Shading bicubic patches

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 , David M. Weimer, Fast Phong shading, ACM SIGGRAPH Computer Graphics, v.20 n.4, p.103-106, Aug. 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: S. A. Coons, SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS, Massachusetts Institute of Technology, Cambridge, MA, 1967
• 4: Tom Duff, Smoothly shaded renderings of polyhedral objects on raster displays, ACM SIGGRAPH Computer Graphics, v.13 n.2, p.270-275, August 1979
• 5: Jeffrey M. Lane , Loren C. Carpenter , Turner Whitted , James F. Blinn, Scan line methods for displaying parametrically defined surfaces, Communications of the ACM, v.23 n.1, p.23-34, Jan. 1980 [doi>10.1145/358808.358815]
• 6: Sheue-Ling Lien , Michael Shantz , Vaughan Pratt, Adaptive forward differencing for rendering curves and surfaces, ACM SIGGRAPH Computer Graphics, v.21 n.4, p.111-118, July 1987
• 7: Bui Tuong Phong, Illumination f o r Computer- Generated Images, UTEC-CSc-73-129, July 1973.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.3 Picture/Image Generation
          Subjects: Display algorithms

Additional Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.1 Types and Design Styles
          Subjects: VLSI (very large scale integration)

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Color, shading, shadowing, and texture

General Terms:
Algorithms, Design