A Study on Filling Holes of the Polygon Model using Implicit Surface Scheme

음함수 곡면기법을 이용한 폴리곤 모델의 홀메움에 관한 연구

  • 유동진 (대진대학교 컴퓨터응용기계설계공학과)
  • Published : 2005.03.01

Abstract

A new approach which combines implicit surface scheme and point projection method is presented in order to fill the arbitrarily shaped holes in the polygon model. In the method a trimmed surface which has an outer boundary curve is generated by using the implicit surface scheme and normal projection of point onto the base surface. The base surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In this paper an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$. The base surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In order to show the validity of the present study, various hole fillings are carried out for the complex polygon model of arbitrary topology.

Keywords

References

  1. Besl, P. J., Mckay, N. D., 'A method for registration of 3-D shape,' IEEE Trans. Pattern Anal Mach. Intell., Vol. 14, pp. 239-256, 1992 https://doi.org/10.1109/34.121791
  2. Schroeder, J., Zarge, J., Lorensen, W., 'Decimation of Triangle Meshes,' Computer Graphics, Vol. 26, pp. 65-70, 1992 https://doi.org/10.1145/142920.134010
  3. Piegl, L. and Tiller, W., 'Filling N-sided regions with NURBS patch,' The Visual Computer, Vol. 15, pp. 77-89,1999 https://doi.org/10.1007/s003710050163
  4. Catrnull, E., Clark, J., 'Recursively generated Bspline surfaces on arbitrary topological meshes,' Computer-Aided Design, Vol. 10,pp. 350-355, 1978 https://doi.org/10.1016/0010-4485(78)90110-0
  5. Jun, Y. T., Park, K. H., Rho, H. M. and Choi, Y., 'A Study on Filling Polygonal Holes in a Polygon-based Reverse Engineering System,' Journal of the Korean Society of Precision Engineering, Vol. 21, No.4, pp. 140-147,2004
  6. Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., Evans, T. R., ' Reconstruction and representation of 3D objects with radial basis functions,' In Proceedings of SIGGRAPH 2001, pp. 67-76, 2001 https://doi.org/10.1145/383259.383266
  7. loater, M. S., Iske, A. A., 'Multistep scattered data interpolation using compactly supported radial basis functions,' Journal of Comp. Appl. Math., Vol. 73, pp. 65-78,1996 https://doi.org/10.1016/0377-0427(96)00035-0
  8. Lazzaro, D., Montefusco, L. B., 'Radial basis functions for multivariate interpolation of large scattered data sets,' Journal of Computational and Applied Math., Vol. 140, pp. 521-536,2002 https://doi.org/10.1016/S0377-0427(01)00485-X
  9. Turk, G. and O'Brien, J. F., 'Variational implicit surfaces,' Tech. Rep. GIT-GVU-99-15, Georgia Institute of Technology, May, 1999
  10. Yoo, D. J., 'A Study on Filling Holes of the Polygon Model,' Journal of the Korean Society of Precision Engineering, Submitted
  11. Les Piegl and Wayne Tiller, The NURBS Book, Springer, 1995