Computing

, Volume 36, Issue 3, pp 229–238

Comments on some B-spline algorithms

  • E. T. Y. Lee
Short Communications

Abstract

Two algorithms appeared (Lee [6] and Boehm [1]), both in this journal, for the computation of derivatives of aB-spline series that are faster than the repeated application of de Boor's algorithm to the derived series. Here we report on some test examples which show, however, that both these are less stable than the repeated de Boor.

AMS Subject Classifications

65-04 65D07 

Key words

B-splines derivatives algorithms 

Bemerkungen zu einigen B-Spline-Algorithmen

Zusammenfassung

In dieser Zeitschrift sind zwei Algorithmen zur Berechnung von Ableitungen einerB-Spline-Reihe erschienen (Lee [6] und Boehm [1]), die weniger Aufwand benötigen als die wiederholte Anwendung des Algorithmus von de Boor auf die abgeleitete Reihe. Wir berichten hier über Testrechnungen, die zeigen, daß diese Algorithmen weniger stabil sind als die wiederholte Anwendung des de Boor-Algorithmus.

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References

  1. [1]
    Boehm, W.: Efficient evaluation of splines. Computing31, 1–7 (1984).Google Scholar
  2. [2]
    Boehm, W., Farin, G., Kahmann, J.: A survey of curve and surface methods in CAGD. Computer Aided Geometric Design1, 1–60 (1984).Google Scholar
  3. [3]
    De Boor, C.: On calculating withB-splines. J. Approx. Theory6, 50–62 (1972).Google Scholar
  4. [4]
    Cox, M. G.: The numerical evaluation ofB-splines. J. Inst. Math. Appl.10, 134–147 (1972).Google Scholar
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    Butterfield, K. R.: The computation of all derivatives of aB-spline basis. J. Inst. Maths Applics17, 15–25 (1976).Google Scholar
  6. [6]
    Lee, E. T. Y.: A simplifiedB-spline computation routine. Computing29, 365–373 (1982).Google Scholar
  7. [7]
    Germain-Bonne, B., Sablonniere, P.: Comparaison des formes de courbes paramètres et de leurs approximants splines. Publication no. 76 du Laboratoire de Calcul de l'Université de Lille, 1976.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • E. T. Y. Lee
    • 1
  1. 1.Boeing Commercial Airplane Co.SeattleUSA

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