De Boor-Fix dual functionals and algorithms for tchebycheffian B-spline curves

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)385-408
Number of pages24
JournalConstructive Approximation
Volume12
Issue number3
DOIs
StatePublished - Jan 1 1996

Keywords

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

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