Discrete Construction of Power Network Voronoi Diagram

  • Yili Tan
  • Ye Zhao
  • Yourong Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7030)


Power Network Voronoi diagrams are difficult to construct when the position relation of road segments are complicated. In traditional algorithm, The distance between objects must be calculated by selecting the minimum distance to their shared borders and doubling this value. When road segments cross or coincide with each other, production process will be extremely complex because we have to consider separately these parts. In this paper, we use discrete construction of network Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional ones. We also construct model according the algorithm. And the application example shows that the algorithm is both simple and useful, and it is of high potential value in practice.


Network voronoi diagram discrete Power network Voronoi diagrams 


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  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. Reine Angew, Math. 133, 97–178 (1907)zbMATHGoogle Scholar
  2. 2.
    Clarkson, K.L.: New applications of random sampling in computational geometry. Discrete and Computational Geometry 2, 195–222 (1987)MathSciNetCrossRefzbMATHGoogle 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. 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)MathSciNetCrossRefzbMATHGoogle 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. Information Processing Letters 109, 440–445 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    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
  10. 10.
    Wu, Y., Zhou, W., Wang, B., Yang, F.: Modeling and characterization of two-phase composites by Voronoi diagram in the Laguerre geometry based on random close packing of spheres. Computational Materials Science 47, 951–996 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yili Tan
    • 1
  • Ye Zhao
    • 2
  • Yourong Wang
    • 3
  1. 1.College of ScienceHebei United UniversityTangshanChina
  2. 2.Department of Mathematics and PhysicsShijiazhuang Tiedao UniversityShijiazhuangChina
  3. 3.Department of BasicTangshan CollegeTangshanChina

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