Object Oriented Surface Design

  • Richard Bartels


This chapter will review some work done at the Computer Graphics Laboratory of the University of Waterloo to build software abstractions with which ideas for new techniques in spline surface design can be supported. Our goal has been to facilitate the construction of prototype surface editors through the use of these abstractions. These editors are concerned with the definition of surfaces for industrial and artistic purposes.

The work built upon the most fundamental of mathematical abstractions: affine geometry; involving one of the commonest definitions of manifolds: parametric splines. Graph and tree abstractions that are linked to geometry are employed to organize the parts of the models that are edited.


Affine Transformation Affine Space Subdivision Surface Spline Surface Control Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Richard Bartels. Object oriented spline software. In P-J. Laurent, A. Le Mé hauté, and L. L. Schumaker, editors, Curves and Surfaces in Geometric Design, pages 27–34. A K Peters, Ltd., 289 Linden Street, Wellesley, MA 02181 USA, June 1994.Google Scholar
  2. [2]
    Cristin Barghiel, Richard Bartels, and David Forsey. Pasting spline surfaces. In T. Lyche and L. L. Schumaker, editors, Mathematical Methods in Computer Aided Geometric Design III, pages 31–40. Vanderbilt University Press, Nashville, Tenn. 37235 USA, 1995.Google Scholar
  3. [3]
    Gerald E. Farin. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press, San Diego, California, third edition, 1993.Google Scholar
  4. [4]
    David R. Forsey and Richard H. Bartels. Hierarchical B-spline refinement. Computer Graphics, 22(4):205–212, August 1988. SIGGRAPH ‘88 conference proceedings.CrossRefGoogle Scholar
  5. [5]
    Günther Greiner, Andreas Kolb, Ronald Pfeifle, Hans-Peter Seidel, Philipp Slusallek, Miguel Encarnação, and Reinhard Klein. A platform for visualizing curves and surfaces. Computer Aided Design (CAD), 27(7):559–566, July 1995.MATHCrossRefGoogle Scholar
  6. [6]
    Ronald N. Goldman. Illicit expressions in vector algebra. ACM Transactions on Graphics, 4(3):223–243, July 1985.CrossRefGoogle Scholar
  7. [7]
    Alexei Kostrikin and Yu Manin. Linear Algebra and Geometry. Gordon and Breach Science Publishers, PO Box 786, Cooper Station, New York, NY 10276 USA, 1989.MATHGoogle Scholar
  8. [8]
    Reinhard Klein and Philipp Slusallek. An object-oriented framework for curves and surfaces. In J. Warren, editor, Curves and Surfaces in Computer Vision and Graphics III (Proceedings SPIE 1830), pages 284–295. SPIE, 1992.Google Scholar
  9. [9]
    Wayne Liu and Stephen Mann. Programming support for blossoming. In Proceedings of Graphics Interface ‘86, pages 95–106. Morgan Kaufmann Publishers, 340 Pine Street, San Francisco, CA 94104 USA, May 1996.Google Scholar
  10. [10]
    D. R. Musser and A. Saini. STL Tutorial and Reference Guide. Addison-Wesley Publishing Company, One Jacob Way, Reading, Mass. 01867 USA, 1996.Google Scholar
  11. [11]
    Haroon Sheikh and Richard Bartels. Towards a generic editor for subdivision surfaces. In A. Pasko, editor, Shape Modeling International ‘87. IEEE Computer Society Press, 10662 Los Vaqueros Circle, Los Alamitos, CA 90720 USA, March 1997. to appear.Google Scholar
  12. [12]
    Larry L. Schumaker. Spline Functions: Basic Theory. John Wiley & Sons, New York, New York, 1981.MATHGoogle Scholar
  13. [13]
    Philipp Slusallek, Reinhard Klein, and Hans-Peter Seidel. An objectoriented framework for curves and surfaces with applications. In Pierre-Jean Laurent, Alain Le Méhauté, and Larry L. Schumaker, editors, Curves and Surfaces in Geometric Design,pages 457–466. A K Peters, 289 Linden Street, Wellesley, MA 02181 USA, 1994.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Richard Bartels
    • 1
  1. 1.Computer Science Department, Computer Graphics LaboratoryUniversity of WaterlooOntarioCanada

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