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.
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Communicated by Edward B. Saff.
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Barry, P.J. de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves. Constr. Approx 12, 385–408 (1996). https://doi.org/10.1007/BF02433050
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DOI: https://doi.org/10.1007/BF02433050