“Shading bicubic patches” by Shantz and Lien

  • ©Michael Shantz and Sheue-Ling Lien

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Title:

    Shading bicubic patches

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Abstract:


    We present several techniques for implementing Phong shading in hardware for bicubic patches. Patches are shaded, not by subdividing into polygons, but by drawing many curves close together leaving no pixel gaps. Each curve is drawn using an adaptive forward difference algorithm which generates the coordinates as well as the shading parameters as cubic functions incrementally evaluated along the curve. The forward difference step size is adaptively adjusted so that it generates approximately one pixel along the curve per forward difference step. The hardware implements Phong shading directly with a surprisingly simple configuration built from general purpose compute units and look-up tables. Two new methods are presented for deriving bicubic approximations to the shading parameters over a bicubic patch. One method uses two Coons patches to approximate the unnormalized N·L, and N·H, and a third Coons patch for N·N, where N is the surface normal, L is the light direction, and H is the direction of maximum highlight. In this case the hardware performs the normalization per pixel. The second method uses two Coons patches to approximate the normalized dot products N·L, and N·H. The method is suitable for both hardware and software implementations.

References:


    1. Gary Bishop and David M. Weimer, “Fast Phong Shading,” Computer Graphics, vol. 20, no. 4, pp. 103 – 106, August 1986.
    2. Edwin Catmull, A Subdivision Algorithm f o r Computer Display o f Curved Surfaces, Computer Science, University of Utah, UTEC-CSc-74-133, December 1974.
    3. Steven A. Coons, Surfaces f o r Computer-Aided Design o f Space Forms, Project MAC, Massachusetts Institute of Technology, MAC-TR-41, June 1967.
    4. Tom Duff, “Smoothly Shaded Renderings of Polyhedral Objects on Raster Displays,” Computer Graphics, vol. 13, no. 2, August 1979.
    5. Jeffrey Lane, Loren Carpenter, Turner Whitted, and James Blinn, “Scan Line Methods for Displaying Parametrically Defined Surfaces,” CACM, vol. 23, no. 1, January 1980.
    6. Sheue-Ling Lien, Michael Shantz, and Vaughan Pratt, “Adaptive Forward Differencing for Rendering Curves and Surfaces,” Computer Graphics, vol. 21, no. 4, July 1987.
    7. Bui Tuong Phong, Illumination f o r Computer- Generated Images, UTEC-CSc-73-129, July 1973.


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