Dynamic Construction of Power Voronoi Diagram

  • Yili Tan
  • Lihong Li
  • Yourong Wang
Part of the Communications in Computer and Information Science book series (CCIS, volume 244)

Abstract

The power Voronoi diagrams are difficult to construct because of their complicated structures. In traditional algorithm, production process which is based on the Delaunay diagram was extremely complex. While dynamic algorithm is only concerned with positions of generators, so it is effective for constructing Voronoi diagrams with complicated shapes of Voronoi polygons. It can be applied to power Voronoi diagram with any generators, and can get over most shortcomings of traditional algorithm. So it is more useful and effective. Model is constructed with dynamic algorithm. And the application example shows that the algorithm is both simple and practicable and of high potential value in practice.

Keywords

Voronoi diagram dynamic power 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Voronoi, G.: Nouvelles.: applications des paramèters continus à la théorie des formes quadratiques. Premier Mémoire: Sur quelques Proprieteés des formes quadratiques positives parfaits. J. Reine Angew Math. 133, 97–178 (1907)MathSciNetMATHGoogle Scholar
  2. 2.
    Clarkson, K.L.: New applications of random sampling in computational geometry. J. Discrete and Computational Geometry 2, 195–222 (1987)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Sud, A., Govindaraju, N., Gayle, R., Dinesh Manocha, Z.: Interactive 3D distance field computation using linear factorization. In: Proceedings of the 2006 Symposium on Interactive 3D Graphics and Games, Redwood City, California, pp. 14–17 (2006)Google Scholar
  4. 4.
    Qian, B., Zhang, L., Shi, Y., Liu, B.: New Voronoi Diagram Algorithm of Multiply-Connected Planar Areas in the Selective Laser Melting. J. Tsinghua Science & Technology 14, 137–143 (2009)CrossRefGoogle Scholar
  5. 5.
    Aurenhammer, F., Drysdale, R.L.S., Krasser, H.: Farthest line segment Voronoi diagrams. Information Processing Letters 100, 220–225 (2006)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Chen, J., Zhao, R., Li, Z.: Voronoi-based k-order neighbour relations for spatial analysis. ISPRS Journal of Photogrammetry and Remote Sensing 59, 60–72 (2004)CrossRefGoogle Scholar
  7. 7.
    Lee, I., Lee, K.: A generic triangle-based data structure of the complete set of higher order Voronoi diagrams for emergency management. Computers, Environment and Urban Systems 33, 90–99 (2009)CrossRefGoogle Scholar
  8. 8.
    Cabello, S., Fort, M., Sellarès, J.A.: Higher-order Voronoi diagrams on triangulated surfaces. J. Information Processing Letters 109, 440–445 (2009)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Siam, J., Siam, J.: Power Diagrams: Properties, Algorithms and Applications. Comput. 16(19), 78–96 (1987)MathSciNetGoogle Scholar
  10. 10.
    Ferenc, J.-S., Néda, Z.: On the size distribution of Poisson Voronoi cells. Physica A: Statistical Mechanics and its Applications 385, 518–526 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yili Tan
    • 1
  • Lihong Li
    • 1
  • Yourong Wang
    • 2
  1. 1.College of ScienceHebei United UniversityTangshanChina
  2. 2.Department of BasicTangshan CollegeTangshanChina

Personalised recommendations