“Rendering parametric surfaces in pen and ink” by Winkenbach and Salesin

  • ©Georges Winkenbach and David H. Salesin




    Rendering parametric surfaces in pen and ink



    This paper presents new algorithms and techniques for rendering parametric free-form surfaces in pen and ink. In particular, we introduce the idea of “controlled-density hatching” for conveying tone, texture, and shape. The fine control over tone this method provides allows the use of traditional texture mapping techniques for specifying the tone of pen-and-ink illustrations. We also show how a planar map, a data structure central to our rendering algorithm, can be constructed from parametric surfaces, and used for clipping strokes and generating outlines. Finally, we show how curved shadows can be cast onto curved objects for this style of illustration.


    1. Norman Chin and Steven Feiner. Near real-time shadow generation using BSP trees. Computer Graphics, 23(3):99-106, 1989.
    2. Manfredo E do Carmo. Differential Geometry of Curves and Surfaces. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.
    3. Debra Dooley and Michael F. Cohen. Automatic illustration of 3D geometric models: Lines. Computer Graphics, 24(2):77-82, March 1990.
    4. Debra Dooley and Michael F. Cohen. Automatic illustration of 3D geometric models: Surfaces. In Proceedings of Visualization ’90, pages 307-314, October 1990.
    5. Gershon Elber. Line art rendering via a coverage of isoparametric curves. IEEE Transaction on Visualization and Computer Graphics, 1(3):231-239, September 1995.
    6. Gershon Elber and Elaine Cohen. Hidden curve removal for free form surfaces. Computer Graphics, 24(4):95-104, August 1990.
    7. H. Fuchs, Z. M. Kedem, and B. F. Naylor. On visible surface generation by a priori tree structures. Computer Graphics, 14(3):124-133, July 1980.
    8. Michel Gangnet, Jean-Claude Herv6, Thierry Pudet, and Jean-Manuel Van Thong. Incremental computation of planar maps. Computer Graphics, 23(3):345-354, July 1989.
    9. Arthur Leighton Guptill. Rendering in Pen and Ink. Watson-Guptill Publications, New York, 1976.
    10. Christoph Hoffman. The problems of accuracy and robustness in geometric computation. Computer, 22:31-42, 1989.
    11. John Lansdown and Simon Schofield. Expressive rendering: A review of nonphotorealistic techniques. IEEE Computer Graphics and Applications, 15(3):29-37, May 1995.
    12. Wolfgang Leister. Computer generated copper plates. Computer Graphics Forum, 13(1):69-77, 1994.
    13. Frank Lohan. Pen and Ink Techniques. Contemporary Books, Inc., Chicago, 1978.
    14. J6r6me Maillot, Hussein Yahia, and Anne Verrout. Interactive texture mapping. Proceedings of SIGGRAPH 93 (Anaheim, California, August 1-6, 1993). In Computer Graphics, Annual Conference Series, 1993.
    15. Bruce Naylor and Lois Rogers. Constructing partitioning trees from B6zier-curves for efficient intersection and visibility. In Proceedings of Graphics Interface ’95, pages 44-55, 1995.
    16. Hans Kohling Pedersen. Decorating implicit surfaces. Proceedings of SIGGRAPH 95 (Los Angeles, California, July 6-11, 1995). In Computer Graphics, Annual Conference Series, 1995.
    17. Tom Porter and Sue Goodman. Manual of Graphic Techniques 4. Charles Scribner’s Sons, New York, 1985.
    18. Takafumi Saito and Tokiichiro Takahashi. Comprehensible rendering of 3D shapes. Computer Graphics, 24(4): 197-206, August 1990.
    19. David H. Salesin. Epsilon Geometry: Building Robust Algorithms from Imprecise Computations. PhD thesis, Stanford University, March 1991. Available as Stanford Report number STAN-CS-91-1398.
    20. Lance Williams. Casting curved shadows on curved surfaces. Computer Graphics, 12(3):270-274, August 1978.
    21. Georges Winkenbach. Computer-Generated Pen-and-Ink Illustration. PhD thesis, University of Washington, May 1996.
    22. Georges Winkenbach and David H. Salesin. Computer-generated penand-ink illustration. Proceedings of SIGGRAPH 94 (Orlando, Florida, July 24-29, 1994). In Computer Graphics, Annual Conference Series, 1994.

ACM Digital Library Publication:

Overview Page: