NURBS skinning surface for ship hull design based on new parameterization method

Original Article


Surface reconstruction from sets of cross-sectional data is important in a variety of applications. The problem of generating a ship hull surface from non-regular cross-sectional curves is addressed. Generating non-uniform rational B-splines (NURBS) surfaces that represent cross-sectional curves is a challenge, since the number of control points is growing due to the non-avoidable process of having compatible cross-sectional curves. A new NURBS parameterization method that yields a minimum number of control points, and is adequate in generating a smooth and fair NURBS surface for ship hulls is proposed. This method allows for multiple knots and close domain knots. The results of applying different parameterization methods on the forward perpendicular (FP) region of a ship hull (organized in eight sections) shows that the proposed method reduces the number of control points and generates a smooth and fair NURBS surface, without sacrificing the original object shape of the FP region.


Compatibility process Non-uniform rational B-splines (NURBS) skinning Parameterization Skinning process 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Piegl LA (1991) On NURBS: a survey. IEEE Comput Graph Appl 10:55–71CrossRefGoogle Scholar
  2. 2.
    Piegl LA, Wayne T (1997) The NURBS book, 2nd edn. Springer-Verlag, Berlin Heidelberg New YorkGoogle Scholar
  3. 3.
    Rogers DF (2001) An introduction to NURBS. Kaufmann, San FranciscoGoogle Scholar
  4. 4.
    Dmitrii B, Ichiro H (2002) Minimal area for surface reconstruction from cross-sections. Vis Comput 18:437–444CrossRefGoogle Scholar
  5. 5.
    Filip DJ, Ball TW (1989) Procedurally skinning lofted surfaces. IEEE Comput Graph Appl 9:27–33CrossRefGoogle Scholar
  6. 6.
    Hyungjun P, Kwangsoo K (1996) Smooth surface approximation to serial cross-sections. Comput Aided Des 28:995–1005CrossRefGoogle Scholar
  7. 7.
    Piegl LA, Wayne T (2002) Surface skinning revisited. IEEE Comput Graph Appl 18:273–283Google Scholar
  8. 8.
    Treece GM, Prager RW, Gee AH, Berman L (2000) Surface interpolation from sparse cross-sections using region correspondence. IEEE Trans Med Imaging 19:1106–1114CrossRefGoogle Scholar
  9. 9.
    Woodward C (1988) Skinning techniques for interactive B-spline interpolation. Comput Aided Des 20:441–451MATHCrossRefGoogle Scholar
  10. 10.
    Hyungjun P (2001) An approximate lofting approach for B-spline surface fitting to functional surfaces. Int J Adv Manuf Technol 18:474–482CrossRefGoogle Scholar
  11. 11.
    Hyungjun P, Hyung BJ, Kwangsoo K (2004) A new approach for lofted B-spline surface interpolation to serial contours. Int J Adv Manuf Technol 23:889–895Google Scholar
  12. 12.
    Piegl LA, Wayne T (2000) Reducing control points in surface interpolation. IEEE Comput Graph Appl 20:70–74CrossRefGoogle Scholar
  13. 13.
    Handscomb DC (1987) Knot elimination: reversal of the Oslo algorithm. Int Series Numer Math 81:103–111MathSciNetGoogle Scholar
  14. 14.
    Kjellander J (1983) Smoothing of cubic parametric splines. Comput Aided Des 15:175–179CrossRefGoogle Scholar
  15. 15.
    Lyche T, Morken K (1988) A data reduction strategy for splines with application to the approximation of functions and data. IMA J Numer Anal 8:185–208MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Matthias E, Hadenfeld J (1994) Knot removal for B-spline curves. Comput Aided Graph Des 8:185–208Google Scholar
  17. 17.
    Wayne T (1992) Knot removal algorithm for NURBS curves and surfaces. IEEE Comput Aided Des 2:445–453Google Scholar
  18. 18.
    Boehm W (1980) Inserting new knots into B-spline curve. Comput Aided Des 12:199–201CrossRefGoogle Scholar
  19. 19.
    Boehm W, Prautzsch H (1985) The efficiency of knot insertion algorithm. Comput Aided Graph Des 2:141–143MATHCrossRefGoogle Scholar
  20. 20.
    Cohen E, Lyche T, Riesenfeld RF (1980) Discrete B-spline and subdivision techniques in CAGD and computer graphics. Comput Graph Image Process 14:87–111CrossRefGoogle Scholar
  21. 21.
    De Boor C (1978) A practical guide to spline. Springer-Verlag, Berlin Heidelberg New YorkGoogle Scholar
  22. 22.
    Lyche T, Cohen E, Morken K (1985) Knot line refinement algorithm for tensor product splines. Comput Aided Graph Des 2:133–139MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2006

Authors and Affiliations

  1. 1.Department of Computer Graphics and Multimedia, Faculty of Computer Science and Information SystemUniversiti TeknologiMalaysia
  2. 2.Department of Marine Technology, Faculty of Mechanical EngineeringUniversiti TeknologiMalaysia

Personalised recommendations