Gn−1 — Functional Splines for Modeling

  • Josef Hoschek
  • Erich Hartmann
Conference paper
Part of the Computer Graphics — Systems and Applications book series (COMPUTER GRAPH.)


Implicit curves and surfaces are used for interpolation, approximation, blending of curves, surfaces and solids and filling of surface holes. The introduced curves and surfaces can be interpreted as functional splines, which fulfil geometric continuity conditions.


Base Surface Intersection Curve Implicit Surface Base Curve Transversal Surface 
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.
    Cohen, S.: Beitrag zur steuerbaren Interpolation von Kurven und Flächen. Dissertation TU Dresden 1982.Google Scholar
  2. 2.
    De Rose, T.D., Loop, Ch.T.: S-patches: A Class of Representations for Multi-Sided Surface Patches. Technical Report 88-05-02 University of Washington, 1988.Google Scholar
  3. 3.
    Do Carmo, M. P.: Differential Geometry of Curves and Surfaces. Prentice Hall 1976.Google Scholar
  4. 4.
    Favard, J.: Cours de Géométrie différentielle locale. Gauthier 1957.Google Scholar
  5. 5.
    Gregory, J.A., Hahn, J.M.: Geometric continuity and convex combination patches. Computer Aided Geometric Design 4, 79–89 (1987).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Garrity, Th, Warren, J.: Geometric Continuity. Computer Aided Geometric-Design 1990.Google Scholar
  7. 7.
    Hahn, J.M.: Filling Polygonial Holes with Rectangular Patches. in Strasser, W.(ed.): Theory and Practice of Geometric Modeling, Springer 1989.Google Scholar
  8. 8.
    Hartmann, E.: Computerunterstützte Darstellende Geometrie. Teubner 1988.Google Scholar
  9. 9.
    Hartmann, E., Li, J.: Smoothing of Corners with Functional Splines. Preprint Fachbereich Mathematik, Technische Hochschule Darmstadt (1989).Google Scholar
  10. 10.
    Hartmann, E.: Blending of’ Implicit Surfaces with Functional Splines. Submitted to Computer-aided design 1990.Google Scholar
  11. 11.
    Hoffmann, Ch., Hoperoft, J.: Automatic surface generation in Computer-aided design. Visual Computer 1, 92–100 (1985).MATHCrossRefGoogle Scholar
  12. 12.
    Hoffmann, Ch., Hoperoft, J.: The Potential Method for Blending Surfaces and Corners. In: Farin, G. E. (ed): Geometric Modeling: Algorithms and new Trends, 347–366, SIAM 1987.Google Scholar
  13. 13.
    Hohenberg, F.: Konstruktive Geometrie in der Technik. Springer 1966.Google Scholar
  14. 14.
    Holmström, I.: Piecewise quadric blending of implicitly defined surfaces. Computer Aided Geometric Design 4, 171–190 (1987).MathSciNetCrossRefGoogle Scholar
  15. 15.
    Hoschek, J.; Hartmann, E.; Li, J.; Feng, Y.Y.: Gn-1-Functional Splines for Interpolation and Approximation of Surfaces and Solids. International Series in Numerical Mathematics, Birkhäuser 1990.Google Scholar
  16. 16.
    Hoschek, J. - Lasser, D: Grundlagen der geometrischen Datenverarbeitung. Teubner 1989.Google Scholar
  17. 17.
    Li, J.; Hoschek, J.; Hartmann, E.: Gn-1 functional splines for interpolation and approximation of curves and surfaces and solids. Computer Aided Geometric Design 1990.Google Scholar
  18. 18.
    Liming, R.A.: Practical Analytical Geometry with Applications to Aircraft. Macmillan 1944.Google Scholar
  19. 19.
    Pratt, V.: Direct Least-Squares Fitting of Algebraic Surfaces. Computer Graphics 21, 145–151 (1987).MathSciNetCrossRefGoogle Scholar
  20. 20.
    Ricci, A.: A constructive geometry for computer graphics. Computer Journal 16, 157–160 (1973).MATHCrossRefGoogle Scholar
  21. 21.
    Sabin, M.A.: Non-rectangular patches suitable for inclusion in a B-Spline surface. In: ten Hagen (ed.): Proceeding Eurographics, North-Holland 1983, 57–69.Google Scholar
  22. 22.
    Scheffers, G.: Anwendungen der Differential-und Integralrechnung auf Geometrie. Vol. I, Springer 1922.Google Scholar
  23. 23.
    Scheffers, G.: Anwendungen der Differential-und Integralrechnung auf Geometrie. Vol. II, 3. ed., Springer 1922.Google Scholar
  24. 24.
    Woodwark, J. R.: Blends in Geometric Modelling. In: Martin, R. R. (ed.):The mathematics of surfaces II, 255–297. Clarendon Press 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Josef Hoschek
    • 1
  • Erich Hartmann
    • 1
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtGermany

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