Discrete Ray-Casting

  • Ivan Salam
  • Philippe Nehlig
  • Eric Andres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)


In this paper, we present a new method of discrete Ray-Casting, using parallel rays, having the property that each point of the scene belongs to one and only one ray. This study is based on the theory of arithmetic discrete geometry. The rays are modeled by Figueiredo-Reveillès’ discrete naive 3D lines that tile the space and that can be incrementally generated.


Discrete Geometry Discrete Ray-Casting Volume Viewing Parallel Projection 


  1. 1.
    E. Andres, Cercles discrets et rotations discrètes (in French), Thèse de doctorat, Université Louis Pasteur, Strasbourg, December 1992.Google Scholar
  2. 2.
    E. Andres, R. Acharya, C. Sibata, Discrete Analytical Hyperplane, Graphical Models and Image Processing, vol. 59, n.5, Sept. 1997, pp. 302–309.CrossRefGoogle Scholar
  3. 3.
    R. Barneva, V. Brimkov, P. Nehlig, Thin Discrete Triangular Meshes, to be published in TCS, preliminary version available as research report # 98/01, LSIIT, Université Louis Pasteur, Pôle API, bvd S. Brand, 67400 Illkirch FRANCEGoogle Scholar
  4. 4.
    J.E. Bresenham, Algorithm for computer control of a digital plotter, ACM. Transaction on Graphics, Vol. 4, No 1, 1965, pp. 25–30.Google Scholar
  5. 5.
    J. Delfosse, W.T. Hewitt, M. MÉriaux, An investigation of discrete Ray-Tracing, 4th DGCI, 1994, Grenoble, pp. 65–76.Google Scholar
  6. 6.
    J. Delfosse, Le Rendu Discret: Voxéelisation, Structures Spaciales et Améliorations (in French), Thèse de doctorat, Université de Poitiers, Décembre 1996.Google Scholar
  7. 7.
    O. Figueiredo, J.-P. ReveilllÈes, A Contribution to 3D Digital Lines, DGCI, 5th Int. Workshop, Clermont-Ferrand, France, September 25-27, 1995, pp. 187–198.Google Scholar
  8. 8.
    J. FranÇon, Sur la topologie d’un plan arithmétique, Theoretical Computer Science, 156, 1996, pp. 159–176.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D. Gordon, R.A. Reynolds, Image Space Shading of 3-dimensional Objects, Computer Vision, Graphics, and Image Processing, 29 (1985), pp. 361–376.CrossRefGoogle Scholar
  10. 10.
    P.S. Heckbert, Survey of Texture MappingIEEE Computer Graphics & Applications, 6, 11 (November 1986), pp. 56–67.CrossRefGoogle Scholar
  11. 11.
    A. Kaufman, D. Cohen, R. Yagel, Normal estimation in 3D discrete space, the Visual Computer, 1992, 8 pp. 278–291.CrossRefGoogle Scholar
  12. 12.
    A. Kaufman, D. Cohen, R. Yagel, Volume graphics, IEEE Computer, Vol. 27, No 7, July 1993, pp. 51–64.Google Scholar
  13. 13.
    P. Nehlig, Applications affines discrètes et antialiassage, Thèse de doctorat, Université Louis Pasteur, Strasbourg, November 1992.Google Scholar
  14. 14.
    P. Nehlig, C. Montani, A Discrete Template Based Plane Casting Algorithm For Volume Viewing, 5th Colloquium: Discrete Geometry for Computer Imagery, Clermont-Ferrand, France, September 25-27, 1995, pp. 71–81.Google Scholar
  15. 15.
    H. Oswald, W. Kropatsch, F. Leberl, A Perspective Projection with Fast Evaluation of Visibility for Discrete Three-Dimensional Scenes, Proc. ISMIII’ 82, International Symposium on Medical and Image Interpretation, IEEE Computer Society Press, Silver Spring, MD (1982), pp. 464–468.Google Scholar
  16. 16.
    L. Papier, J. FranÇon, Evaluation de la normale au bord d’un objet discret 3D, Revue Internationale de CFAO et d’infographie, Ed. Hermes, december 1998.Google Scholar
  17. 17.
    J.-P. ReveillÈes, Géométrie discrète, calcul en nombres entiers et algorithmique (in French), thèse d’ état, Université Louis Pasteur, Strasbourg, December 1991.Google Scholar
  18. 18.
    H.K. Tuy, L.T. Tuy, Direct 2-D Display of 3-D Objects, IEEE Computer Graphics Appl.4, 10 (1984), pp. 29–33.Google Scholar
  19. 19.
    R. Yagel, A. Kaufman, Template-Based Volume Viewing, Computer Graphics Forum, Eurographic 92 Conference issue (Cambridge, UK) 11, 3 (September 1992), pp. 153–157Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Ivan Salam
    • 1
  • Philippe Nehlig
    • 1
  • Eric Andres
    • 1
  1. 1.IRCOM-SIC, bât. SP2MIFuturoscope CedexFrance

Personalised recommendations