“Vectorized procedural models for natural terrain: Waves and islands in the sunset” by Max

  • ©Nelson L. Max




    Vectorized procedural models for natural terrain: Waves and islands in the sunset



    A ray-tracing procedural model is described, in which ocean waves and islands are rendered by different but related algorithms. The algorithms are based on analytic formulas involving arithmetic operations, trigonometric functions, and square roots, and are organized for a vectorizing compiler on a Cray 1, a “supercomputer” with a vector pipeline architecture. Height field methods are used, one vertical scan line at a time, to trace the direct rays to the ocean, where they are reflected. Approximate methods are then applied to find whether the reflected rays meet any other object on their way to the sky. The output, at eight bits per pixel, gives information for shading, e.g. the angle of the surface normal for rays meeting the islands, or the angle of elevation from the horizon for rays continuing unobstructed to the sky. The output is recorded on a magnetic tape for each frame in one cycle of the wave motion, and plotted offline on a Dicomed D-48 color film recorder. The eight bits per pixel are interpreted by a color translation table, which is gradually changed as the wave cycle is repeated to simulate the changing illumination during sunset.


    1. Newell, M. The Utilization of Procedure Models in Digital Image Synthesis. PhD Thesis, University of Utah (1975)
    2. Rubin, S., and Whitted, T., A 3-Dimensional Representation for Fast Rendering of Complex Scenes. Computer Graphics Vol. 14, No. 3 (1980) pp. 110-116
    3. Schachter, B., Long Crested Wave Models. Computer Graphics and Image Processing Vol. 12 (1980) pp. 187-201
    4. Pyramid Catalogue, (1981) Pyramid, Box 1048 Santa Monica, or poster available from Jannes Art Publishing, Chicago
    5. Whitted, T., An Improved Illumination Model for Shaded Display. Comm. ACM Vol. 23, No. 6, (1980) pp. 343-349
    6. Minnaert, M., Light and Color in the Open Air. Dover Publications, Inc. (1954) New York
    7. Shoup, R., Color Table Animation. Computer Graphics Vol. 13, No. 2 (1979) pp. 286-292
    8. Longuet-Higgins, M., The Statistical Analysis of a Random, Moving Surface. Proc. Roy. Soc. of London Vol. 249 (1957) pp. 321-387
    9. Stokes, G.G., Mathematical and Physical Papers. Vol. 1 (1880) p. 341, Cambridge University Press
    10. Schwartz, L., Computer Extension and Analytic Continuation of Stokes’ Expansion of Gravity Waves. J. Fluid Mech. Vol. 62, part 3 (1974) pp. 553-578
    11. Fishman, B., and Schachter, B., Computer Display of Height Fields. Computers and Graphics Vol. 5 (1980) pp. 53-60
    12. Blinn, J., Models of Light Reflection for Computer Synthesized Pictures. Computer Graphics Vol. 11, No. 2 (1977) pp. 192-198
    13. Blinn, J., Simulation of Wrinkled Surfaces. Computer Graphics Vol. 12, No. 3 (1978) pp. 286-292
    14. Cook, R., and Torrance, K., Reflectance Models for Computer Graphics. Vol. 15, No. 13 (1981)

ACM Digital Library Publication: