Refraction in Discrete Ray Tracing

  • David Rodgman
  • Min Chen
Part of the Eurographics book series (EUROGRAPH)


Refraction is an important graphics feature for synthesizing photorealistic images. This paper presents a study on refraction rendering in volume graphics using discrete ray tracing. We describe four basic approaches for determining the relative refractive index at each sampling position, and examine their relative merits. We discuss two types of anomalies associated with some approaches and three different mechanisms for controlling sampling intervals. We apply the refraction rendering to objects with uniform as well as non-uniform optical density, and objects built upon mathematical scalar fields as well as volumetric datasets. In particular, the study shows that the normal estimation plays a critical role in synthesizing aesthetically pleasing images. The paper also includes the results of various tests, and our quantitative and qualitative analysis.


Scalar Field Interval Length Spatial Object Graphic Scene Volume Dataset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Kaufman, D. Cohen and R. Yagel, “Volume Graphics”, IEEE Computer, 26(7), pp. 51–64 (1993).Google Scholar
  2. 2.
    M. Chen, A. E. Kaufman and R. Yagel (eds), Volume Graphics, Springer, London, (2000).MATHGoogle Scholar
  3. 3.
    W. Lorensen and H. Cline, “Marching cubes: a high resolution 3D surface construction algorithm”, ACM/SIGGRAPH Computer Graphics, 21(4), pp. 163–169, (1987).CrossRefGoogle Scholar
  4. 4.
    M. Levoy, ‘Display of surfaces from volume data”, IEEE Computer Graphics and Applications, 8(5), pp. 29–37, (1988).CrossRefGoogle Scholar
  5. 5.
    P. Sabella, “A rendering algorithm for visualizing 3D scalar fields”, ACM/SIGGRAPH Computer Graphics, 22(4), pp. 51–58, (1988).CrossRefGoogle Scholar
  6. 6.
    L. Westover, ‘Footprint evaluation for volume rendering”, ACM/SIGGRAPH Computer Graphics, 24 (4), pp. 59–64, (1988).Google Scholar
  7. 7.
    R. Yagel, D. Cohen and A. Kaufman, “Discrete Ray Tracing”, IEEE Computer Graphics and Applications, 12(9), pp. 19–28 (1992).CrossRefGoogle Scholar
  8. 8.
    L. Sobierajski and A. Kaufman, “Volumetric Raytracing”, Proceedings of IEEE Symposium on Volume Visualization, pp. 11–18 (1994).Google Scholar
  9. 9.
    N. Stolte and R. Caubet. “Discrete Ray-Tracing of Huge Voxels Spaces”, In Eurographics’95, pages 383–394, Maastricht, August (1995).Google Scholar
  10. 10.
    J. F. Blinn, “A generalization of algebraic surface drawing”, ACM Transactions on Graphics, 1(3), pp. 235–256, (1982).CrossRefGoogle Scholar
  11. 11., Snell’s Law,, December 2000.
  12. 12.
    M. Born, E. Wolf, Principles of Optics, Pergamon Press, New York, 5th Ed., (1975).Google Scholar
  13. 13.
    D. S. Kay, “Transparency for Computer Synthesized Images”, Proc. SIGGRAPH, pp. 158164 (1979).Google Scholar
  14. 14.
    T. Whitted, “An Improved Illumination Model for Shaded Display”, Communications of the ACM, pp. 343–349 (1980).Google Scholar
  15. 15.
    A. S. Glassner et al. An Introduction to Ray Tracing, Academic Press, London, (1989).MATHGoogle Scholar
  16. 16.
    R. Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, New York, (1989).Google Scholar
  17. 17.
    R. Satherley and M. W. Jones, “Extending Hypertextures to Non-Geometrically Definable Volume Data”, In Chen, Kaufman, and Yagel (eds), Volume Graphics, pp. 211–225, Springer, 2000.Google Scholar
  18. 18.
    S. Treavett and M. Chen, “Pen-and-Ink rendering in volume visualization”, Proc. IEEE Visualization 2000, Salt Lake City, Utah (2000).Google Scholar
  19. 19.
    A. Winter and M. Chen, “vlib: a volume graphics API”, submitted to VG01: international Workshop on Volume Graphics, (2001).Google Scholar
  20. 20.
    R. Yagel, D. Cohen, A. Kaufman, “Normal Estimation in 3D Discrete Space”, The Visual Computer, pp 278–291 (1992).Google Scholar
  21. 21.
    T. Moller, R. Machiraju, K. Mueller, R. Yagel, “A Comparison of Normal Estimation Schemes”, IEEE Proceedings of Visualization 97, pp 19–26 (1997).Google Scholar
  22. 22.
    J. D. Foley, A. van Dam, S K. Feiner and J. F. Hughes, Computer Graphics: Principles and Practice, Addison-Wesley, Reading, (1990).Google Scholar
  23. 23.
    M. Chen and J. V. Tucker, “Constructive Volume Geometry”, Computer Graphics Forum, 19(4), pp. 281–293, 2000.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 2001

Authors and Affiliations

  • David Rodgman
    • 1
  • Min Chen
    • 1
  1. 1.Department of Computer ScienceUniversity of Wales SwanseaSwanseaUK

Personalised recommendations