“Real-time rendering of trimmed surfaces” by Rockwood, Heaton and Davis

  • ©Alyn P. Rockwood, Kurt Heaton, and Tom Davis




    Real-time rendering of trimmed surfaces



    Rational tensor product surfaces, (Bézier, NURBS, Hermite, polynomial, etc.) are rendered in real-time by uniform faceting. The described methods are modular and can be balanced for optimal implementation on different hardware platforms. Discretization anomalies such as angularities, Mach banding, cracking etc. are avoided by tessellating the surface patches and segmenting the trimming curves based on the view.


    1. Akeley, K. and Jermoluk, T. High-Performance Polygon Rendering. Proceedings of S IGG RAPH ’88 (A tl anta, August 1-5, 1988). In Computer Graphics 22, 4 (August 1988), 239-240.
    2. Apgar, B., Bersack, B, and Mammen, A. A Display System for the Stellar Graphics Supercomputer Model GS1000. Proceedings of SIGGRAPH’88 (Atlanta, August 1-5, 1988). In Computer Graphics 22, 4 (August 1988), 255-262.
    3. Boehm, W., Farin, G.E. and Kahmann, J. A Survey of Curve and Surface Methods in CAGD. In Computer Aidid Geometric Design 1 (1984) 1-60.
    4. Catmull,E. ASubdivisionAlgorithmforComputerDisplay of Curved Surfaces, doctoral dissertation, Univ. of Utah, Salt Lake City (1974).
    5. Clark, J.H. A Fast Algorithm for Rendering Parametric Surfaces. Supplement, proceedings of SIGGRAPH’79. In Computer Graphics 13, 2 (L979), 289-299.
    6. Deering, M, et, al. The Triangle Processor and Normal Vector Shader: A VLSI System for High Performance Graphics. Proceedings of SIGGRAPH’88 (Atlanta, August -5, 1988). In Computer Graphics 22,4 (August 1988), 21- 30.
    7. DeRose, A.D. and Holman, T.j. The Triangle: A Multiprocessor Architecture for Fast Curve and Surface Generation. In TR 87-08-07 University of Washington, Seattle, WA (August 1987).
    8. Farouki, R. Concise Piecewise-Linear Approximation. Internal IBM Research Document, Yorktown Heights, NY.
    9. Farin, G.E. Curves and Surfaces for Computer Aided Design. Academic Press, Inc., Boston (1988).
    10. Foley, J. and Van Dam, A. Fundamentals of Interactive Computer Graphics. Addison-Wesley Publishers, 1982.
    11. Forrest, A.R. On the Rendering of Surfaces. In Computer Graphics 13, 2 (August 1979), 253-259.
    12. Garey, M., Johnson, D.S., Preparata, F. P. and Tarjan, R. E. Triangulating a Simple Polygon. lnlnfo.Proc.Lett. 7,4, (1978), 175-180.
    13. Gharachorloo, N. et. aI. Subnanosecond Pixel Rendering with Million Transistor Chips. Proceedings of SIGGRAPH’86 (Atlanta, August 1-5, 1986). In Computer Graphics 22, 4 (August 1988), 41-49,
    14. Kajiya, J.T. Ray Tracing Parametric Patches. Proceedings of SIGGRAPH’82. In Computer Graphics 16, 3 (1982), 245-254.
    15. Lane, J.M., et, al. Scan Line Methods for Displaying Parametrically Defined Surfaces. Comm. In ACM 23, 1 (1980) 23-34.
    16. Lane, J. and Riesenfeld, R.F. Bounds On Polynomials. In BIT21 (1981) 112-117.
    17. Rockwood, A.P. A Generalized Scanning Technique for Display of Parametrically Defined Surfaces. In IEEE Computer Graphics and its Applications 7, 8 (August t 987), 15-26.
    18. Sederberg, T. Private communication (1988).
    19. Sederberg, T. and Wang, X. Rational Hodographs. In CAGD 4 (1987), 333-335.
    20. Shantz, M. and Chang, S. Renderiag Trimmed NURBS with Adaptive Forward Differencing. Proceedings of SIGGRAPH’88 (Atlanta, August I-5, 1988). In Computer Graphics 22, 4 (August 1988), 189-198.
    21. Shantz, M, and Lien, S. Shading B icubic Patche’s. Proceedings of SIGGRAPH’87 (Anaheim, July 27-31, 1987). In Computer Graphics 21,4 (July 1987), 189-196.
    22. Sweeney, A.J. and Barrels, R.H. Ray Tracing Free-Form B-Spline Surfaces. In IEEE Computer Graphics and its Applications 6, 2 (February 1986) 41-49.

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