Automatic Mesh Generation on Poorly Parameterized NURBS Surfaces

불균일한 매개변수로 정의된 NURBS 곡면에서의 요소망 자동 생성

  • 채수원 (고려대학교 기계공학과) ;
  • 박정민 (한국과학기술원 기계공학과)
  • Published : 2003.06.01


The NURBS surfaces are widely employed for exchanging geometric models between different CAD/CAE systems. However if the input NURBS surfaces are poorly parameterized, most surface meshing algorithms may fail or the constructed meshes can be ill-conditioned. In this paper presents a new method is presented that can generate well conditioned meshes even on poorly parameterized NURBS surfaces by regenerating NURBS surfaces. To begin with, adequate points are sampled on original poorly parameterized surfaces and new surfaces are created by interpolating these points. And then, mesh generation is performed on new surfaces. With this method, models with poorly parameterized NURBS surfaces can be meshed successfully.


  1. Kolb, A. and Seidel, H. P., 'Interpolating Scattered Data With C2 Surfaces,' Compuer-Aided Design, Vol. 27, No. 4, pp. 277-282, 1995
  2. Neilson, G. M., 'A Method for Interpolating Scattered Data Based upon a Minimum Norm Network,' American Math. Soc. Math. Comput, Vol. 40, pp. 253-271, 1993
  3. Weiyin, M. and Kruth, J. P., 'Parameterization of Randomly Measured Points for Least Squares Fitting of B-Spline Curves and Surfaces,' Computer-Aided Design, Vol. 27, No. 9, pp. 663-675, 1995
  4. Cho Jae Hyung and Cho Myung-Woo, 'Reverse Engineering for Sculptured Surface by Using NURBS Approximation,' J. of the KSPE, Vol. 19, No. 8, pp. 108-115, 2002
  5. Razdan, A., 'Healing NURB Surface,' Ph. D Thesis, Arizona State Univ., 1997
  6. Razdan, A. and Farin,G., 'Determination of End Conditions for NURBS Surface Interpolation,' Computer-Aided Geometric Design, Vol. 15, pp. 757-768, 1998
  7. Chae Soo-Won and Kwon Ki-Youn, 'Quadrilateral Mesh Generation on Trimmed NURBS Surfaces,' KSME International Journal, Vol. 15, No. 4, pp. 592-601, 2001
  8. Filip, D., Magedson, R. and Markot, R., 'Surface Algorithm Using Bounds of Derivatives,' Computer-Aided Geometric Design, Vol. 3, pp. 295-311, 1986
  9. Piegl, L. and Tiller, W., The NURBS Book, Springer, Germany, 1995
  10. Farin, G., Curves and Surfaces for Computer Aided Geometric Design- A Practical Guide, Fourth Edition, Academic Press, 1997