We propose a method to adapt a three dimensional surface mesh. The data needed to optimize the mesh have been reduced to an initial mesh. The method is based on a meshfree technique dedicated to solve PDE denoted as diffuse interpolation. In this paper, much emphasis has been given to the building of a geometrical model based on a local Hermite interpolation calculated from the nodes of the initial mesh and from the normal vectors to the surface calculated from the mesh. The determination of an interpolating local surface equation, however continuous over the domain, enables us to locate nodes on the surface with respect to the curvature during a refinement process. It also allows us to control the coarsening of the mesh. The local surface equation is used to compute the principal curvatures on the surface for two main purposes, error estimation and feature recognition.
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