Journal of Ship and Ocean Technology

The Society of Naval Architects of Korea (대한조선학회)
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Generation of Discrete $G^1$ Continuous B-spline Ship Hullform Surfaces from Curve Network Using Virtual Iso-parametric Curves

  • Rhim, Joong-Hyun (EzGraph, Co., Ltd.) ;
  • Cho, Doo-Yeoun (Dept. of Naval Architecture & Ocean Engineering, Seoul National University) ;
  • Lee, Kyu-Yeul (Dept. of Naval Architecture & Ocean Engineering and Research Institute of Marine System Engineering, Seoul National University) ;
  • Kim, Tae-Wan (Dept. of Naval Architecture & Ocean Engineering and Research Institute of Marine System Engineering, Seoul National University)
  • Published : 2006.06.01
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Abstract

Ship hullform is usually designed with a curve network, and smooth hullform surfaces are supposed to be generated by filling in (or interpolating) the curve network with appropriate surface patches. Tensor-product surfaces such as B-spline and $B\'{e}zier$ patches are typical representations to this interpolating problem. However, they have difficulties in representing the surfaces of irregular topological type which are frequently appeared in the fore- and after-body of ship hullform curve network. In this paper, we proposed a method that can automatically generate discrete $G^1$ continuous B-spline surfaces interpolating given curve network of ship hullform. This method consists of three steps. In the first step, given curve network is reorganized to be of two types: boundary curves and reference curves of surface patches. Especially, the boundary curves are specified for their surface patches to be rectangular or triangular topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. In the second step, surface fitting points and cross boundary derivatives are estimated by constructing virtual iso-parametric curves at discrete parameters. In the last step, discrete $G^1$ continuous B-spline surfaces are generated by surface fitting algorithm. Finally, several examples of resulting smooth hullform surfaces generated from the curve network data of actual ship hullform are included to demonstrate the quality of the proposed method.

Keywords

References

  1. Rhim, J. H. and K. Y. Lee. 1997. Remeshing algorithm of curve network of ship hullform and Interpolating hullform surfaces with Gregory patches (Written in Korean). Proceedings of the Society of CAD/CAM Engineers, 327-334
  2. Levin, A. 1999. Combined subdivision schemes for the design of surfaces satisfying boundary conditions. Computer Aided Geometric Design, 16,5,345-354 https://doi.org/10.1016/S0167-8396(98)00051-X
  3. Levin, A. 1999. Interpolating nets of curves by smooth subdivision surfaces. Proc. of SIGGRAPH 1999,57-64
  4. Nasri, A. 1987. Polyhedral subdivision methods for free form surfaces. ACM Transactions on Graphics, 8, 1, 89-9 https://doi.org/10.1145/62054.62056
  5. Nasri, A. 1997. Curve interpolation in recursively generated surfaces over arbitrary topology. Computer Aided Geometric Design, 14, 1, 13-30 https://doi.org/10.1016/S0167-8396(96)00018-0
  6. Nasri, A. 2000. Recursive subdivision of polygonal complexes and its applications in CAGD. Computer Aided Geometric Design, 17,7, 1-25 https://doi.org/10.1016/S0167-8396(99)00034-5
  7. Nasri, A. 2000. A polygonal approach for interpolating meshes of curves by subdivision surfaces. Proc. Geometric Modeling and Processing. 262-273
  8. Nasri, A. 2001. Constructing polygonal complexes with shape handles for curve interpolation by subdivision surfaces. Computer-Aided Design, 33, 11, 753-765 https://doi.org/10.1016/S0010-4485(01)00093-8
  9. Cho, D. Y., K. Y. Lee and T. W. Kim. 2005. Generation of discrete $G^1$continuous ship hullform surfaces from curve network and surface fairing (Written in Korean). Proceedings of the Society of CAD/CAM Engineers
  10. Hoschek, J. 1987. Approximate conversion of spline curves. Computer Aided Geometric Design, 4, 1-3, 59-66 https://doi.org/10.1016/0167-8396(87)90019-7
  11. Coons, H. 1967. Surfaces for computer aided design of space forms Technical report, MIT. Project MAC-TR 41
  12. Farin, G. 2002. Curves and Surfaces for CAGD, 5th ed. Academic Press
  13. Lee, K. Y., J. H. Rhim, S. U. Lee, D. Y. Cho and Y. B. Choi. 2001. Development of Sophisticated Hull Form CAD System 'EzHULL' Based on Non-Manifold Model and 'X-topology. The 8th International Symposium on Practical Design of Ships and Other Floating Structures(PRADS 2001), 315-321