Visualization of Generalized Voronoi Diagrams
Voronoi diagrams are an important data structure in computer science. However well studied mathematically, understanding such diagrams for different metrics, orders, and site shapes is a complex task. We propose a new method to visualize k-order diagrams and give an efficient adaptive implementation for this method. The algorithm is easy to customize for different metrics and site shapes. Its real-time performance makes it suitable for interactive planning and analysis of complex Voronoi configurations in 2D. We illustrate the method for different combinations of metrics and site shapes.
KeywordsVoronoi Diagram Medial Axis Voronoi Cell Cell Edge Fire Station
Unable to display preview. Download preview PDF.
- 1.P. Agarwal, M. De Berg, J. Matousek, and O. Schwarzkopf, Constructing levels in arrangements and higher order Voronoi diagrams, SIAM J. Comp., no. 27, 1998, pp. 654–667.Google Scholar
- 2.F. Aurenhammer, Voronoi Diagrams: A Survey of a Fundamental Geometric Data Structure, ACM Computing Surveys, no. 23, 1991, pp. 345–405.Google Scholar
- 3.D. Lee and C. Wong, Voronoi diagrams in the L1 and Linf metrics with 2-dimensional storage applications, SIAM J. Computing, no. 9, 1980, pp. 200–211.Google Scholar
- 5.M. De Berg, M. Van Krefeld, M. Overmars, O. Schwarzkopf, Computational Geometry-Algorithms and Applications, Springer, 1998.Google Scholar
- 6.M. Sakamoto and M. Takagi, Patterns of weighted Voronoi tessellations, Sci. Forum, no. 3, 1988, pp. 103–111.Google Scholar
- 7.J. Vleugels and M. Overmars Approximating Generalized Voronoi Diagrams in Any Dimension, Technical Report UU-CS-1995-14, Utrecht University, 1995.Google Scholar
- 8.K. Hoff, T. Culver, J. Keyser, M, Lin, D. MANOCHA, Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware, Proc. SIGGRAPH’ 99, ACM Press, 1999, pp. 277–286.Google Scholar
- 9.J.J. Van Wijk, H. Van De Wetering, Cushion Treemaps: Visualization of Hierarchical Information, Proc. Information Visualization’ 99, IEEE Press, pp. 73–78.Google Scholar
- 10.M. Bruls, J. J. Van Wijk, K. Huizing, Squarified Treemaps, Proc. IEEE VisSym 2000, Springer, 2000, pp. 33–42Google Scholar
- 11.Strategic Simulations, INC., Panzer General 3D, http://www.ssionline.com/, 1999.