Multiresolution Approximations of Generalized Voronoi Diagrams

  • I. Boada
  • N. Coll
  • J. A. Sellarès
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)


A framework to support multiresolution approximations of planar generalized Voronoi diagrams is presented. Our proposal is: (1) A multiresolution model based on a quadtree data structure which encodes approximations of a generalized Voronoi diagram at different levels of detail. (2) A user driven refinement strategy which generates from the quadtree a continuous polygonal approximation of the Voronoi diagram.


Leaf Node Voronoi Diagram Computational Geometry Common Edge Voronoi Region 
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.


  1. 1.
    Alani, H., Jones, C.B., Tudhope, D.: Voronoi-based region approximation for geographical information retrieval with gazetteers. Int. J. Geographical Information Science 15(4), 287–306 (2001)CrossRefGoogle Scholar
  2. 2.
    Amenta, N., Bern, M., Kamvysselis, M.: A new Voronoi-based surface reconstruction algorithm. In: Proceedings of Siggraph 1998, pp. 415–421. ACM, New York (1998)CrossRefGoogle Scholar
  3. 3.
    Aurenhammer, F.: Voronoi diagrams: A survey of a fundamental geometric data structure. ACM Computer Surveys 23(3), 686–695 (1991)CrossRefGoogle Scholar
  4. 4.
    Aurenhammer, F., Klein, R.: Voronoi diagrams. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 201–290. Elsevier, Amsterdam (2000)CrossRefGoogle Scholar
  5. 5.
    Behnke, S.: Local Multiresolution Path Planning. In: Polani, D., Browning, B., Bonarini, A., Yoshida, K. (eds.) RoboCup 2003. LNCS (LNAI), vol. 3020, pp. 332–343. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry; Algorithms and applications, 2nd edn. Springer, Berlin (2000)zbMATHGoogle Scholar
  7. 7.
    Boada, I., Coll, N., Sellarès, J.A.: The Voronoi-Quadtree: construction and visualization. In: Eurographics 2002 Short Presentations, pp. 349–355 (2002)Google Scholar
  8. 8.
    Boada, I., Coll, N., Sellarès, J.A.: Hierarchical Planar Voronoi Diagram Approximations. In: Proceedings of 14th Canadian Conference on Computational Geometry, pp. 40–45 (2002)Google Scholar
  9. 9.
    Boada, I., Coll, N., Sellarès, J.A.: Dynamically maintaining a hierarchical planar Voronoi diagram approximation. In: Kumar, V., et al. (eds.) ICCSA 2003. LNCS, vol. 2669, pp. 836–846. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Kambhampati, S., Davis, L.S.: Multiresolution Path Planning for Mobile Robot’s. IEEE Journal of Robotics Automation RA-2(3), 135–145 (1986)CrossRefGoogle Scholar
  11. 11.
    Lavender, D., Bowyer, A., Davenport, J., Wallis, A., Woodwark, J.: Voronoi diagrams of set-theoretic solid models. IEEE Computer Graphics and Applications 12(5), 69–77 (1992)CrossRefGoogle Scholar
  12. 12.
    Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Application of Voronoi Diagrams. John Wiley, Chichester (2000)zbMATHGoogle Scholar
  13. 13.
    Samet, H.: Applications of Spatial Data Structures: computer graphics, image processing, and GIS. Addison-Wesley, Reading (1993)Google Scholar
  14. 14.
    Teichmann, T., Teller, S.: Polygonal approximation of Voronoi diagrams of a set of triangles in three dimensions. Technical Report 766. Laboratory of Computer science, MIT (1997)Google Scholar
  15. 15.
    Telea, A.C., van Wijk, J.J.: Visualization of Generalized Voronoi Diagrams. In: Proceedings of IEEE VisSym 2001, pp. 165–174. Springer, Heidelberg (2001)Google Scholar
  16. 16.
    Vleugels, J., Overmars, M.: Approximating Generalized Voronoi Diagrams in Any Dimension. Int. J. on Computational Geometry and Applications 8, 201–221 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Gold, C.: Voronoi Diagrams page on the Web: Applications,

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • I. Boada
    • 1
  • N. Coll
    • 1
  • J. A. Sellarès
    • 1
  1. 1.Institut Informàtica i AplicacionsUniversitat de GironaSpain

Personalised recommendations