Skip to main content

On the Computation of 3D Visibility Skeletons

  • Conference paper
Computing and Combinatorics (COCOON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

Included in the following conference series:

Abstract

The 3D visibility skeleton is a data structure that encodes the global visibility information of a set of 3D objects. While it is useful in answering global visibility queries, its large size often limits its practical use. In this paper, we address this issue by proposing a subset of the visibility skeleton, which is empirically about 25% to 50% of the whole set. We show that the rest of the data structure can be recovered from the subset as needed, partially or completely. The running time complexity, which we analyze in terms of output size, is efficient. We also prove that the subset is minimal in the sense that the complexity bound ceases to hold if the subset is restricted further.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brönnimann, H., Devillers, O., Dujmović, V., Everett, H., Glisse, M., Goaoc, X., Lazard, S., Na, H.-S., Whitesides, S.: Lines and free line segments tangent to arbitrary three-dimensional convex polyhedra. SIAM Journal on Computing 37(2), 522–551 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brönnimann, H., Everett, H., Lazard, S., Sottile, F., Whitesides, S.: Transversals to line segments in three-dimensional space. Discrete and Computational Geometry 34(3), 381–390 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Demouth, J.: Événements visuels et limites d’ombres. PhD thesis, Univ. Nancy 2 (2008)

    Google Scholar 

  4. Dobkin, D.P., Kirkpatrick, D.G.: Determining the separation of preprocessed polyhedra: a unified approach. In: Kirchner, H., Wechler, W. (eds.) ALP 1990. LNCS, vol. 463, pp. 400–413. Springer, Heidelberg (1990)

    Google Scholar 

  5. Durand, F.: Visibilité tridimensionnelle: étude analytique et applications. PhD thesis, Université Joseph Fourier - Grenoble I (1999)

    Google Scholar 

  6. Koenderink, J., van Doorn, A.: The singularities of the visual mapping. Biological Cybernetics 24, 51–59 (1976)

    Article  MATH  Google Scholar 

  7. Pocchiola, M., Vegter, G.: The visibility complex. International Journal of Computational Geometry and Applications 6(3), 279–308 (1996); Proceedings of the 9th ACM Annual Symposium on Computational Geometry (SoCG ’93)

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhang, L., Everett, H., Lazard, S., Weibel, C., Whitesides, S.: On the size of the 3D visibility skeleton: experimental results. In: Halperin, D., Mehlhorn, K. (eds.) Esa 2008. LNCS, vol. 5193, pp. 805–816. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lazard, S., Weibel, C., Whitesides, S., Zhang, L. (2010). On the Computation of 3D Visibility Skeletons. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_50

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14031-0_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics