Triangular and Quadrilateral Finite Element Mesh Generation on Poorly Parameterized Free-Form Surfaces

Abstract The non-uniform rational B-spline (NURBS) surfaces are widely employed for the exchange of geometric models between different computer aided design and computer aided engineering systems. However, if the input surfaces are poorly parameterized, surface meshing algorithms may fail or the constructed meshes could be ill conditioned. This paper presents a new method that can generate well-conditioned meshes, even on poorly parameterized freeform surfaces, by regenerating NURBS surfaces. At the outset, adequate points are sampled on the poorly parameterized original surfaces. New surfaces are then created by interpolating these points. Finally, mesh generation is performed on the new surfaces. By employing this method, models with poorly parameterized surfaces can be successfully meshed.

[1]  D. White,et al.  6th International Meshing Roundtable '97 , 1997 .

[2]  Pierre Alliez,et al.  Isotropic Remeshing of Surfaces: A Local Parameterization Approach , 2003, IMR.

[3]  Anshuman Razdan,et al.  Determination of end conditions for NURB surface interpolation , 1998, Comput. Aided Geom. Des..

[4]  Hans-Peter Seidel,et al.  Interpolating scattered data with C2 surfaces , 1995, Comput. Aided Des..

[5]  Man-Soo Joun,et al.  General approach to automatic generation of quadrilaterals on three‐dimensional surfaces , 1998 .

[6]  Anshuman Razdan.  Healing Nurb surfaces , 1996 .

[7]  Jeffrey A. Talbert,et al.  Development of an automatic, two‐dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition , 1990 .

[8]  David R. White,et al.  Redesign of the Paving Algorithm : Robustness Enhancements through Element by Element Meshing , 2007 .

[9]  Myung-Woo Cho,et al.  Reverse Engineering for Sculptured Surfaces by Using NURBS Approximation , 2002 .

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

[11]  Steven J. Owen,et al.  A Survey of Unstructured Mesh Generation Technology , 1998, IMR.

[12]  Ted D. Blacker,et al.  Paving: A new approach to automated quadrilateral mesh generation , 1991 .

[13]  G. Nielson.  A method for interpolating scattered data based upon a minimum norm network , 1983 .

[14]  Weiyin Ma,et al.  Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces , 1995, Comput. Aided Des..

[15]  Pierre Alliez,et al.  Anisotropic polygonal remeshing , 2003, ACM Trans. Graph..

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

[17]  Djordje Brujic,et al.  Triangulation of unordered data using trimmed NURBS computer aided design models , 2000 .

[18]  신보성,et al.  사각형 유한요소망의 자동생성 ( Automatic Mesh Generation with Quadrilateral Finite Elements ) , 1993 .

[19]  Mark Meyer,et al.  Interactive geometry remeshing , 2002, SIGGRAPH.

[20]  Soo Won Chae,et al.  Quadrilateral mesh generation on trimmed NURBS surfaces , 2001 .

[21]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .