Comptes Rendus
Numerical analysis
NURBS or not NURBS?
Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 747-750.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.027

Marie-Laurence Mazure 1

1 Université Grenoble Alpes, Laboratoire Jean Kuntzmann, CNRS, UMR 5224, BP 53, 38041 Grenoble Cedex 9, France
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Marie-Laurence Mazure. NURBS or not NURBS?. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 747-750. doi : 10.1016/j.crma.2016.01.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.027/

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