Ray-tracing and 3-D objects representation in the BCC and FCC grids

  • Luis Ibáñez
  • Chafiaâ Hamitouche
  • Christian Roux
From Principles to Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)


This paper describes a ray-tracing and an object description method for objects sampled not in the usual cubic grid, but in BCC (Body Centered Cubic) and FCC (Face Centered Cubic) grids, which are well known in crystallography. The use of this kind of grids is motivated by their interesting characteristics: they reduce the density of samples needed to represent a signal without information loss and they have better topological properties than the cubic grid.


Image Representation Rendering Visualization 


  1. 1.
    D.E.Dndgeou, B.M. Mecsereau Multidimensional digital signal processing Prentice-Hall,Eglewood Cliffs; NJ; 1984.Google Scholar
  2. 2.
    C.Kitto Introduction to solid-state physics John Wiley & Sons In*. 1971.Google Scholar
  3. 3.
    J.Serra Image Analysis and Mathematical Morphology. Academic Press Inc. 1982.Google Scholar
  4. 4.
    Arie E. Kaufman, Volume Synthesis 6th International Workshop, Discrete Geometry for Computer Imagery 96, Lyon, France, November 1996. Lecture Notes in Computer Sciences, Springer Verlag.Google Scholar
  5. 5.
    J.J.Jacq, C.Roux, A Direct Multi-Volume Rendering Method Aiming at Comparisions of 3-D Images and Models IEEE Transactions on information technology in biomedicine, Vol 1., No.1, pp 30–43, march 1997.Google Scholar
  6. 6.
    G.T.Herman, 3D Display; A Survey From Theory to Applications Computerized Medical Imaging and Graphics, Vol. 17, Nos 4/5, pp 231–242, 1993.Google Scholar
  7. 7.
    W.Kriiger, P.Schröder. Data parallel volume rendering pp 37–52. in Scientific Visualization, Academic Press. 1994.Google Scholar
  8. 8.
    U.Tiede, et al, Investigation of Medical 3D-Rendering Algorithms IEEE Computer Graphics & Applications, Vol. 10, No.2, pp 41–53, 1990.Google Scholar
  9. 9.
    G.Sakas, M.Grimm, A.Savapoulos Optimized Maximum Intensity Projection (MIP). in Rendering Techniques'95, Proceedings of the Eurographics Workshop in Dublin, Ireland, June 12–14, Springer Verlag, 1995.Google Scholar
  10. 10.
    S. Matej, R.M. Lewit Efficient 3-D Grids for Image Reconstruction Using Spherically Symmetric Volume Elements IEEE Transactions on Nuclear Science, Vol 42, No.4, August 1995, pp 1361–1370.Google Scholar
  11. 11.
    J.E. Bresenham Algorithm for computer control of a digital plotter IBM Systems Journal, 1965, Vol 4. pp 25–30.Google Scholar
  12. 12.
    Li Min Luo, Ch. Hamitouche, L. Dillenseger, J.L. Coatrieux A Moment-Based Three-Dimensional Edge Operator, IEEE Transactions on Biomedical Engineering,. Vol 40, No.7, Jul 1993. pp 693–703.Google Scholar
  13. 13.
    L. Ibáñez, C. Hamitouche, C. Roux Moment-based operator for sub-voxel surface extraction in medical imaging International Conference on Image Processing ICIP'96, Lausanne, Switzerland, September 1996.Google Scholar
  14. 14.
    L. Ibáñez, C. Hamitouche, C. Roux Determination of discrete sampling grids with optimal topological and spectral properties 6th International Workshop, Discrete Geometry for Computer Imagery 96, Lyon, France, November 1996. Lecture Notes in Computer Science, Springer Verlag.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Luis Ibáñez
    • 1
  • Chafiaâ Hamitouche
    • 1
  • Christian Roux
    • 1
  1. 1.Département Image et Traitement de l'InformationENST — Bretagne, Technopôle de Brest-IroiseBrestFrance

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