Skip to main content

Power Diagrams and Intersection Detection

  • Conference paper
Computational Science and Its Applications - ICCSA 2011 (ICCSA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6784))

Included in the following conference series:

  • 1332 Accesses

Abstract

We propose a new algorithm for the detection of all intersections between a set of balls and a general query object. The proposed algorithm does not impose any restrictive condition on the set of balls and utilises power diagrams to minimize the amount of intersection tests. The price for this is power diagram computation in a preprocessing step.

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. Agarwal, P., Guibas, L., Nguyen, A., Russel, D., Zhang, L.: Collision detection for deforming necklaces. Comput. Geom. Theory Appl. 28, 137–163 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Amenta, N., Choi, S., Kolluri, R.K.: The power crust. In: SMA 2001: Proceedings of the sixth ACM symposium on Solid modeling and applications, pp. 249–266. ACM Press, New York (2001)

    Chapter  Google Scholar 

  3. Aurenhammer, F.: Power diagrams: Properties, algorithms and applications. SIAM Journal on Computing 16(1), 78–96 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. Aurenhammer, F.: Improved algorithms for discs and balls using power diagrams. Journal of Algorithms 9(2), 151–161 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Aurenhammer, F.: Voronoi diagrams—a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345–405 (1991)

    Article  Google Scholar 

  6. Bajaj, C.L., Pascucci, V., Shamir, A., Holt, R.J., Netravali, A.N.: Dynamic maintenance and visualization of molecular surfaces. Discrete Appl. Math. 127(1), 23–51 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Boissonnat, J.D., Karavelas, M.I.: On the combinatorial complexity of euclidean voronoi cells and convex hulls of d-dimensional spheres. In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2003, pp. 305–312. Society for Industrial and Applied Mathematics, Philadelphia (2003)

    Google Scholar 

  8. Bowyer, A.: Computing Dirichlet tessellations. The Computer Journal 24(2), 162–166 (1981)

    Article  MathSciNet  Google Scholar 

  9. Devillers, O., Pion, S., Teillaud, M.: Walking in a triangulation. Internat. J. Found. Comput. Sci. 13, 106–114 (2001)

    MATH  MathSciNet  Google Scholar 

  10. Edelsbrunner, H., Facello, M., Fu, P., Liang, J.: Measuring proteins and voids in proteins. In: Proceedings of the 28th Hawaii International Conference on System Sciences, HICSS 1995, p. 256. IEEE Computer Society, Washington, DC, USA (1995)

    Google Scholar 

  11. Edelsbrunner, H.: The union of balls and its dual shape. In: Proceedings of the ninth annual symposium on Computational geometry, SCG 1993, pp. 218–231. ACM, New York (1993)

    Chapter  Google Scholar 

  12. Edelsbrunner, H., Facello, M., Liang, J.: On the definition and the construction of pockets in macromolecules. Tech. rep. Champaign, IL, USA (1995)

    Google Scholar 

  13. Edelsbrunner, H., Shah, N.R.: Incremental topological flipping works for regular triangulations. In: SCG 1992: Proceedings of the eighth annual symposium on Computational geometry, pp. 43–52. ACM Press, New York (1992)

    Chapter  Google Scholar 

  14. Gavrilova, M.L.: On a nearest-neighbor problem in minkowski and power metrics. In: Alexandrov, V., Dongarra, J., Juliano, B., Renner, R., Tan, C. (eds.) ICCS-ComputSci 2001. LNCS, vol. 2073, pp. 663–672. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Guibas, L.J., Xie, F., Zhang, L.: Kinetic collision detection: Algorithms and experiments. In: ICRA 2001, pp. 2903–2910 (2001)

    Google Scholar 

  16. Kim, D.S., Cho, Y., Kim, D.: Euclidean voronoi diagram of 3d balls and its computation via tracing edges. Comput. Aided Des. 37, 1412–1424 (2005)

    Article  MATH  Google Scholar 

  17. Li, L.G., Zhang, L.: Euclidean proximity and power diagrams. In: In Proc. 10th Canadian Conference on Computational Geometry, pp. 90–91 (1998)

    Google Scholar 

  18. Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial tessellations: Concepts and applications of Voronoi diagrams, 2nd edn. Probability and Statistics, 671 pages. Wiley, NYC (2000)

    Book  MATH  Google Scholar 

  19. Slonim, D.K.: Algorithms for modeling and measuring proteins. Tech. rep., Cambridge, MA, USA (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zemek, M., Kolingerová, I. (2011). Power Diagrams and Intersection Detection. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21931-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21931-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21930-6

  • Online ISBN: 978-3-642-21931-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics