Geometrically continuous piecewise Chebyshevian NU(R)BS
| Autor: | Marie-Laurence Mazure |
|---|---|
| Přispěvatelé: | Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA) |
| Rok vydání: | 2020 |
| Předmět: |
blossoms
Pure mathematics rational splines Computer Networks and Communications Applied Mathematics Identity matrix geometric design 010103 numerical & computational mathematics 01 natural sciences Chebyshev filter Mathematics::Numerical Analysis Piecewise Chebyshevian splines 010101 applied mathematics Computational Mathematics Spline (mathematics) NURBS Computer Science::Graphics Piecewise Equivalence relation [MATH]Mathematics [math] 0101 mathematics shape effects Software Mathematics |
| Zdroj: | BIT Numerical Mathematics BIT Numerical Mathematics, 2020, 60, pp.687-714. ⟨10.1007/s10543-019-00795-y⟩ BIT Numerical Mathematics, Springer Verlag, 2020, 60, pp.687-714. ⟨10.1007/s10543-019-00795-y⟩ |
| ISSN: | 1572-9125 0006-3835 |
| DOI: | 10.1007/s10543-019-00795-y |
| Popis: | International audience; By piecewise Chebyshevian splines we mean splines with pieces taken from different Extended Chebyshev spaces all of the same dimension, and with connection matrices at the knots. Within this very large and crucial class of splines, we are more specifically concerned with those which are good for design, in the sense that they possess blossoms, or, equivalently, refinable B-spline bases. In practice, this subclass is known to be characterised by the existence of (infinitely many) piecewise generalised derivatives with respect to which the continuity between consecutive pieces is controlled by identity matrices. Somehow inherent in the previous characterisation, the construction of all associated rational spline spaces creates an equivalence relation between piecewise Chebyshevian spline spaces good for design, among which the famous classical rational splines. We investigate this equivalence relation along with the natural question: Is it or not worthwhile considering the rational framework since it does not enlarge the set of resulting splines? This explains the parentheses inside the acronym NU(R)BS. |
| Databáze: | OpenAIRE |
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