has been originally designed for simple 2D spatial objects. We observe that a large number of topological relationships, especially the ones between two complex 3D objects are still not distinguished in these models. Thus, we propose a new modeling strategy that is based on point set topology. We explore all possible neighborhood configurations of an arbitrary point in the Euclidean space where two volume objects are embedded, and define corresponding neighborhood configuration flags. Then, by composing the Boolean values of all flags, we uniquely identify a topological relationship between two complex volume objects.

Keywords

Spatial Database Building Information Model Spatial Object Topological Relationship Spatial Query 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Egenhofer, M.J., Herring, J.: A Mathematical Framework for the Definition of Topological Relationships.. In: Int. Symp. on Spatial Data Handling, pp. 803–813 (1990)Google Scholar
  2. 2.
    Clementini, E., Felice, P.D., Oosterom, P.: A Small Set of Formal Topological Relationships Suitable for End-user Interaction. In: 3rd Int. Symp. on Advances in Spatial Databases, pp. 277–295 (1993)Google Scholar
  3. 3.
    McKenney, M., Pauly, A., Praing, R., Schneider, M.: Dimension-refined Topological Predicates. In: 13th ACM Symp. on Geographic Information Systems (ACM GIS), pp. 240–249 (2005)Google Scholar
  4. 4.
    Chen, J., Li, C., Li, Z., Gold, C.: A Voronoi-based 9-intersection Model for Spatial Relations. International Journal of Geographical Information Science 15(3), 201–220 (2001)CrossRefGoogle Scholar
  5. 5.
    Schneider, M., Behr, T.: Topological Relationships between Complex Spatial Objects. ACM Trans. on Database Systems (TODS) 31(1), 39–81 (2006)CrossRefGoogle Scholar
  6. 6.
    Egenhofer, M.J.: Topological Relations in 3D. Technical report (1995)Google Scholar
  7. 7.
    Zlatanova, S.: On 3D Topological Relationships. In: 11th Int. Conf. on Database and Expert Systems Applications (DEXA), p. 913 (2000)Google Scholar
  8. 8.
    Borrmann, A., van Treeck, C., Rank, E.: Towards a 3D Spatial Query Language for Building Information Models. In: Proceedings of the Joint International Conference for Computing and Decision Making in Civil and Building Engineering (2006)Google Scholar
  9. 9.
    Pigot, S.: Topological Models for 3D Spatial Information Systems. In: International Conference on Computer Assisted Cartography (Auto-Carto), pp. 368–392 (1991)Google Scholar
  10. 10.
    Guo, W., Zhan, P., Chen, J.: Topological Data Modeling for 3D GIS. Int. Archives of Photogrammetry and Remote Sensing 32(4), 657–661 (1998)Google Scholar
  11. 11.
    Billen, R., Zlatanova, S., Mathonet, P., Boniver, F.: The Dimensional Model: a Framework To Distinguish Spatial Relationships. In: Int. Symp. on Advances in Spatial Databases, pp. 285–298 (2002)Google Scholar
  12. 12.
    Schneider, M., Weinrich, B.E.: An Abstract Model of Three-Dimensional Spatial Data Types. In: 12th ACM Symp. on Geographic Information Systems (ACM GIS), pp. 67–72 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tao Chen
    • 1
  • Markus Schneider
    • 1
  1. 1.Department of Computer and Information Science and EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations