A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes.

Alexandra Claisse (1) , Pascal Frey (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At rst, we show the existence and the uniqueness of a viscosity solution to this problem. Then we propose a numerical scheme for solving the nonlinear level set equation on unstructured triangulations adapted to the data sample. We show the consistency of this scheme. In addition, we show how to compute nodewise rst and second order derivatives. Some application examples of curve or surface construction are provided to illustrate the potential and to demonstrate the accuracy of this method.

Mots clés: Numerical analysis; Level set method; Mean curvature evolution; Hamilton-Jacobi equation; Nonlinear PDE problem; Surface reconstruction; Unstructured mesh

Domaines: Analyse numérique [cs.NA]

Alexandra Claisse, Pascal Frey. A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes.. 2011. ⟨hal-00559751⟩