ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
권호 표지

Surface Fairing with Boundary Continuity Based on the Wavelet Transform

  • Received : 2000.06.27
  • Published : 2001.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

The surface modeling capability of CAD systems is widely used to design products bounded by free form surfaces and curves. However, the surfaces or curves generated by popular data fitting methods usually have shape imperfections such as wiggles. Thus, fairing operations are required to remove the wiggles, which makes the surfaces or curves smooth. This paper proposes a new method based on the wavelet transform for fairing the surfaces or curves while preserving the continuity with adjacent surfaces or curves. The wavelet transform gives a hierarchical perspective of the surfaces and the curves, which can be decomposed into the overall sweep and details, i.e., local deviations from sweep like the wiggles. The proposed fairing method provides a similar effect on the mathematical surface as that of the grinding operation using sandpaper on the physical surface.

Keywords

References

  1. Computer Graphics (Proceedings of SIGGRAPH '88) v.22 no.4 Hierachical B-spline Refinement Forsey, D.;Bartels, R.
  2. An Introduction to Wavelets Chui, C.K.
  3. Wavelets on a Bounded Interval, Numerical Methods of Approximation Theory Chui, C.K.;Quak, E.;Braess, D.(ed.);Schumaker, L.L.(ed.)
  4. IEEE Transaction on Pattern Analysis and Machine Intelligence v.11 no.7 A Theory for Multiresolution Signal Decomposition: The Wavelet Representation Mallat, S.
  5. IEEE Transactions on Image Processing v.5 no.1 Wavelet Descriptor of Planar Curves: Theory and Applications Chuang, G.C.H.;Kuo, C.C.J.
  6. Symposium on Interactive 3D graphics Hierarchical and Variational Geometric Modeling with Wavelets Gortler, S.;Hanrahan, P.(ed.);Winget, J.(ed.)
  7. IEEE Computer Graphics and Applications v.9 no.2 Curvature and the Fairness of Curves and Surfaces Farin, G.;Sapidis, N.
  8. Computer Graphics Forum v.3 Variational Design and Fairing of Spline Surfaces Greiner, G.
  9. Computer-Aided Design v.23 no.7 Designing Faired Parametric Surfaces Rando, T.;Roulier, J.
  10. Computer Graphics v.26 no.2 Functional Optimization for Fair Surface Design Moreton, H.;Sequin, C.
  11. Computer Graphics (Proceedings of SIGGRAPH '94) v.28 Multiresolution Curves Finkelstein, A.;Salesin, D.
  12. ACM Transactions on Graphics v.16 no.1 Multiresolution Analysis for Surfaces of Arbitrary Topological Type Lounsbery, M.;DeRose, T.;Warren, J.
  13. Wavelets for Computer Graphics: Theory and Applications Stollnitz, E.;DeRose, T.;Salesin, D.
  14. Principles of CAD/CAM/CAE Systems Lee, K.
  15. Curves and Surfaces for Computer-Aided Geometric Design Farin, G.
  16. The NURBS Book Piegl, L.;Tiller, W.