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G1 Blending B-Spline Surfaces and Optimization

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Book cover Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2008)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 14))

Abstract

Recently, some results on G 1 continuity conditions for two adjacent B-spline surfaces such as bicubic or biquartic B-spline surfaces have been developed in the literature. However, the blending and the optimization problems related to these surfaces were not studied. Then, we give in this paper a method which allows to solve a G 1 blending problem of two B-spline surfaces and an algorithm for finding optimal surfaces.

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References

  1. Bartels, R., Beatty, J., Barsky, B.: An Introduction on Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufman, Los Altos (1987)

    MATH  Google Scholar 

  2. Che, X., Liang, X., Li, Q.: G 1 continuity for adjacent NURBS surfaces. Computer Aided Geometric Design 22(4), 285–298 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Coons, S.: Surface patches and B-spline curves. In: Barnhill, R., Riesenfeld, R. (eds.) Computer Aided Geometric Design, pp. 1–16. Academic Press, London (1974)

    Chapter  Google Scholar 

  4. Du, W.-H., Schmitt, F.: On the G 1 continuity of piecewise Bézier surfaces: a review with new results. Computer Aided Design 22(9), 556–573 (1990)

    Article  MATH  Google Scholar 

  5. Farin, G., Hoschek, J., Kim, M.S.: Handbook of computer aided geometric design. Computer-Aided Design 37 (2005)

    Google Scholar 

  6. Ferguson, D.R.: Construction of curves and surfaces using numerical optimization techniques. Computer-Aided Design 18, 15–21 (1986)

    Article  Google Scholar 

  7. Ferguson, D.R., Frank, P.D., Jones, A.K.: Surface Sharp control using constrained optimization on the B-spline representation. Computer Aided Geometric Design 5, 87–103 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Manning, J.: Continuity conditions for spline curves. The Computer J. 17(2), 181–186 (1974)

    Article  MATH  Google Scholar 

  9. Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, Heidelberg (1997)

    Book  MATH  Google Scholar 

  10. Shi, X., Wang, T., Wu, P., Liu, F.: Reconstruction of convergent G 1 smooth B-spline surfaces. Computer-Aided Geometric Design 21, 893–913 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Szilvasi-Nagy, M.: Shaping and fairning of tubular B-spline surfaces. Computer Aided Design 14, 699–706 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zheng, J., Wang, G., Liang, Y.: GC n continuity conditions for adjacent Bézier patches and their constructions. Computer Aided Geometric Design 13, 521–548 (1995)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Ecole Supérieure de Technologie , Laboratoire MATSI, Université Mohammed I, Oujda, Maroc

    Bachir Belkhatir & Driss Sbibih

  2. Laboratoire de l’Informatique Théorique et Appliquée, UFR Scientifique MIM Université Paul Verlaine-Metz, Ile du Saulcy, 57045, Metz, France

    Ahmeh Zidna

Authors
  1. Bachir Belkhatir
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  2. Driss Sbibih
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  3. Ahmeh Zidna
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Editor information

Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, UFR MIM,, Paul Verlaine University of Metz, Metz, France

    Hoai An Le Thi

  2. Faculty of Sciences, Technology and Communications, University of Luxembourg, Luxembourg

    Pascal Bouvry

  3. Laboratory of Mathematics, National Institute for Applied Sciences, Rouen Mont, Saint Aignan, France

    Tao Pham Dinh

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© 2008 Springer-Verlag Berlin Heidelberg

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Belkhatir, B., Sbibih, D., Zidna, A. (2008). G1 Blending B-Spline Surfaces and Optimization. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2008. Communications in Computer and Information Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87477-5_49

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  • DOI: https://doi.org/10.1007/978-3-540-87477-5_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87476-8

  • Online ISBN: 978-3-540-87477-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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