Hyperbolic Voronoi Diagram
- Zahra NilforoushanAffiliated withFaculty of Math. and Computer Sc., AmirKabir University of Tech.
- , Ali MohadesAffiliated withFaculty of Math. and Computer Sc., AmirKabir University of Tech.
Voronoi diagrams are among the most extensively studied objects in computational geometry with useful applications in different areas of science. To understand impacts of non-Euclidean geometry on computational geometry, this paper investigates the Voronoi diagram in hyperbolic space specially the one in the Poincaré hyperbolic disk, which is a 2-dimensional manifold with negative curvature. We first prove some lemma in Poincaré hyperbolic disk and then give an incremental algorithm to construct Voronoi diagram.
- Hyperbolic Voronoi Diagram
- Book Title
- Computational Science and Its Applications - ICCSA 2006
- Book Subtitle
- International Conference, Glasgow, UK, May 8-11, 2006, Proceedings, Part V
- pp 735-742
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- Editor Affiliations
- 16. Department of Computer Science, University of Calgary,
- 17. Department of Mathematics and Computer Science, University of Perugia
- 18. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota
- 19. OptimaNumerics Ltd.,
- 20. Clayton School of IT, Monash University
- 21. Department of Chemistry, University of Perugia
- 22. School of Computing, Soongsil University
- 23. School of Information and Communication Engineering, Sungkyunkwan University
- Author Affiliations
- 24. Faculty of Math. and Computer Sc., AmirKabir University of Tech., 424 Hafez Ave., Tehran, Iran
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