Utilisation des floraisons pour les processus de subdivision dans les espaces de Chebyshev

Abstract : Geometric design algorithms are well suited to derive polynomial or piecewise polynomial parametric curves. These algorithms can be nicely converted to blossoms. Furthermore thanks to blossoms we also can generalize some design algorithms in order to derive parametric curves in Chebyshevian spaces.Blossoms quite naturally lead to subdivision schemes. They can be used to derive parametric polynomial splines. In the non-stationary case they they also can derive polynomial splines, and Chebyshevian splines (ie splines in various Chebyshevian spaces) as well. Finally we use blossoms as "algorithmic modeling" subdivision schemes in order to derive algorithms for splines whose pieces are in different Chebyshevian spaces.
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Martine Brilleaud. Utilisation des floraisons pour les processus de subdivision dans les espaces de Chebyshev. Géométrie algébrique [math.AG]. Université Grenoble Alpes, 2017. Français. ⟨NNT : 2017GREAM013⟩. ⟨tel-01681322v2⟩

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