The Discrete Tube: A Spatial Acceleration Technique for Efficient Diffraction Computation

  • Lilian Aveneau
  • Eric Andres
  • Michel Mériaux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

Keller’s Geometrical Theory of Diffraction [8] allows to render scenes with dihedron diffraction account. The Diffraction algorithm presented in [2] is too slow, since its complexity is linear with respect to the number of dihedra. In order to accelerate it, we propose to reduce the complexity with a discrete based algorithm. Considering that diffraction mainly occurs inside the n-first Fresnel’s ellipsoids [11], we can limit the diffraction computation to dihedra inside such ellipsoids. For efficiency we propose to use an ellipsoid approximation, the discrete tube. We describe two different algorithms for computing such a discrete tube. Their results are discussed, and show an important acceleration compared to the previous method.

Keywords

Discrete Algorithm Rendering techniques Diffraction GTD Ray-Tracing 

References

  1. 1.
    Eric Andres, Raj Acharya, and Claudio Sibata. Discrete analytical hyperplanes. Graphical Models And Image Processing, 59(5):302–309, September 1997.CrossRefGoogle Scholar
  2. 2.
    Lilian Aveneau and Michel Mériaux. Phénomènes ondulatoires en synthèse d’images. Revue internationale de CFAO et d’informatique graphique, 12(4):405–425, 1997.Google Scholar
  3. 3.
    M. Born and E. Wolf. Principles of Optics. Pergammon Press, New York, 6th edition, 1980.Google Scholar
  4. 4.
    Daniel Cohen. Voxel traversal along a 3D line. In Paul Heckbert, editor, Graphics Gems IV, pages 366–369. Academic Press, Boston, 1994.Google Scholar
  5. 5.
    Djamchid Ghazanfarpour and Jean-Marc Hasenfratz. A beam tracing with precise antialiasing for polyhedral scenes. Computer & Graphics, 22(1), 1998.Google Scholar
  6. 6.
    Andrew Glassner. An introduction to Ray Tracing. Academic Press, 1989.Google Scholar
  7. 7.
    H. Haken, Light, volume 1: Waves, Photons & Atoms. North-Holland, 1986.Google Scholar
  8. 8.
    Joseph B. Keller, Geometrical theory of diffraction. Journal of the Optical Society of America, 52(2):116–130, February 1962.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Robert G. Kouyoumjian and Prabhakar H. Pathak. A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface. Proceedings of the IEEE, 62(11):1449–1461, November 1974.Google Scholar
  10. 10.
    Eihachiro Nakamae, Kazufumi Kaneda, Takashi Okamoto, and Tomoyuki Nishita. A lighting model aiming at drive simulators. Computer Grahics, 24(4):395–404, August 1990.CrossRefGoogle Scholar
  11. 11.
    Radolphe Vauzelle. Un modèle de diffraction en 3D dans le 1 er ellipsoïde de Fresnel. PhD thesis, Université de Poitiers, 1994.Google Scholar
  12. 12.
    Turner Whitted. An improved illumination model for shaded display. Communication of the ACM, 23(6):343–349, June 1980.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Lilian Aveneau
    • 1
  • Eric Andres
    • 1
  • Michel Mériaux
    • 1
  1. 1.IRCOM SIC, UMR 6615 CNRSFuturoscope CedexFrance

Personalised recommendations