Skip to main content

Hierarchical Representation of 3D Polyhedra

  • Chapter
Dynamic Simulations of Multibody Systems
  • 335 Accesses

Abstract

Collision detection is undoubtly the most time-consuming step in a dynamicsimulation engine. In theory, as the simulation evolves, every object needs to be checked for collisions against all other objects in the simulation. Whenever a collision is detected, the simulation engine needs to trace back in time to the instant before the collision, and determine the collision point and collision normal from the relative geometric displacement of the colliding objects.

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 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.00
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.

Notes and Comments

  1. S. Gottschalk, M. C. Lin, and D. Manocha. Obbtree: A hierarchical structure for rapid interference detection. Computer Graphics (Proceedings SIGGRAPH), 30: 171 - 180, 1996.

    Google Scholar 

  2. S. Gottschalk. The separating axis test. Technical Report TR-96-24, University of North Carolina, Chapel Hill, 1996.

    Google Scholar 

  3. Gino van den Bergen. Efficient collision detection of complex deformable models using aabb trees. Journal of Graphics Tools, 2 (4): 1 - 13, 1997.

    Article  MATH  Google Scholar 

  4. H. Samet. Spatial Data Structures: Quadtree, Octrees and Other Hierarchical Methods. Addison-Wesley, 1989.

    Google Scholar 

  5. Chris Hecker. How to simulate a ponytail, part 1. Game Developer Magazine, pages 34 - 42, March 2000.

    Google Scholar 

  6. Franco P. Preparata and Michael Ian Shamos. Computational Geometry: An Introduction. Springer-Verlag, 1985.

    Google Scholar 

  7. Herbert Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, 1987.

    Google Scholar 

  8. Gene H. Golub and Charles F. Van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, 1996.

    MATH  Google Scholar 

  9. Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press, 1991.

    Google Scholar 

  10. Brian V. Mirtich. Impulse-based Dynamic Simulation of Rigid Body Systems. PhD thesis, University of California, Berkeley, 1996.

    Google Scholar 

  11. S. Gottschalk. The separating axis test. Technical Report TR-96-24, University of North Carolina, Chapel Hill, 1996.

    Google Scholar 

  12. James Arvo. A simple method for box-sphere intersection testing. Graphics Gems, 1: 335 - 339, 1990.

    Google Scholar 

  13. Jack Ritter. An efficient bounding sphere. Graphics Gems, 1: 301 - 303, 1990.

    Google Scholar 

  14. Evaggelia-Aggeliki Karabassi, Georgios Papaioannou, Theoharis Theoharis, and Alexander Boehm. Intersection test for collision detection in particle systems. Journal of Graphics Tools, 4 (1): 25 - 37, 1999.

    Article  Google Scholar 

  15. Martin Held. ERIT: A collection of efficient and reliable intersection tests. Journal of Graphics Tools, 2 (4): 25 - 44, 1997.

    Article  Google Scholar 

  16. Georg Glaeser. Fast Algorithms for 3D-Graphics. Springer-Verlag, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Coutinho, M.G. (2001). Hierarchical Representation of 3D Polyhedra. In: Dynamic Simulations of Multibody Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3476-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3476-8_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2902-0

  • Online ISBN: 978-1-4757-3476-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics