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.
KolbA.SeidelH. P.Interpolating scattered data with C2 surfaces. Computer-Aided Des., 1995, 27(4), 277–282.
2.
NeilsonG. M.A method for interpolating scattered data based upon a minimum norm network. Am. Math. Soc. Math. Computation, 1993, 40, 253–271.
3.
WeiyinM.KruthJ. P.Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces. Computer-Aided Des., 1995, 27(9), 663–675.
4.
ChoJ. H.ChoM. W.Reverse engineering for sculptured surfaces by using NURBS approximation. J. Korean Soc, Precision Engng, 2002, 19(8), 108–115.
5.
RisticM.BrujicD.HandayaniS.Triangulation of unordered data using trimmed NURBS computer aided design models. Proc. Instn Mech. Engrs Part B: J. Engineering Manufacture, 2000, 214(B6), 509–514.
6.
RazdanA.Healing NURB surface. PhD Thesis, Arizona State University, 1995.
7.
RazdanA.FarinG.Determination of end conditions for NURBS surface interpolation. Computer-Aided Geometric Des., 1998, 15, 757–768.
8.
FarinG.Curves and surfaces for computer aided geometric design - a practical guide, 4th edition, 1997 (Academic Press, New York).
9.
ChaeS. W.KwonK. Y.Quadrilateral Mesh Generation on Trimmed NURBS Surfaces. Korean Soc Mech. Engrs Int. J., 2001, 15(4), 592–601.
10.
AlliezP.MeyerM.DesbrunM.Interactive geometry remeshing. In Proceedings of the 29th International Conference on Computer graphics and interactive techniques (ACM SIGGRAPH 2002), 2002, pp. 347–354 (Association for Computing Machinery, New York).
11.
SurazhskyV.AlliezP.GotsmanC.Isotropic remeshing of surfaces: A local parameterization approach. In Proceedings of the 12th International Meshing Roundtable, 2003, pp. 215–224, (Sandia National Laboratories, Santa Fe, New Mexico).
LeeM. C.JounM. S.General approach to automatic generation of quadrilaterals on three-dimensional surfaces. Commun. Numer. Meth. Engng14, 609–620.
16.
ChaeS. W.JeoungJ. W.Unstructured surface meshing using operators. In Proceedings of the Sixth International Meshing Roundtable, 1997, pp. 281–291, (Sandia National Laboratories, Utah, USA).
17.
OwenS. J.A survey of unstructured mesh generation technology. In Proceedings of the Seventh International Meshing Roundtable, 1998, pp. 239–267 (Sandia National Laboratories, Michigan, USA).
18.
TalbertJ. A.ParkinsonA. R.Development of an automatic, two dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definitions. Int. J. Numer. Meth. Engng, 1991, 29, 1551–1567.
19.
ChaeS. W.ShinB. S.MinJ. K.On the automatic mesh generation with quadrilateral finite elements. Trans. Korean Soc. Mech. Engrs, 1993, 17(2), 2995–3006.
20.
BlackerT. D.StephensonM. B.Paving: A new Approach to automated quadrilateral mesh generation. Int. J. Numer. Meth. Engng, 1991, 32, 811–847.
21.
WhiteD. R.KinneyP.Redesign of the paving algorithms: Robustness enhancements through element by element meshing. In Proceedings of the Sixth International Meshing Roundtable, 1997, pp. 323–335 (Sandia National Laboratories, Utah, USA).
22.
ChaeS. W.BatheK. J.On automatic mesh construction and mesh refinement in finite element analysis. J. Computers Structs, 1989, 32(3–4), 911–936.
