High quality geometric meshing of CAD surfaces

Abstract

A wide range of surfaces can be defined by means of composite parametric surfaces as is the case for most CAD modelers. There are, essentially, two approaches to meshing parametric surfaces: direct and indirect. Popular direct methods include the octree-based method, the advancing-front-based method and the paving-based method working directly in the tridimensional space. The indirect approach consists in meshing the parametric domain and mapping the resulting mesh onto the surface. Using the latter approach, we propose a general "geometry accurate" mesh generation scheme using geometric isotropic or anisotropic metrics. In addition, we introduce a new methodology to control the mesh gradation for these geometric meshes in order to obtain finite element geometric meshes. Application examples are given to show the pertinence of our approach.