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

Authors:
A. Claisse;P. Frey
Affiliations:
UPMC Univ Paris 06, UMR 7598, Laboratoire J.-L. Lions, F-75005 Paris, France;UPMC Univ Paris 06, UMR 7598, Laboratoire J.-L. Lions, F-75005 Paris, France
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At first, 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 first 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.