Abstract
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.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
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)
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)
Aurenhammer, F.: Voronoi diagrams: A survey of a fundamental geometric data structure. ACM Computer Surveys 23(3), 686–695 (1991)
Aurenhammer, F., Klein, R.: Voronoi diagrams. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 201–290. Elsevier, Amsterdam (2000)
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)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry; Algorithms and applications, 2nd edn. Springer, Berlin (2000)
Boada, I., Coll, N., Sellarès, J.A.: The Voronoi-Quadtree: construction and visualization. In: Eurographics 2002 Short Presentations, pp. 349–355 (2002)
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)
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)
Kambhampati, S., Davis, L.S.: Multiresolution Path Planning for Mobile Robot’s. IEEE Journal of Robotics Automation RA-2(3), 135–145 (1986)
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)
Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Application of Voronoi Diagrams. John Wiley, Chichester (2000)
Samet, H.: Applications of Spatial Data Structures: computer graphics, image processing, and GIS. Addison-Wesley, Reading (1993)
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)
Telea, A.C., van Wijk, J.J.: Visualization of Generalized Voronoi Diagrams. In: Proceedings of IEEE VisSym 2001, pp. 165–174. Springer, Heidelberg (2001)
Vleugels, J., Overmars, M.: Approximating Generalized Voronoi Diagrams in Any Dimension. Int. J. on Computational Geometry and Applications 8, 201–221 (1998)
Gold, C.: Voronoi Diagrams page on the Web: Applications, http://www.voronoi.com/section_1.htm
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boada, I., Coll, N., Sellarès, J.A. (2004). Multiresolution Approximations of Generalized Voronoi Diagrams. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25944-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-25944-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22129-6
Online ISBN: 978-3-540-25944-2
eBook Packages: Springer Book Archive