“Ray tracing with cones” by Amanatides

  • ©John Amanatides




    Ray tracing with cones



    A new approach to ray tracing is introduced. The definition of a “ray” is extended into a cone by including information on the spread angle and the virtual origin. The advantages of this approach, which tries to model light propagation with more fidelity, include a better method of anti-aliasing, a way of calculating fuzzy shadows and dull reflections, a method of calculating the correct level of detail in a procedural model and texture map, and finally, a procedure for faster intersection calculation.


    1. Amanatides, J., and Fournier, A., “Ray Casting using Divide and Conquer in Screen Space”, Proc. Intl. Conf. of Engineering and Computer Graphics, Beijing, China, Aug. 27 – Sept. 1 1984.
    2. Blinn, J.F., and Newell, M.E., “Texture and Reflection in Computer Generated Images”, Comm. ACM, Vol. 19(10), October 1976, pp. 542-547.
    3. Clark, J.H., “Hierarchical Geometric Models for Visible Surface Algorithms”, Comm. ACM, VoL 19(10), October 1976, pp.547-554.
    4. Crow, F.C., “Shadow Algorithms for Computer Graphics”, Computer Graphics, Vol. 11(3), July 1977, pp. 242-248.
    5. Crow. F.C., “The Aliasing Problem in Computer-Generated Shaded Images”, Comm. ACM, Vol. 20(11), November 1977, pp. 799-805.
    6. Crow, F.C., “A Comparison of Antialiasing Techniques”, IEEE Computer Graphics and Applications, Vol. 1(1), January 1981, pp. 40-48.
    7. Flume, E., Fournier, A., and Rudolph, L., “A Parallel Scan Conversion Algorithm with Anti-Aliasing for a General Purpose Ultracomputer”, Computer Graphics, Vol. 17(3), July 1983, pp. 141-150.
    8. Fournier, A., Fussell, D., and Carpenter, L., “Computer Rendering of Stochastic Models”, Comm. ACM, Vol. 25(6), June 1982, pp. 371-384.
    9. Goldstein, R.A., and Nagel, R., “3-D Visual Simulation”, Simulation, January 1971, pp. 25-31.
    10. Hall, R.A., and Greenberg, D.P., “A Testbed for Realistic Image Synthesis”, IEEE Computer Graphics and Applications, Vol. 3(8), November 1983, pp. 10-20.
    11. Hanrahan, P., “Ray Tracing Algebraic Surfaces”, Computer Graphics, Vol. 17(3), July 1983, pp.83-90.
    12. Hect, E., and Zajac, A., OPTICS, Addison Wesley Publishing Company, Reading Massachusetts, 1974.
    13. Kajiya, J.T., “New Techniques For Ray Tracing Procedurally Defined Objects”, Computer Graphics, Vol. 17(3), July 1983, pp. 91-102.
    14. Rubin, S.M., and Whitted, T., “A 3-Dimensional Representation for Fast Rendering of Complex Scenes”, Computer Graphics, Vol. 14(3), July 1980, pp. 110-116.
    15. Roth, S.D., “Ray Casting for Modeling Solids”, Computer Graphics and Image Processing, Vol. 18, 1982, pp. 109-144.
    16. Warnock, J., A Hidden-Surface Algorithm for Computer Generated Half-Tone Pictures, Univ. Utah Computer Sci. Dept., TR 4-15, 1969, NTIS AD-733 671.
    17. Whitted, T., “An Improved Illumination Model for Shaded Display”, Comm. ACM, Vol. 23(6), June 1980, pp. 343-349.
    18. Williams, L., “Pyramidal Parametrics”, Computer Graphics, Vol. 17(3), July 1983, pp. 1-11.

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