An adaptive method for the automatic triangulation of 3D parametric surfaces

Computer-Aided Design, Elsevier, Vol 30, Num 2, pp.139-149, 1998

MESHING
RESEARCH
CORNER

Laboratoire de Productique, Departement de Genie Mecanique, Universite du Quebec Trois-Rivieres, CP 500, Trois-Rivieres G9A-5H7, Quebec, Canada

Abstract
We have developed automatic mesh generation procedures based on advancing front methods and featuring a priori nodal density calculations. A crucial step in the overall method consists of discretizing the edges and surfaces of an input B-Rep structure with the ability to respect as closely as possible this nodal density function across the part, which is highly interesting for analysis or representation purposes. The work presented here focuses on the discretization of three-dimensional parametric surfaces with strong variations of curvature with respect to a nodal density function with steep gradients. This algorithm is particularly suitable for FE mesh generation purposes and also in many engineering applications for which a 3D model has to be triangulated. We will tackle, in this context, the use of the technique in order to mesh parametric surfaces with a specified discretization tolerance. In this paper, we also present a new quality indicator for triangular and tetrahedral meshes in the context of a priori nodal density constraints.