Construction d'une courbe régulière d'approximation d'un ensemble de points

Abstract

In this Note, we deal with the problem of constructing a regular (smooth) curve Γ such that ∀ x ∈ Γ , d ( x , V ) ⩽ ε , where d ( x , V ) = min x ¯ ∈ V ‖ x − x ¯ ‖ for a given point cloud V assumed to belong to the boundary of an open subset of R 2 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. To cite this article: A. Claisse, P. Frey, C. R. Acad. Sci. Paris, Ser. I 346 (2008).