Curvature continuous blend surfaces

  • Günther Greiner
  • Hans-Peter Seidel
Conference paper
Part of the IFIP Series on Computer Graphics book series (IFIP SER.COMP.)


We describe a method to generate blend surfaces which fit with continuous curvature to the primary surfaces. This blend surface is obtained as the bicubic tensor spline minimizing a variational problem. Among all the bicubic tensor splines which give a curvature continuous blend surface, the one is chosen which minimizes a bilinear functional. In Section 2 we summarize and extend the results of a previous paper in such a way that they are applicable to our problem. In Section 3 we outline in detail the procedure how to generate a blend surface based on these results.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. A. Adams, Sobolev spaces, Academic Press 1975MATHGoogle Scholar
  2. [2]
    M. I. G. Bloor, M. J. Wilson, Generating blend surfaces using partial differential equations. CAD 1989, pp. 165–171Google Scholar
  3. [3]
    R. Courant, D. Hilbert, Methoden der Mathematischen Physik, Springer-Verlag, Berlin Heidelberg 1968.Google Scholar
  4. [4]
    A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York 1969.MATHGoogle Scholar
  5. [5]
    G. Greiner, Blending techniques based on variational principles, to appear Google Scholar
  6. [6]
    C. Hoffmann, J. Hopcroft, The potential method for blending surfaces, in G. Farin (ed.), Geometric modelling: algorithms and new trends, SIAM, Philadelphia 1987, pp. 347–364.Google Scholar
  7. [7]
    H. P. Moreton, C. H. Séquin, Functional Optimization for fair surface design, Siggraph ’92, pp. 167–176Google Scholar
  8. [8]
    H. Pottmann, Scattered data interpolation based upon generalized minimum norm networks, Preprint Nr. 1232, TH Darmstadt, May 1989Google Scholar
  9. [9]
    J. R. Rossignac, A. A. G. Requicha, Constant-radius blending in solid modelling, Compu. Mech. Eng. 3 (1984), pp. 65–73.Google Scholar
  10. [10]
    G. Strang, G. J. Fix, An analysis of the finite element method, Prentic Hall, Englewood Cliffs 1973.MATHGoogle Scholar
  11. [11]
    W. Welch, A. Witkin, Variational surface modeling, Siggraph ’92, pp. 157–166Google Scholar
  12. [12]
    J. R. Woodwark, Blends in geometric modelling, in R. R. Martin (ed.), The mathematics of surfaces II, Oxford University Press, Oxford 1987, pp. 255–297.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Günther Greiner
    • 1
  • Hans-Peter Seidel
    • 1
  1. 1.IMMD IX Graphische DatenverarbeitungUniversität ErlangenErlangenGermany

Personalised recommendations