Particle Swarm Optimization for Bézier Surface Reconstruction

  • Akemi Gálvez
  • Angel Cobo
  • Jaime Puig-Pey
  • Andrés Iglesias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5102)


This work concerns the issue of surface reconstruction, that is, the generation of a surface from a given cloud of data points. Our approach is based on a metaheuristic algorithm, the so-called Particle Swarm Optimization. The paper describes its application to the case of Bézier surface reconstruction, for which the problem of obtaining a suitable parameterization of the data points has to be properly addressed. A simple but illustrative example is used to discuss the performance of the proposed method. An empirical discussion about the choice of the social and cognitive parameters for the PSO algorithm is also given.


Particle Swarm Optimization Particle Swarm Particle Swarm Optimization Algorithm Surface Reconstruction Particle Swarm Optimization Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Barhak, J., Fischer, A.: Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques. IEEE Trans. on Visualization and Computer Graphics 7(1), 1–16 (2001)CrossRefGoogle Scholar
  2. 2.
    Bradley, C., Vickers, G.W.: Free-form surface reconstruction for machine vision rapid prototyping. Optical Engineering 32(9), 2191–2200 (1993)CrossRefGoogle Scholar
  3. 3.
    Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43 (1995)Google Scholar
  4. 4.
    Eberhart, R.C., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 Congress on Evolutionary Computation, pp. 81–86 (2001)Google Scholar
  5. 5.
    Echevarría, G., Iglesias, A., Gálvez, A.: Extending neural networks for B-spline surface reconstruction. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) ICCS-ComputSci 2002. LNCS, vol. 2330, pp. 305–314. Springer, Heidelberg (2002)Google Scholar
  6. 6.
    El-Mounayri, H., Kishawy, H., Tandon, V.: Optimized CNC end-milling: a practical approach. International Journal of Computer Integrated Manufacturing 15(5), 453–470 (2002)CrossRefGoogle Scholar
  7. 7.
    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. In: Gervasi, O., Gavrilova, M.L. (eds.) ICCSA 2007, Part II. LNCS, vol. 4706, pp. 680–693. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Gu, P., Yan, X.: Neural network approach to the reconstruction of free-form surfaces for reverse engineering. Computer Aided Design 27(1), 59–64 (1995)CrossRefGoogle Scholar
  9. 9.
    Hoffmann, M., Varady, L.: Free-form surfaces for scattered data by neural networks. J. Geometry and Graphics 2, 1–6 (1998)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proc. of SIGGRAPH 1992, vol. 26(2), pp. 71–78 (1992)Google Scholar
  11. 11.
    Iglesias, A., Gálvez, A.: A new artificial intelligence paradigm for computer aided geometric design. In: Campbell, J.A., Roanes-Lozano, E. (eds.) AISC 2000. LNCS (LNAI), vol. 1930, pp. 200–213. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Iglesias, A., Echevarría, G., Gálvez, A.: Functional networks for B-spline surface reconstruction. Future Generation Computer Systems 20(8), 1337–1353 (2004)CrossRefGoogle Scholar
  13. 13.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942–1948 (1995)Google Scholar
  14. 14.
    Kennedy, J.: The particle swarm: social adaptation of knowledge. In: IEEE International Conference on Evolutionary Computation, Indianapolis, Indiana, USA, pp. 303–308 (1997)Google Scholar
  15. 15.
    Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  16. 16.
    Knopf, G.K., Kofman, J.: Free-form surface reconstruction using Bernstein basis function networks. In: Dagli, C.H., et al. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks, vol. 9, pp. 797–802. ASME Press (1999)Google Scholar
  17. 17.
    Pottmann, H., Leopoldseder, S., Hofer, M., Steiner, T., Wang, W.: Industrial geometry: recent advances and applications in CAD. Computer-Aided Design 37, 751–766 (2005)CrossRefGoogle Scholar
  18. 18.
    Varady, T., Martin, R.: Reverse Engineering. In: Farin, G., Hoschek, J., Kim, M. (eds.) Handbook of Computer Aided Geometric Design. Elsevier, Amsterdam (2002)Google Scholar
  19. 19.
    Vaz, I.F., Vicente, L.N.: A particle swarm pattern search method for bound constrained global optimization. Journal of Global Optimization 39, 197–219 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Weiss, V., Andor, L., Renner, G., Varady, T.: Advanced surface fitting techniques. Computer Aided Geometric Design 19, 19–42 (2002)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Akemi Gálvez
    • 1
  • Angel Cobo
    • 1
  • Jaime Puig-Pey
    • 1
  • Andrés Iglesias
    • 1
  1. 1.Department of Applied Mathematics and Computational SciencesUniversity of CantabriaSantanderSpain

Personalised recommendations