Skip to main content
SpringerLink
Log in
Book cover

Nature-Inspired Computation in Engineering pp 151–175Cite as

Nature-Inspired Swarm Intelligence for Data Fitting in Reverse Engineering: Recent Advances and Future Trends

  • Chapter
  • First Online:

Part of the book series: Studies in Computational Intelligence ((SCI,volume 637))

Abstract

This chapter discusses the very important issue of data fitting with curves and surfaces in reverse engineering. In this problem, given a (usually massive) cloud of (generally noisy) data points, the goal is to approximate its underlying structure through a parametric free-form curve or surface. The process begins with the conversion of this problem from the purely geometric approach based on the point cloud to the mathematical formulation of this problem as a nonlinear continuous optimization problem. Furthermore, this problem is generally multimodal and of a very high dimension, and exhibits challenging features such as noisy data and/or irregular sampling, making it hard (if not impossible) to be properly addressed by traditional mathematical optimization techniques. In this chapter, we claim that this curve/surface data fitting problem can be successfully addressed by following a nature-inspired computational intelligence approach. To focus our discussion, we consider three recent nature-inspired swarm intelligence approaches: firefly algorithm, cuckoo search algorithm, and bat algorithm. We briefly discuss how these methods can be applied to tackle this issue. Some examples of application recently reported in the literature are briefly described. Finally, we envision some future trends and promising lines of research in the field.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Barnhill, R.E.: Geometric Processing for Design and Manufacturing. SIAM, Philadelphia (1992)

    Book  MATH  Google Scholar 

  2. Pottmann, H., Leopoldseder, S., Hofer, M., Steiner, T., Wang, W.: Industrial geometry: recent advances and applications in CAD. Comput. Aided Des. 37, 751–766 (2005)

    Article  Google Scholar 

  3. Farin, G.: Curves and surfaces for CAGD, 5th edn. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  4. Patrikalakis, N.M., Maekawa, T.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  5. Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, Oxford (1993)

    MATH  Google Scholar 

  6. Powell, M.J.D.: Curve fitting by splines in one variable. In: Hayes, J.G. (ed.) Numerical Approximation to Functions and Data. Athlone Press, London (1970)

    Google Scholar 

  7. Park, H.: An error-bounded approximate method for representing planar curves in B-splines. Comput. Aided Geom. Des. 21, 479–497 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wang, W.P., Pottmann, H., Liu, Y.: Fitting B-spline curves to point clouds by curvature-based squared distance minimization. ACM Trans. Graphics 25(2), 214–238 (2006)

    Article  Google Scholar 

  9. Park, H., Lee, J.H.: B-spline curve fitting based on adaptive curve refinement using dominant points. Comput. Aided Des. 39, 439–451 (2007)

    Google Scholar 

  10. Barhak, J., Fischer, A.: Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques. IEEE Trans. Visual. Comput. Graphics 7(1), 1–16 (2001)

    Google Scholar 

  11. Gu, P., Yan, X.: Neural network approach to the reconstruction of free-form surfaces for reverse engineering. Comput. Aided Des. 27(1), 59–64 (1995)

    Article  Google Scholar 

  12. Hoffmann, M.: Numerical control of Kohonen neural network for scattered data approximation. Numer. Algorithms 39, 175–186 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kumar, S.G., Kalra, P.K., Dhande, S.G.: Curve and surface reconstruction from points: an approach based on self-organizing maps. Appl. Soft Comput. 5(5), 55–66 (2004)

    Google Scholar 

  14. Yu, Y.: Surface reconstruction from unorganized points using self-organizing neural networks. Proc. IEEE Vis. 99, 61–64 (1999)

    Google Scholar 

  15. Iglesias, A., Gálvez, A.: A new artificial intelligence paradigm for computer aided geometric design. Lect. Notes Artif. Intell. 2001, 200–213 (1930)

    MATH  Google Scholar 

  16. Iglesias, A., Gálvez, A.: Hybrid functional-neural approach for surface reconstruction. Math. Prob. Eng. 351648, 13 (2014)

    Google Scholar 

  17. Echevarría, G., Iglesias, A., Gálvez, A.: Extending neural networks for B-spline surface reconstruction. Lect. Notes Comput. Sci. 2330, 305–314 (2002)

    Article  MATH  Google Scholar 

  18. Iglesias, A., Echevarría, G., Gálvez, A.: Functional networks for B-spline surface reconstruction. Future Gener. Comput. Syst. 20(8), 1337–1353 (2004)

    Article  MATH  Google Scholar 

  19. Iglesias, A., Gálvez, A.: Curve fitting with RBS functional networks. In: Proceedings of International Conference on Convergence Information Technology-ICCIT’2008, Busan (Korea), pp. 299–306. IEEE Computer Society Press, Los Alamitos, California (2008)

    Google Scholar 

  20. Sarfraz, M., Raza, S.A.: Capturing outline of fonts using genetic algorithms and splines. In: Proceedings of Fifth International Conference on Information Visualization IV’2001, pp. 738–743. IEEE Computer Society Press (2001)

    Google Scholar 

  21. Gálvez, A., Iglesias, A., Puig-Pey, J.: Iterative two-step genetic-algorithm method for efficient polynomial B-spline surface reconstruction. Inf. Sci. 182(1), 56–76 (2012)

    Article  MathSciNet  Google Scholar 

  22. Yoshimoto, F., Harada, T., Yoshimoto, Y.: Data fitting with a spline using a real-coded algorithm. Comput. Aided Des. 35, 751–760 (2003)

    Article  Google Scholar 

  23. Gálvez, A., Cobo, A., Puig-Pey, J., Iglesias, A.: Particle swarm optimization for Bézier surface reconstruction. Lect. Notes Comput. Sci. 5102, 116–125 (2008)

    Article  Google Scholar 

  24. Gálvez, A., Iglesias, A.: Efficient particle swarm optimization approach for data fitting with free knot B-splines. Comput. Aided Des. 43(12), 1683–1692 (2011)

    Article  Google Scholar 

  25. Gálvez, A., Iglesias, A.: Particle swarm optimization for non-uniform rational B-spline surface reconstruction from clouds of 3D data points. Inf. Sci. 192(1), 174–192 (2012)

    Article  Google Scholar 

  26. Loucera, C., Gálvez, A., Iglesias, A.: Simulated annealing algorithm for Bézier curve approximation. In: Proceedings of Cyberworlds 2014, pp. 182–189. IEEE Computer Society Press, Los Alamitos, CA (2014)

    Google Scholar 

  27. Jing, L., Sun, L.: Fitting B-spline curves by least squares support vector machines. In: Proceedings of the 2nd International Conference on Neural Networks & Brain, pp. 905–909. IEEE Press, Beijing (China) (2005)

    Google Scholar 

  28. Gálvez A., Iglesias A., Avila, A.: Immunological-based approach for accurate fitting of 3D noisy data points with Bézier surfaces. In: Proceedings of the Internation Conference on Computer Science-ICCS’2013. Procedia Computer Science, vol. 18, pp. 50–59 (2013)

    Google Scholar 

  29. Gálvez, A., Iglesias, A., Avila, A.: Applying clonal selection theory to data fitting with rational Bézier curves. In: Proceedings of the Cyberworlds 2014. IEEE Computer Society Press. Los Alamitos, CA, 221–228 (2014)

    Google Scholar 

  30. Gálvez, A., Iglesias, A., Avila, A., Otero, C., Arias, R., Manchado, C.: Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting. Appl. Soft Comput. 26, 90–106 (2015)

    Article  Google Scholar 

  31. Zhao, X., Zhang, C., Yang, B., Li, P.: Adaptive knot adjustment using a GMM-based continuous optimization algorithm in B-spline curve approximation. Comput. Aided Des. 43, 598–604 (2011)

    Google Scholar 

  32. Gálvez, A., Iglesias, A., Cabellos, L.: Tabu search-based method for Bézier curve parameterization. Int. J. Softw. Eng. Appl. 7(5), 283–296 (2013)

    Google Scholar 

  33. Keller, R.E., Banshaf, W., Mehnen, J., Weinert, K: CAD surface reconstruction from digitized 3D point data with a genetic programming/evolution strategy hybrid. In: Advances in Genetic Programming 3, pp. 41–65. MIT Press, Cambridge, MA, USA (1999)

    Google Scholar 

  34. Gálvez A., Iglesias A., New memetic self-adaptive firefly algorithm for continuous optimization. Int. J. Bio-Inspired Comput. (in press)

    Google Scholar 

  35. Gálvez, A., Iglesias, A.: A new iterative mutually-coupled hybrid GA-PSO approach for curve fitting in manufacturing. Appl. Soft Comput. 13(3), 1491–1504 (2013)

    Article  Google Scholar 

  36. Gálvez, A., Iglesias, A., Cobo, A., Puig-Pey, J., Espinola, J.: Bézier curve and surface fitting of 3D point clouds through genetic algorithms, functional networks and least-squares approximation. Lect. Notes Comput. Sci. 4706, 680–693 (2007)

    Article  Google Scholar 

  37. Engelbretch, A.P.: Fundam. Comput. Swarm Intell. Wiley, Chichester (2005)

    Google Scholar 

  38. Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)

    Google Scholar 

  39. Mitchell, M.: An Introduction to Genetic Algorithms (Complex Adaptive Systems). MIT Press (1998)

    Google Scholar 

  40. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley (1989)

    Google Scholar 

  41. Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  42. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp. 1942–1948. Perth, Australia (1995)

    Google Scholar 

  43. Yang, X.S.: Nature-Inspired Metaheuristic Algorithms, 2nd edn. Luniver Press, Frome (2010)

    Google Scholar 

  44. Yang, X.S.: Engineering Optimization: An Introduction with Metaheuristic Applications. Wiley, New Jersey (2010)

    Book  Google Scholar 

  45. Yang, X.S.: Firefly algorithms for multimodal optimization. Lect. Notes Comput. Sci. 5792, 169–178 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  46. Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2(2), 78–84 (2010)

    Article  Google Scholar 

  47. Yang, X.S., Deb, S.: Cuckoo search via Lévy flights. In: Proceedings fo the World Congress on Nature & Biologically Inspired Computing (NaBIC), pp. 210–214. IEEE (2009)

    Google Scholar 

  48. Yang, X.S., Deb, S.: Engineering optimization by cuckoo search. Int. J. Math. Model. Numer. Optim. 1(4), 330–343 (2010)

    MATH  Google Scholar 

  49. Yang, X.S.: A new metaheuristic bat-inspired algorithm. In: Gonzalez, J.R. et al. (eds.) Nature Inspired Cooperative Strategies for Optimization (NISCO 2010). Studies in Computational Intelligence, vol. 284, pp. 65–74. Springer, Berlin (2010)

    Google Scholar 

  50. Yang, X.S., Gandomi, A.H.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29(5), 464–483 (2012)

    Article  Google Scholar 

  51. Yang, X.S.: Bat algorithm: literature review and applications. Int. J. Bio-Inspired Comput. 5(3), 141–149 (2013)

    Article  Google Scholar 

  52. Yang, X.S.: Bat algorithm for multiobjective optimization. Int. J. Bio-Inspired Comput. 3(5), 267–274 (2011)

    Article  Google Scholar 

  53. Gálvez A., Iglesias A.: Firefly algorithm for Bézier curve approximation. In: Proceedings of International Conference on Computational Science and Its Applications—ICCSA’2013. IEEE Computer Society Press, pp. 81–88 (2013)

    Google Scholar 

  54. Gálvez A., Iglesias A.: Cuckoo search with Lévy flights for weighted Bayesian energy functional optimization in global-support curve data fitting. Sci. World J. 138760, 11 (2014)

    Google Scholar 

  55. Iglesias, A., Gálvez, A., Collantes, M.: Bat algorithm for curve parameterization in data fitting with polynomial Bézier curves. In: Proceedings of Cyberworlds 2015, pp. 107–114. IEEE Computer Society Press, Los Alamitos, CA (2015)

    Google Scholar 

  56. Iglesias, A., Gálvez, A.: Memetic firefly algorithm for data fitting with rational curves. In: Proceedings of Congress on Evolutionary Computation-CEC’2015, Sendai (Japan), pp. 507–514. IEEE CS Press, CA (2015)

    Google Scholar 

  57. Iglesias, A., Gálvez, A., Collantes, M.: Global-support rational curve method for data approximation with bat algorithm. In: Proceedings of AIAI’2015, Bayonne (France). IFIP AICT, vol. 458, pp. 191–205 (2015)

    Google Scholar 

  58. Gálvez A., Iglesias A.: Firefly algorithm for polynomial Bézier surface parameterization. J. Appl. Math. 237984, 9 (2013)

    Google Scholar 

  59. Iglesias, A., Gálvez, A., Collantes, M.: A bat algorithm for polynomial Bezier surface parameterization from clouds of irregularly sampled data points. In: Proceedings of ICNC2015, Zhangjiajie (China) pp. 1034–1039. IEEE Computer Society Press, Los Alamitos CA (2015)

    Google Scholar 

  60. Gálvez A., Iglesias A.: From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM. Sci. World J. 283919, 10 (2013)

    Google Scholar 

  61. Gálvez A., Iglesias A.: Firefly algorithm for explicit B-Spline curve fitting to data points. Math. Probl. Eng. 528215, 12 (2013)

    Google Scholar 

  62. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)

    Article  Google Scholar 

  63. Gálvez, A., Iglesias, A., Puig-Pey, J.: Computing parallel curves on parametric surfaces. Appl. Math. Model. 38, 2398–2413 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  64. Puig-Pey, J., Gálvez, A., Iglesias, A.: Helical curves on surfaces for computer-aided geometric design and manufacturing. Lect. Notes Comput. Sci. 3044, 771–778 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  65. Puig-Pey, J., Gálvez, A., Iglesias, A.: Some applications of scalar and vector fields to geometric processing of surfaces. Comput. Graphics 29(5), 723–729 (2005)

    Article  Google Scholar 

  66. Puig-Pey, J., Gálvez, A., Iglesias, A., Corcuera, P., Rodríguez, J.: Some problems in geometric processing of surfaces. In: Advances in Mathematical and Statistical Modeling (Series: Statistics for Industry and Technology, SIT), pp. 293–304. Birkhauser, Boston (2008)

    Google Scholar 

  67. Puig-Pey, J., Gálvez, A., Iglesias, A., Rodríguez, J., Corcuera, P., Gutiérrez, F.: Polar isodistance curves on parametric surfaces. Lect. Notes Comput. Sci. 2330, 161–170 (2002)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University (Funabashi, Japan), and the University of Cantabria (Santander, Spain). The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. A special recognition is also owe to Prof. Xin-She Yang for his kind assistance during the process of dealing with the methods described in this chapter and the very helpful material he provided us during several stages of this work.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de Los Castros, s/n, E-39005, Santander, Spain

    Andrés Iglesias & Akemi Gálvez

  2. Department of Information Science, Faculty of Sciences, Narashino Campus, Toho University, 2-2-1 Miyama, Funabashi, 274-8510, Japan

    Andrés Iglesias

Authors
  1. Andrés Iglesias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akemi Gálvez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrés Iglesias .

Editor information

Editors and Affiliations

  1. School of Science and Technology, Middlesex University, London, United Kingdom

    Xin-She Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Iglesias, A., Gálvez, A. (2016). Nature-Inspired Swarm Intelligence for Data Fitting in Reverse Engineering: Recent Advances and Future Trends. In: Yang, XS. (eds) Nature-Inspired Computation in Engineering. Studies in Computational Intelligence, vol 637. Springer, Cham. https://doi.org/10.1007/978-3-319-30235-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30235-5_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30233-1

  • Online ISBN: 978-3-319-30235-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation