Abstract
The interactive design of parametric curves and surfaces places a tremendous computational burden on general-purpose workstations. We describe two architectures for a VLSI co-processor chip that generates a large class of spline descriptions extremely quickly. This architecture is based on a generalization of the de Casteljau algorithm for Bézier curves and the de Boor algorithm forB-splines that generates points on a curve or surface in a data-flow fashion. The first chip, Apex I, maps the data-flow structure directly into silicon, allowing it to generate curves and surfaces at a rate approaching two million points per second. The second chip, Apex II, performs the same computation in a more flexible way that allows the generation of higher degree curves at the cost of lower performance. This paper only briefly reviews the theory underlying the architecture, focusing instead on the design and implementation of the Apex chips.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Annaratone M (1986) Digital CMOS circuit design. Kluwer Academic Publ., Norwell, Massachusetts
Barry PJ (1987) Urn models, recursive schemes, and computer aided geometric design. PhD Thesis, Dept Mathem, Univ Utah, Salt Lake City, Utah (June 1987)
Bartels HR, Beatty JC, Barsky BA (1987) An introduction to splines for use in computer graphics and geometric modeling. Morgan-Kaufman Publ, Los Altos, California
Cheng F, Hsieh K-R, Huang R-R, Chin Y-H (1985) Bézier curve generator: a hardware approach to curve generation. Proc 2nd Int Symp VLSI Technol Syst Appl (May 1985) Taipei, Taiwan, pp 278–281
Cohen M, Littlefield R, Mann S, Sloan K (1988) 3D I/O. Tech Rep No 88-06-01, Dept Comput Sci FR-35 Univ Washington Seattle, WA (June 1988)
DeRose TD, Holman TJ (1987) The triangle: a multiprocessor architecture for fast curve and surface generation. Tech Rep No 87-08-07, Dept Comput Sci, Univ Washington, FR-35, Seattle, WA 98195 (August 1987)
DeRose TD, Holman TJ (1989) A comparison of multiprocessor architectures for curve and surface generation (submitted)
Farin G (1988) Curves and surfaces for computer aided geometric design: a practical guide. Academic Press
Goldman RN (1983) An urnful of blending functions. IEEE Comput Graph Appl 3 (7):49–54
Langridge R, Ferrin T, Kuntz I, Connolly M (1981) Real-time color graphics in studies of molecular interactions. Science 211 (4483):61
Lien S-L, Shantz M, Pratt V (1987) Adaptive forward differencing for rendering curves and surfaces. Comput Graph 21 (4):111–118
Max NL (1983) Computer representation of molecular surfaces. IEEE Comput Graph Appl 3 (5):21–29
Northwest Laboratory for Integrated Systems (1987) VLSI design tools reference manual, release 3.1. Dept Comput Sci, Univ Washington, Seattle, Washington (February 1987)
Scott WS, Mayo RN, Hamachi G, Ousterhout JK (eds) (1986) VLSI tools. EECS Dept, Univ California at Berkeley, Berkeley, California