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Part of the book series: Advances in Soft Computing ((AINSC,volume 34))

Abstract

The global optimization strategy of Simulated Annealing is applied to the optimization of knot parameters of NURBS for curve fitting, the objective being the reduction of fitting error to obtain a smooth curve. This is accomplished by using a unit weight vector and a fixed number of control points calculated using the least squares technique, while the sum of squared errors is taken as the objective function.

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References

  1. Chou J.J. & Piegl L.A. (1992), “Data Reduction Using Cubic Rational B-Splines,” IEEE Computer Graphics & Applications.

    Google Scholar 

  2. Goldberg D.E. (1989), “Genetic Algorithms in Search,” Optimization and Machine Learning, Addisson-Wesley.

    Google Scholar 

  3. Hoffmann M. & Juhasz I (2001), “Shape Control of Cubic B-spline and NURBS Curves by Knot Modifications”, Proceedings of the fifth international conference on information visualizaton (IV′2001)-UK, IEEE Computer Society.

    Google Scholar 

  4. Huang D. & Yan H. (2003), “NURBS Curve Controlled Modelling for Facial Animation,” 27, Computers & Graphics, pp. 373–385.

    Article  Google Scholar 

  5. Kirkpatrick S., Gelatt Jr. C. & Vecchi M. (1983), “Optimization by Simulated Annealing,”, Science, 220(4598): pp. 498–516.

    MathSciNet  Google Scholar 

  6. Limaiem A., Nassef A. & Elmaghraby H.A. (1996), “Data Fitting using Dual Krigging and Genetic Algorithms,” CIRP Annals, Vol. 45, pp. 129–134.

    Article  Google Scholar 

  7. Metropolis N., Roshenbluth A., Rosenbluth M., Teller A. & Teller E. (1953), “Equation of State Calculations by Fast Computing machines,” J. Chem. Phys., Vol.21, No. 6, pp. 1087–1092.

    Article  Google Scholar 

  8. Piegl L. (1991), “On NURBS: A Survey,” IEEE computer graphics & applications, Vol. 11(1): pp. 55–71.

    Article  Google Scholar 

  9. Piegl L., & Tiller W. (1995), “The NURBS Book,” Springer-Verlag, Berlin.

    MATH  Google Scholar 

  10. Pontrandolfo F., Monno G. & Uva A.E. (2001), “Simulated Annealing Vs Genetic Algorithms for Linear Spline Approximation of 2D Scattered Data,” Proc. of XII adm international conference, International Conference on Design Tools and Methods in Industrial Engineering, Rimini, Italy.

    Google Scholar 

  11. Prahasto T. & Bedi S. (2000), “Optimization of Knots for the Multi Curve B- Spline Approximation,” IEEE conference on geometric modeling and processing, Hong Kong, China.

    Google Scholar 

  12. Quddus A. (1998), “Curvature Analysis Using Multi-resolution Techniques,”. PhD Thesis, King Fahd University of Petroleum & Minerals. Dhahran, Saudi Arabia.

    Google Scholar 

  13. Rao S. S. (1999), “Engineering Optimization, Theory and Practice,” John-Wiley and Sons, New York.

    Google Scholar 

  14. Sarfraz, M, and Raza, A, (2002), Visualization of Data using Genetic Algorithm, Soft Computing and Industry: Recent Applications, Eds.: R. Roy, M. Koppen, S. Ovaska, T. Furuhashi, and F. Hoffmann, ISBN: 1-85233-539-4, Springer, 535–544.

    Google Scholar 

  15. Sarfraz, M., and Raza, S. A., (2001), Capturing Outline of Fonts using Genetic Algorithm and Splines, The Proceedings of IEEE International Conference on Information Visualization-IV′2001-UK, IEEE Computer Society Press, USA, 738–743.

    Chapter  Google Scholar 

  16. Sait, S. M. and Youssef, H. (1999), Iterative Computer Algorithms with Applications in Engineering: Solving Combinatorial Optimization Problems, 1st edition, IEEE Computer Society Press Los Alamitos, CA, USA.

    MATH  Google Scholar 

  17. Sarkar B. and Menq C. H. (1991), “Smooth Surface Approximation and Reverse Engineering,” Computer Aided Design, Vol. 23, pp. 623–628.

    Article  MATH  Google Scholar 

  18. Sarkar B. & Menq C. H. (1991), “Parameter Optimization in Approximating Curves and Surfaces to Measurment Data,” Computer Aided Geometric Design, Vol. 8, pp.267–290.

    Article  MATH  MathSciNet  Google Scholar 

  19. Shalaby M. M., Nassef A. O., and Metwalli S. M., (2001), “On the Classification of Fitting Problems for Single Patch Free-Form Surfaces in Reverse Engineering,” Proceedings of the ASME Design Automation Conference, Pittsburgh.

    Google Scholar 

  20. Xie H. & Qin H. (2001), “Automatic Knot Determination of NURBS for Interactive Geometric Design,” IEEE conference on Shape Modelling & Applications, Geneva, Italy.

    Google Scholar 

  21. Yau H. T., and Chen J. S. (1997), “Reverse Engineering of Complex Geometry Using Rational B-Splines,” International Journal of Advanced Manufacturing Technology, Vol. 13, pp. 548–555.

    Article  Google Scholar 

  22. Yoshimoto Y., Moriyama M. and Harada T. (1999), “Automatic Knot Replacement by a Genetic Algorithm for Data Fitting with a Spline” Proceedings of the International Conference on Shape Modeling and Applications, Aizu-Wakamatsu, Japan, pp.162–169.

    Google Scholar 

  23. Youssef A. M. (2001), “Reverse Engineering of Geometric Surfaces using Tabu Search Optimization Technique,” Master Thesis, Cairo University, Egypt.

    Google Scholar 

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Sarfraz, M., Riyazuddin, M. (2006). Curve Fitting with NURBS using Simulated Annealing. In: Abraham, A., de Baets, B., Köppen, M., Nickolay, B. (eds) Applied Soft Computing Technologies: The Challenge of Complexity. Advances in Soft Computing, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31662-0_8

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  • DOI: https://doi.org/10.1007/3-540-31662-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31649-7

  • Online ISBN: 978-3-540-31662-6

  • eBook Packages: EngineeringEngineering (R0)

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