Analyse numérique
Construction d'une courbe régulière d'approximation d'un ensemble de points
[Construction of a regular curve to approximate a point set]
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 1017-1022.

In this Note, we deal with the problem of constructing a regular (smooth) curve Γ such that xΓ, d(x,V) ε, where d(x,V)=minx¯Vxx¯ for a given point cloud V assumed to belong to the boundary of an open subset of R2 and for ε small. To approximate this curve, we solve a minimization problem based on a levelset formulation. The particularity of the corresponding numerical scheme is to solve on an anisotropic triangulation of a convex domain Ω enclosing V. A numerical example is provided to show the efficiency of the proposed approach.

Dans cette Note, on s'intéresse au problème de la construction d'une courbe régulière Γ telle que xΓ, d(x,V)ε, où d(x,V)=minx¯Vxx¯ pour un ensemble de points donné V supposé appartenir à la frontière d'un ouvert de R2, et pour ε, petit fixé. Pour approcher cette courbe, on résout un problème de minimisation basé sur une formulation de type ligne de niveau. La particularité du schéma numérique utilisé est qu'il s'appuie sur une triangulation anisotrope d'un domaine convexe Ω contenant V. Un exemple de construction est proposé pour illustrer cette approche.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.021
Claisse, Alexandra 1; Frey, Pascal 1, 2

1 UPMC Université Paris-06, UMR 7598, laboratoire Jacques-Louis-Lions, 75005 Paris, France
2 Universidad de Chile, UMI 2807, Centro de Modelamiento Matemática, Santiago, Chile
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Claisse, Alexandra; Frey, Pascal. Construction d'une courbe régulière d'approximation d'un ensemble de points. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 1017-1022. doi : 10.1016/j.crma.2008.07.021. http://www.numdam.org/articles/10.1016/j.crma.2008.07.021/

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