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 Gamma such that for all(x) epsilon Gamma, d(x, V) <= epsilon, where d(x, V) = min((x) over bar epsilon V) parallel to x - (x) over bar parallel to for a given point cloud V assumed to belong to the boundary of an open subset of R-2 and for E 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 Q enclosing V. A numerical example is provided to show the efficiency of the proposed approach.