Section: New Results

High Quality Geometric Meshing of CAD Surfaces

Participants : P. Laug [correspondant], H. Borouchaki

We propose a general scheme of an indirect approach for generating isotropic and anisotropic geometric meshes of a surface constituted by a conformal assembly of parametric patches, based on the concept of metric. The different steps of the scheme are considered and, in particular, the definition of the geometric metric at each point of the surface (internal to a patch, belonging to an interface or boundary curve, or extremity of such a curve) as well as its corresponding induced metric in parametric domains.

Isotropic or anisotropic geometric metrics can locally produce significant size variations (internal to a patch or across interface curves) and can even be discontinuous across the interface curves. The larger the rate of the mesh size variation, the worse is the shape quality of the resulting mesh. To control this size variation, various methodologies based on metric reduction have been proposed in the case of a continuous isotropic metric. We introduce a novel iterative mesh gradation approach for discontinuous metrics. The approach uses a particular metric reduction procedure in order to ensure the convergence of the gradation process. In particular, we show that in the worst case the anisotropic discontinuous geometric metric map is reduced to an isotropic continuous geometric metric map for which the gradation is controlled [27] .