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International Symposium on Visual Computing

ISVC 2015: Advances in Visual Computing pp 755–766Cite as

Computing Voronoi Diagrams of Line Segments in ℝ K in O(n log n) Time

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9475))

Abstract

The theoretical bounds on the time required to compute a Voronoi diagram of line segments in 3D are the lower bound of Ω(n 2) and the upper bound of O(n 3+ε). We present a method here for computing Voronoi diagrams of line segments in O(2a k n log 2n + 2b k n log 2n + 14n + 12c 1 n) for k-dimensional space. We also present a modification to the Bowyer-Watson method to bring its runtime down to a tight O(n log n).

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Author information

Authors and Affiliations

  1. Holcomb Technologies, Irving, TX, 75062, USA

    Jeffrey W. Holcomb

  2. Department of Computer Engineering, University of Texas at Dallas, Richardson, TX, 75080, USA

    Jeffrey W. Holcomb & Jorge A. Cobb

Authors
  1. Jeffrey W. Holcomb
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  2. Jorge A. Cobb
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Corresponding author

Correspondence to Jeffrey W. Holcomb .

Editor information

Editors and Affiliations

  1. University of Nevada, Reno, Nevada, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, California, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, Nevada, USA

    Darko Koracin

  5. University of Houston, Houston, Texas, USA

    Ioannis Pavlidis

  6. IBM T.J. Watson Research Center, Yorktown Heights, New York, USA

    Rogerio Feris

  7. Purdue University, West Lafayette, Indiana, USA

    Tim McGraw

  8. Side Effects Software, Santa Monica, California, USA

    Mark Elendt

  9. The DiVE, Durham, North Carolina, USA

    Regis Kopper

  10. Texas A&M University, College Station, Texas, USA

    Eric Ragan

  11. Kent State University, Kent, Ohio, USA

    Zhao Ye

  12. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Gunther Weber

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© 2015 Springer International Publishing Switzerland

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Holcomb, J.W., Cobb, J.A. (2015). Computing Voronoi Diagrams of Line Segments in ℝ K in O(n log n) Time. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2015. Lecture Notes in Computer Science(), vol 9475. Springer, Cham. https://doi.org/10.1007/978-3-319-27863-6_71

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  • DOI: https://doi.org/10.1007/978-3-319-27863-6_71

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27862-9

  • Online ISBN: 978-3-319-27863-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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