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Extension of B-Spline Curves with G 2 Continuity

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Advances in Visual Computing (ISVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5359))

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Abstract

This paper presents a new method for extending B-Spline curve. Cubic Bézier curve is used to construct the extending segment and G 2 continuity is used to describe the smoothness of joint point. Optimization objective functions are established based on the minimum precise exact energy and the minimum precise curvature variation of the extending curve, respectively. The degree of freedom of the extended curve is determined by minimizing the objective functions. The non-linear optimization can be transform to non-linear least-square problem which can be linearized by a Gauss-Newton iterative algorithm. New control points are computed by extending curve and original curve. The comparison of the curves with different objective functions is included.

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References

  1. Farin, G.: Curves and surfaces for computer aided geometric design[M], 4th edn. Academic Press, San Diego (1997)

    MATH  Google Scholar 

  2. Piegl, L., Tiller, W.: The NURBS book[M], 2nd edn. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  3. Tokuyama, Y., Konno, K.: Reparameterization of piecewise rational Bezier curves and its applications[J]. The Visual Computer 17(6), 329–336 (2001)

    MATH  Google Scholar 

  4. Shetty, S., White, P.R.: Curvature-continuous extensions for rational B-spline curves and surfaces[J]. Computer-Aided Design 23(7), 484–491 (1991)

    Article  MATH  Google Scholar 

  5. Hu, S., Chiew-Lan, Zhang, S.: An extension algorithm for B-splines by curve unclamping[J]. Computer-Aided Design 34(5), 415–419 (2002)

    Article  Google Scholar 

  6. Hartmann, E.: Parametric G n blending of curves and surfaces[J]. The Visual Computer 17(1), 1–13 (2001)

    Article  MATH  Google Scholar 

  7. Kallay, M.: A method to approximate the space curve of minimal energy and prescribed length[J]. Computer-Aided Design 19(2), 73–76 (1987)

    Article  MATH  Google Scholar 

  8. Kjellander, J.A.P.: Smoothing of cubic parametric splines[J]. Computer-Aided Design 15(5), 175–179 (1983)

    Article  Google Scholar 

  9. Lee, E.T.Y.: Energy, fairness and a counterexample[J]. Computer-Aided Design 22(1), 37–40 (1990)

    Article  MATH  Google Scholar 

  10. Poliakoff, J.F.: An improved algorithm for automatic faring of non-uniform parametric cubic splines[J]. Computer-Aided Design 28, 59–66 (1996)

    Article  MATH  Google Scholar 

  11. Kjellander, J.A.P.: Smoothing of bicubic parametric splines[J]. Computer-Aided Design 15(5), 288–293 (1983)

    Article  Google Scholar 

  12. Kaufmann, E., Klass, R.: Smoothing surface using reflection lines for families of splines[J]. Computer-Aided Design 20, 312–326 (1988)

    Article  MATH  Google Scholar 

  13. Holladay, J.D.: Smoothest curve interpolation[J]. Math. Tables Aids Computation 11, 233–243 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, C., Zhang, P., Cheng, F.: Fairing spline curves and surfaces by minimizing energy[J]. Computer-Aided Design 33(13), 913–923 (2001)

    Article  MATH  Google Scholar 

  15. Su, B., Liu, D.: Computational Geometry[M]. Science and Technology Press of Shanghai, Shanghai (1981)

    Google Scholar 

  16. Zhou, Y., Zhang, C.: Extension of the Cubic Bzier Curve with G 2 Constraint[J]. Journal of Computer-Aided Design and Computer Graphics 17(3), 425–430 (2005)

    Google Scholar 

  17. Fan, H., Zhang, C.-M., Li, J.-J.: Extension algorithm for B-splines with GC 2-continuous. Chinese Journal of Computers 28(6), 933–938 (2005)

    MathSciNet  Google Scholar 

  18. Kelley, C.T.: Iterative methods for optimization[M]. Society for Industrial and Applied Mathematics, Philadelphia (1999)

    Book  MATH  Google Scholar 

  19. Carmo, M.P.D.: Differential geometry of curves and surfaces[M]. Prentice-Hall, Englewood Cliffs (1976)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, China

    Yuan-feng Zhou & Cai-ming Zhang

  2. School of Computer Science and Technology, Shandong Economic University, China

    Cai-ming Zhang & Shan-shan Gao

Authors
  1. Yuan-feng Zhou
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  2. Cai-ming Zhang
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  3. Shan-shan Gao
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Mitsubishi Electric Research Laboratories, P.O. Box 02139, Cambridge, MA, USA

    Fatih Porikli

  7. Computer and Information Science and Engineering, University of Florida, P.O. Box, FL 32611-6120, Gainsville, USA

    Jörg Peters

  8. IBM T.J. Watson Research Center, 19 Skyline Drive, NY 10532, Hawthorne, USA

    James Klosowski

  9. 128 Memorial Mall, Stewart B001, IN 47907, West Lafayette, USA

    Laura Arns

  10. Denver Museum of Nature and Space, 2001 Colorade Blvd. Denver,, CO 80205, USA

    Yu Ka Chun

  11. Departmen of Computer Science,, NC State University, Campus Box 8206, NC 27695-8206, Raleigh, USA

    Theresa-Marie Rhyne

  12. Los Alamos National Labs, P.O. Box 1663, NM 87545, Los Alamos, USA

    Laura Monroe

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© 2008 Springer-Verlag Berlin Heidelberg

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Zhou, Yf., Zhang, Cm., Gao, Ss. (2008). Extension of B-Spline Curves with G 2 Continuity. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89646-3_109

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  • DOI: https://doi.org/10.1007/978-3-540-89646-3_109

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89645-6

  • Online ISBN: 978-3-540-89646-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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