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 language | English (US) |
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Pages (from-to) | 385-408 |
Number of pages | 24 |
Journal | Constructive Approximation |
Volume | 12 |
Issue number | 3 |
DOIs | |
State | Published - 1996 |
Externally published | Yes |
Keywords
- Blossoming
- Connection matrix
- De Boor-Fix dual functionals
- Differentiation
- Evaluation
- Geometric continuity
- Knot insertion
- Tchebycheffian B-spline
- Total positivity
- Zeros