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

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.

[1]  William H. Frey,et al.  An apporach to automatic three‐dimensional finite element mesh generation , 1985 .

[2]  Klaus-Jürgen Bathe,et al.  On automatic mesh construction and mesh refinement in finite element analysis , 1989 .

[3]  N. Weatherill,et al.  Unstructured grid generation using iterative point insertion and local reconnection , 1995 .

[4]  R. de Borst,et al.  An algorithm for mesh rezoning with application to strain localization problems , 1995 .

[5]  Paul-Louis George,et al.  Fully automatic mesh generator for 3D domains of any shape , 1990, IMPACT Comput. Sci. Eng..

[6]  Roland W. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 2. Surface meshes , 1996 .

[7]  Robert P. Markot,et al.  Surface algorithms using bounds on derivatives , 1986, Comput. Aided Geom. Des..

[8]  K. Ho-Le,et al.  Finite element mesh generation methods: a review and classification , 1988 .

[9]  Paul-Louis George,et al.  Génération automatique de maillages : applications aux méthodes d'éléments finis , 1991 .

[10]  J. Z. Zhu,et al.  The finite element method , 1977 .

[11]  Pierre Ladevèze,et al.  Mesh optimization for problems with steep gradients , 1994 .

[12]  G. Xie,et al.  Graded mesh generation and transformation , 1994 .

[13]  Nigel P. Weatherill,et al.  A procedure for efficient generation of solution adapted unstructured grids , 1995 .

[14]  Roland W. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 1. Fundamental aspects of triangulation and point creation , 1996 .

[15]  Jean-Christophe Cuillière.  Pré-optimisation de maillages automatiques tridimensionnels pour les méthodes numériques : application à l'ingénierie simultanée , 1993 .

[16]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[17]  P. Frey,et al.  Fully automatic mesh generation for 3-D domains based upon voxel sets , 1994 .

[18]  Paresh Parikh,et al.  Generation of three-dimensional unstructured grids by the advancing-front method , 1988 .

[19]  Jean-Christophe Cuillière.  A direct method for the automatic discretization of 3D parametric curves , 1997, Comput. Aided Des..

[20]  W. Frey.  Selective refinement: A new strategy for automatic node placement in graded triangular meshes , 1987 .

[21]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[22]  Ibrahim Zeid,et al.  CAD/CAM theory and practice , 1991 .

[23]  David A. Field.  The legacy of automatic mesh generation from solid modeling , 1995, Comput. Aided Geom. Des..

[24]  Peter Hansbo,et al.  On advancing front mesh generation in three dimensions , 1995 .

[25]  Alain Rassineux.  Maillage automatique tridimensionnel par une méthode frontale pour la méthode des éléments finis , 1995 .

[26]  O. Zienkiewicz,et al.  Finite element Euler computations in three dimensions , 1988 .

[27]  S. H. Lo,et al.  Finite element mesh generation over analytical curved surfaces , 1996 .

[28]  Bernd E. Hirsch,et al.  Triangulation of trimmed surfaces in parametric space , 1992, Comput. Aided Des..

[29]  Mark S. Shephard,et al.  Trends in automatic three-dimensional mesh generation , 1988 .