General calculations using graphics hardware, with application to interactive caustics

  • Chris Trendall
  • A. James Stewart
Part of the Eurographics book series (EUROGRAPH)


Graphics hardware has been developed with image production in mind, but current hardware can be exploited for much more general computation. This paper shows that graphics hardware can perform general calculations, which accelerate the rendering process much earlier than at the latter image generation stages. An example is given of the real time calculation of refractive caustics.


Computer Graphic Voronoi Diagram Graphic Hardware Height Field Bottom Plane 
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  1. 1.
    James Arvo. Backward ray tracing. Developments in Ray Tracing. ACM SIGGRAPH Course Notes, 12:259–263, 1986.Google Scholar
  2. 2.
    David Blythe, Brad Grantham, Mark J. Kilgard, Tom McReynolds, and Scott R. Nelson. Advanced graphics programming techniques using OpenGL. In SIGGRAPH 99 Course Notes, August, 1999.Google Scholar
  3. 3.
    Christian-A. Bohn. Kohonen feature mapping through graphics hardware. In 3rd Int. Conf. on Computational Intelligence and Neurosciences, 1998.Google Scholar
  4. 4.
    Brian Cabral and Leith Casey Leedom. Imaging vector fields using line integral convolution. Computer Graphics (SIGGRAPH ’93 Proceedings), pages 263–272, August 1993.Google Scholar
  5. 5.
    NVIDIA Corporation. Nvidia OpenGL Extension Specifications., April, 2000.Google Scholar
  6. 6.
    Paul Haeberli and Mark Segal. Texture mapping as a fundamental drawing primitive. Fourth Eurographics Workshop on Rendering, June:259–266, 1993.Google Scholar
  7. 7.
    Pat Hanrahan, Bill Mark, Kekoa Proudfoot, Svetoslav Tzvetkov, David Ebert, Wolfgang Heidrich, and Philipp Slusallek. Stanford Real-Time Programmable Shading Project. http://graphics.stanford.EDU/projects/shading/, 2000.Google Scholar
  8. 8.
    Eugene Hecht and Alfred Zajac. Optics. Addison Wesley Longman, Inc., 1979.Google Scholar
  9. 9.
    Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. In SIGGRAPH ’84 Proceedings, pages 119–127, July, 1984.Google Scholar
  10. 10.
    Wolfgang Heidrich. High-quality Shading and Lighting for Hardware-accelerated Rendering. PhD thesis, University of Erlangen-Nurenberg, April, 1999.Google Scholar
  11. 11.
    Wolfgang Heidrich, Hendrick Lensch, Michael F. Cohen, and Hans-Peter Seidel. Light field techniques for reflections and refractions. In Rendering Techniques ’99 (Proceedings of the Eurographics Rendering Workshop), August, 1999.Google Scholar
  12. 12.
    Wolfgang Heidrich and Hans-Peter Seidel. Efficient rendering of anisotopic surfaces using computer graphics hardware. Proceedings of the Image and Multi-dimensional Digital Signal Processing Workshop (IMDSP), 1998.Google Scholar
  13. 13.
    Wolfgang Heidrich and Hans-Peter Seidel. View-independent environment maps. Euro-graphics/SIGGRAPH Workshop on Graphics Hardware, pages 39–45, 1998.Google Scholar
  14. 14.
    Wolfgang Heidrich and Hans-Peter Seidel. Realistic, hardware-accelerated shading and lighting. In Computer Graphics (SIGGRAPH ’99 Proceedings), August, 1999.Google Scholar
  15. 15.
    Wolfgang Heidrich, Rudiger Westermann, Hans-Peter Seidel, and Thomas Ertl. Applications of pixel textures in visualization and realistic image synthesis. In ACM Symposium on Interactive 3D Graphics, August, 1999.Google Scholar
  16. 16.
    Kenneth E. Hoff III, Tim Culver, John Keyser, Ming Lin, and Dinesh Manocha. Fast computation of generalized Voronoi diagrams using graphics hardware. Computer Graphics (SIGGRAPH ’99 Proceedings), pages 277–286, August, 1999.Google Scholar
  17. 17.
    Silicon Graphics Inc. Pixel texture extension. Specification,, 1999.Google Scholar
  18. 18.
    Jed Lengyel, Mark Reichert, Bruce R. Donald, and Donald P. Greenberg. Real-time robot motion planning using rasterizing computer graphics hardware. Computer Graphics, 24(4):327–335, August, 1990.CrossRefGoogle Scholar
  19. 19.
    Michael D. McCool and Wolfgang Heidrich. Texture shaders. In SIGGRAPH/Eurographics Workshop on Graphics Hardware, 1999.Google Scholar
  20. 20.
    A Miné and F Neyret. Perlin textures in real time using OpenGL. Technical Report RR-3713, iMAGIS-GRAVIR/IMAG/INRIA, 1999.Google Scholar
  21. 21.
    Mark S. Peercy, Marc Olano, John Airey, and P. Jeffrey Ungar. Interactive multi-pass programmable shading. In Computer Graphics (SIGGRAPH 2000 Proceedings), July, 2000.Google Scholar
  22. 22.
    Detlev Stalling, Malte Zöckler, and Hans-Christian Hege. Fast display of illuminated field lines. IEEE Transactions on Visualization and Computer Graphics, 3(2): 118–128, 1997.CrossRefGoogle Scholar
  23. 23.
    Jos Stam. Random caustics: Natural textures and wave theory revisited. In ACM SIGGRAPH Visual Proceedings, page 151, 1996.Google Scholar
  24. 24.
    Jerry Tessendorf. Simulating ocean water. In SIGGRAPH 99 Course Notes, August, 1999.Google Scholar
  25. 25.
    Chris Trendall and James Stewart. An example of hardware mathematics: Refractive caustics., 2000.Google Scholar
  26. 26.
    Mark Watt. Light-water interaction using backward beam tracing. Computer Graphics, 24(4):327–335, 1990.CrossRefGoogle Scholar
  27. 27.
    Mason Woo, Jackie Neider, Tom Davis, and Dave Shreiner. OpenGL Programming Guide. Addison Wesley Longman, Inc., third edition, 1999.Google Scholar

Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • Chris Trendall
    • 1
    • 2
  • A. James Stewart
    • 1
    • 2
  2. 2.University of TorontoCanada

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