Surfaces In An Object-Oriented Geometric Framework

  • Reinhard Klein
Conference paper

Abstract

To use the advantages of different surface representations, such as tensor-product surfaces, surfaces over triangular regions, implicitly defined surfaces, etc., it is necessary to integrate these surface types with a large variety of algorithms into one programming environment. Inheritance and polymorphism of object-oriented languages offer the opportunity to realize an implementation, which is not bound to a certain representation of the surface. The most reasonable way to benefit from such an object-oriented approach is to use existing algorithms and if necessary to develop new algorithms that are based on the functionality provided by as many surface representations as possible. An object-oriented design for surfaces is presented and the advantages of such a design are illustrated by examples.

Keywords

Encapsulation Reso 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Gershon Elber an Elaine Cohen. Hybrid symbolic and numeric operators as tool for analysis offreeform surfaces. In B. Falcidieno, T.L. Kunii, editors, Modeling in Computer Graphics, pages 275–288. Springer-Verlag, 1993.Google Scholar
  2. [2]
    J. Beck, R. Farouki, J. Hinds. Surface analysis methods. IEEE Computer Graphics and Applications, 6 (12): 18–36, 1986.CrossRefGoogle Scholar
  3. [3]
    M. P. do Carmo. Differentialgeometrie von Kurven und Flächen. Vieweg, Braunschweig/Wiesbaden, 1976.Google Scholar
  4. [4]
    Gershon Elber and Elaine Cohen. Hidden curve removal for free form surfaces. In Forest Baskett, editor, Computer Graphics (SIGGRAPH’90 Proceedings), volume 24, pages 95–104, August 1990.Google Scholar
  5. [5]
    Gershon Elber, Elaine Cohen. Second-order surface analysis using hybrid symbolic and numeric operators. ACM Transactions on Graphics, 12 (2): 160–178, 1993.CrossRefMATHGoogle Scholar
  6. [6]
    Gerald Farin. Curves and Surfaces for Computer Aided Geometric Design. Academic Press, 1990.Google Scholar
  7. [7]
    R. Farouki. Graphical methods för surface differential geometry. In R. Martin, editor, The Mathematics of Surfaces II, pages 363–386. Oxford University Press, 1987.Google Scholar
  8. [8]
    R.T. Farouki. Concise piecewise-linear approximation of algebraic curves. IBM Research Division, 1988.Google Scholar
  9. [9]
    D. Filip, R. Magedson, R. Markot. Surface algorithms using bounds on derivatives. Computer Aided Geometric Design, 3 (4): 295–311, 1986.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    Thomas A. Foley, David A. Lane, Gregory M. Nielson, Ramamani Ramaraj. Visualizing functions over a sphere. IEEE Computer Graphics and Applications, 10 (1): 32–40, January 1990.CrossRefGoogle Scholar
  11. [11]
    A. Forrest. Interactive interpolation and approximation by bezier polynomials. Computer Journal, 15: 71–79, 1972.MathSciNetMATHGoogle Scholar
  12. [12]
    G. Greiner, R. Klein, P. Slusallek. Design of blending-surfaces in an object-oriented framework. In P.-J. Laurent, A. Le Méhauté, editors, Curves and Surfaces. Academic Press, 1993.Google Scholar
  13. [13]
    T. Hermann. Rolling ball blends, self-intersection. In J. Warren, editor, Curves and Surfaces in Computer Vision and Graphics III, chapter 4, pages 204–211. SPIE - The Invernational Society for Optical Engineering, Nov. 1992.Google Scholar
  14. [14]
    R. Klass. Correction of local surface irregularities using refiection lines. Comput. Aided Des., 12: 73–77, March 1980.CrossRefGoogle Scholar
  15. [15]
    R. Klass, B. Kuhn. Fillet and surface intersections defined by rolling balls. Computer Aided Geometric Design, 9 (3): 185–193, August 1992.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    R. Klein, J. Krämer. Delaunay triangulations of planar domains. Technical report, Wilhelm-Schickard-Institut, Graphisch Interaktive Systeme, Universität Tübingen, 1993.Google Scholar
  17. [17]
    R. Klein, P. Slusallek. Object-oriented framework for curves and surfaces. In J.D. Warren, editor, Curves and Surfaces in Computer Vision and Graphics III, pages 284–295. SPIE, november 1992.Google Scholar
  18. [18]
    D. T. Lee, A. K. Lin. Generalized Delaunay triangulations for planar graphs. Discrete Comput. Geom., 1: 201–217, 1986.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    S.B. Lippman. C+ + Primer. Addison Wesley, 2 edition, 1991.Google Scholar
  20. [20]
    H. Pottmann, H. Hagen, A. Divivier. Visualizing functions on a surface. J. Visualization and Animation, 2 (2): 52–58, Apr./June 1991.Google Scholar
  21. [21]
    A. Rockwood, J. Owen. Blending surfaces in solid modeling. In G. Farin, editor, Geometric Modeling: Algorithms and New Trends, pages 367–383. SIAM, Philadelphia, 1987.Google Scholar
  22. [22]
    X. Sheng, B. E. Hirsch. Triangulation of trimmed surfaces in parametric space. Computer Aided Design, 24 (8): 437–444, August 1992.CrossRefMATHGoogle Scholar
  23. [23]
    B. Stroustrup. The C++ Programming Language. Addison Wesley, 2 edition, 1991.Google Scholar
  24. [24]
    T. Varady, J. Vida, R. Martin. Parametric blending in a boundary representation solid modeller. In D. C. Handscomb, editor, The Mathematics of Surfaces III, pages 171–198. Clarendon Press, 1989.Google Scholar
  25. [25]
    J. Woodwark. Blends in geometric modelling. In R. Martin, editor, The Mathematics of Surfaces II, pages 255–298. Oxford University Press, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Reinhard Klein
    • 1
  1. 1.Wilhelm-Schickard-Institut für Informatik, Graphisch-Interaktive-Systeme (WSI/GRIS)Universität TübingenTübingenGermany

Personalised recommendations