[NURBS ou pas ?]
On peut assez naturellement considérer que la plus grande classe d'espaces de splines utiles pour le design est celle des espaces de splines à sections dans différents espaces « quasi-Chebyshev généralisés » reliées entre elles par des matrices de connexion, espaces qui, de plus, contiennent les constantes et possédent des floraisons. Nous avons récemment donné une construction itérative étonnamment simple de cette classe très difficile. Une application adéquate d'une étape de cette itération peut être interprétée comme la construction de splines rationnelles (donc de NURBS) associées, tout se passant à l'intérieur de la même classe.
The view adopted here is that the largest class of splines which are useful for design is composed of all spaces of geometrically continuous piecewise quasi-Chebyshevian splines that contain constants and possess blossoms. We recently described an iterative construction of all spaces of this class. This note announces the possibility of building associated rational spline spaces (and therefore, associated NURBS) while remaining in the same class. This is obtained when applying in an appropriate way one step of this construction.
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@article{CRMATH_2016__354_7_747_0,
author = {Mazure, Marie-Laurence},
title = {NURBS or not {NURBS?}},
journal = {Comptes Rendus. Math\'ematique},
pages = {747--750},
publisher = {Elsevier},
volume = {354},
number = {7},
year = {2016},
doi = {10.1016/j.crma.2016.01.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.01.027/}
}
Mazure, Marie-Laurence. NURBS or not NURBS?. Comptes Rendus. Mathématique, Tome 354 (2016) no. 7, pp. 747-750. doi : 10.1016/j.crma.2016.01.027. http://www.numdam.org/articles/10.1016/j.crma.2016.01.027/
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