Skip to main content
SpringerLink
Log in
Book cover

Geometric Modelling pp 135–152Cite as

Shape Improvement of Surfaces

  • Conference paper

Part of the book series: Computing Supplement ((COMPUTING,volume 13))

Abstract

An automatic and local fairing algorithm for bicubic B-spline surfaces is proposed. A local fairness criterion selects the knot, where the spline surface has to be faired. A fairing step is then applied, which locally modifies the control net by a constrained least-squares approximation. It consists of increasing locally the smoothness of the surface from C 2 to C 3. Some extensions of this method are also presented, which show how to build further methods by the same basic fairing principle.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beier, K.-P.: Highlight-line algorithm for real-time surface quality assessment. Comput. Aided Des. 26, 268–277(1994).

    Article  MATH  Google Scholar 

  2. Böhm, W.: Inserting new knots into B-spline curves. Comput. Aided Des. 12, 199–201 (1980).

    Article  Google Scholar 

  3. Bonneau, G.-P., Hagen, H.: Variational design of rational Bézier curves and surfaces. In: Curves and surfaces in geometric design (Laurent, P.-J., Le Méhauté, A., Schumaker, L. L., eds.), pp. 51–58. Wellesley: A. K. Peters, 1994.

    Google Scholar 

  4. Brunet, P.: Increasing the smoothness of bicubic spline surfaces. Comput. Aided Geom. Des. 2, 157–164(1985).

    Article  MathSciNet  MATH  Google Scholar 

  5. De Boor, C.: A practical guide to splines. New York: Springer 1978.

    Book  MATH  Google Scholar 

  6. Eck, M., Hadenfeld, J.: Knot removal for B-spline curves. Comput. Aided Geom. Des. 12, 259–282(1995).

    Article  MathSciNet  MATH  Google Scholar 

  7. Farin, G., Rein, G., Sapidis, N., Worsey, A. J.: Fairing cubic B-spline curves. Comput. Aided Geom. Des. 4, 91–103 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  8. Ferguson, D. R., Frank, P. D., Jones, K.: Surface shape control using constrained optimization on the B-spline representation. Comput. Aided Geom. Des. 5, 87–103 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  9. Greiner, G.: Variational design and fairing of spline surfaces. Proc. Eurographics 1994, 143–154.

    Google Scholar 

  10. Hadenfeld, J.: Local energy fairing of B-spline surfaces. In: Mathematical methods for curves and surfaces (Dæhlen, M., Lyche, T., Schumaker L. L., eds.). Nashville & London: Vanderbilt University Press, 1995.

    Google Scholar 

  11. Hagen, H.: Geometric spline curves. Comput. Aided Geom. Des. 2, 223–227 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  12. Hagen, H., Schulze, G.: Automatic smoothing with geometric surface patches. Comput. Aided Geom. Des. 4, 231–235 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  13. Hagen, H., Santarelli, P.: Variational design of smooth B-spline surfaces. In: Topics in surface modeling (Hagen, H. ed.), pp. 85–92. Philadelphia: SIAM, 1992.

    Google Scholar 

  14. Hahmann, S.: Visualization techniques for surface analysis. In: Data visualization techniques (Bajaj, C. ed.), 1998.

    Google Scholar 

  15. Hahmann, S., Konz, S.: Knot-removal surface fairing using search strategies. CAD 30(20), pp. 131–138(1998).

    Google Scholar 

  16. Hoschek, J., Lasser, D.: Fundamentals of CAGD. Wellesley: A. K. Peters, 1993.

    Google Scholar 

  17. Kjellander, J. A.: Smoothing of cubic parametric splines. Comput. Aided Des. 15, 175–179 (1983).

    Article  Google Scholar 

  18. Kjellander, J. A.: Smoothing of bicubic parametric surfaces. Comput. Aided Des. 15, 289–293 (1983).

    Google Scholar 

  19. Klass, R.: Correction of local irregularities using reflection lines. Comput. Aided Des. 12, 73–77 (1980).

    Article  Google Scholar 

  20. Lott, N. J., Pullin, D. I.: Method for fairing B-spline surfaces. Comput. Aided Des. 20, 597–604 (1988).

    Article  MATH  Google Scholar 

  21. Lyche, T., Morken, K.: Knot removal for parametric B-spline curves and surfaces. Comput. Aided Geom. Des. 4, 217–230 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  22. Mehlum, E.: Nonlinear spline. In: Computer aided geometric design (Barnhill, R., Riesenfeld, R., eds.), pp. 173–208. New York: Academic Press, 1974.

    Google Scholar 

  23. Moreton, H. P., Séquin, C. H.: Functional optimization for fair surface design. Comp. Graph. 26, 167–176(1992).

    Article  Google Scholar 

  24. Nielson, G. M.: Some piecewise polynomial alternatives to splunes under tension. In: Computer aided geometric design (Barnhill, R., Riesenfeld, R., eds.), pp. 209–235. New York: Academic Press, 1974.

    Google Scholar 

  25. Nowacki H., Reese, D.: Design and fairing ship surfaces. In: Surfaces in CAGD (Barnhill R., Böhm, W., eds.), pp. 121–134, Amsterdam: North-Holland, 1983.

    Google Scholar 

  26. Poeschl, T.: Detecting surface irregularities using isophotes. Comput. Aided Geom. Des. 1, 163–168 (1984).

    Article  MATH  Google Scholar 

  27. Rando, T., Roulier, J. A.: Designing faired parametric surfaces. Comput. Aided Des. 23, 492–497(1991).

    Article  MATH  Google Scholar 

  28. Sapidis, N., Farin, G.: Automatic fairing algorithm for B-spline curves. Comput. Aided Des. 22 121–129(1990).

    Article  MATH  Google Scholar 

  29. Schumaker, L. L.: Spline functions: basic theory. New York: Wiley, 1981.

    MATH  Google Scholar 

  30. Strang, G.: Introduction to applied mathematics, Wellesley-Cambridge Press, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire LMC-IMAG, University of Grenoble, B.P. 53, F-38041, Grenoble cedex 9, France

    S. Hahmann

Authors
  1. S. Hahmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Arizona State University, Tempe, AZ, USA

    Gerald Farin

  2. Institut für Informatik und angewandte Grafik, Universität Bern, Bern, Switzerland

    Hanspeter Bieri

  3. Fachbereich Maschinenbau, Universität Kaiserslautern, Kaiserslautern, Germany

    Guido Brunnett

  4. Pixar Animation Studios, Richmond, CA, USA

    Tony De Rose

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Wien

About this paper

Cite this paper

Hahmann, S. (1998). Shape Improvement of Surfaces. In: Farin, G., Bieri, H., Brunnett, G., De Rose, T. (eds) Geometric Modelling. Computing Supplement, vol 13. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6444-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6444-0_11

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83207-3

  • Online ISBN: 978-3-7091-6444-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation