Constructive Approximation

, Volume 12, Issue 3, pp 385–408 | Cite as

de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves

  • P. J. Barry


The de Boor-Fix dual functionals are a potent tool for deriving results about piecewise polynomial B-spline curves. In this paper we extend these functionals to Tchebycheffian B-spline curves and then use them to derive fundamental algorithms that are natural generalizations of algorithms for piecewise polynomial B-spline algorithms. Then, as a further example of the utility of this approach, we introduce “geometrically continuous Tchebycheffian spline curves,” and show that a further generalization works for them as well.

AMS classification

41A15 65D17 

Key words and phrases

Blossoming de Boor-Fix dual functionals Connection matrix Differentiation Evaluation Geometric continuity Knot insertion Tchebycheffian B-spline Total positivity Zeros 


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Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • P. J. Barry
    • 1
  1. 1.Computer Science DepartmentUniversity of MinnesotaMinneapolisUSA

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