The Calculation of Parametric NURBS Surface Interval Values Using Neural Networks

  • Erkan Ülker
  • Ahmet Arslan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)


Three dimensional coordinate values of parametric NURBS (Non-Uniform Rational B-Splines) surfaces are obtained from two dimensional parameters u and v. An approach for generating surfaces produces a model by giving a fixed increase to u and v values. However, the ratio of three dimensional parameters increases and fixed increase of u and v values is not always the same. This difference of ratio costs unrequired sized breaks. In this study an artificial neural network method for simulation of a NURBS surface is proposed. Free shaped NURBS surfaces and various three dimensional object simulations with different patches can be produced using a method projected as network training with respect to coordinates which are found from interval scaled parameters. Experimental results show that this method in imaging modeled surface can be used as a simulator.


Artificial Neural Network Computer Graphic Artificial Neural Network Model NURBS Curve Artificial Neural Network 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.
    Zeid, İ.: CAD/CAM Theory and Practice. McGraw-Hill, New York (1991)Google Scholar
  2. 2.
    Shim, H., Suh, E.: Contact treatment algorithm for the trimmed NURBS surface. Journal of Materials Processing Technology 104, 200–206 (2000)CrossRefGoogle Scholar
  3. 3.
    Hearn, D.: Computer graphics. Prentice Hall, New Jersey (1994)zbMATHGoogle Scholar
  4. 4.
    Aziguli, W., Goetting, M., Zeckzer, D.: Approximation of NURBS curves and surfaces using adaptive equidistant parameterizations. Tsinghua Science&Technology 10, 316–322 (2005)CrossRefGoogle Scholar
  5. 5.
    Che, X., Liang, X., Li, Q.: G1 continuity conditions of adjacent NURBS surfaces. Computer Aided Geometric Design 22, 285–298 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Yang, J., Abdel-Malek, K.: Approximate swept volumes of NURBS surfaces or solids. Computer Aided Geometric Design 22, 1–26 (2004)MathSciNetGoogle Scholar
  7. 7.
    Ma, W., But, W.-C., He, P.: NURBS based adaptive slicing for efficient rapid prototyping. Computer Aided Geometric Design 36, 1309–1325 (2004)Google Scholar
  8. 8.
    Yau, H.-T., Kuo, M.-J.: NURBS machining and feed rate adjustment for high-speed cutting of complex sculptured surfaces. International Journal of Production Research, Taylor & Francis 39 (2001)Google Scholar
  9. 9.
    Kumar, S., Manocha, D., Lastra, A.: Interactive display of large NURBS models, IEEE Transactions on Visualization and Computer Graphics 2, 323–336 (1996)Google Scholar
  10. 10.
    Wang, Q., Hua, W., Li, G., Bao, H.: Generalized NURBS curves and surfaces, Geometric Modeling and Processing. In: Proceedings, pp. 365–368 (2004)Google Scholar
  11. 11.
    Hatna, A., Grieve, B.: Cartesian machining versus parametric machining: a comparative study. International Journal of Production Research, Taylor & Francis 38 (2000)Google Scholar
  12. 12.
    Piegl, L., Tiller, W.: Geometry-based triangulation of trimmed NURBS Surfaces. Computer Aided Design 30(1), 11–18 (1998)CrossRefGoogle Scholar
  13. 13.
    Castillo, E., Iglesias, A., Gutiérrez, J.M., Alvarez, E.,, J.I.: Functional Networks. In: An application to fitting surfaces, World Multiconference on Systemics, Cybernetics and Informatics, Proceedings of the ISAS 1998 Fourth International Conference on Information Systems, Analysis and Synthesis, vol. 2, pp. 579–586 (1998)Google Scholar
  14. 14.
    Iglesias, A., Galvez, A.: Applying Functional Networks to CAGD: the Tensor Product Surface Problem. In: Fourth International Conference on Computer Graphics and Artificial Intelligence, pp. 105–115 (2000)Google Scholar
  15. 15.
    Iglesias, A., Galvez, A.: Fitting 3D data points by extending the neural networks paradigm. In: Computational Methods and Experimental Measurements. Series: Computational Engineering, vol. 3, pp. 809–818. WIT Press /Computational Mechanics Publications, Southampton (2001)Google Scholar
  16. 16.
    Iglesias, A., Gálvez, A.: Applying Functional Networks to Fit Data Points From B-spline Surfaces, Fitting 3D data points by extending the neural networks paradigm. In: Proceedings of the Computer Graphics International, CGI 2001, Hong-Kong, China, pp. 329–332. IEEE Computer Society Press, Los Alamitos (2001)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Iglesias, A., Echevarria, G., Galvez, A.: Functional Networks for B-spline Surface Reconstruction, Future Generation Computer Systems. Special Issue on Computer Graphics and Geometric Modeling 20(8), 1337–1353 (2004)Google Scholar
  19. 19.
    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
  20. 20.
    Mishkoff, H.C.: Understanding Artificial Intelligence. Radio Shack (1986)Google Scholar
  21. 21.
    Gevarter, W.B.: Intelligence Machines: An Introductory. Prentice-Hall, Englewood Cliffs (1985)Google Scholar
  22. 22.
    Hoffman, M., Varady, L.: Free-form surfaces for scattered data by neural networks. Journal for Geometry and Graphics 2, 1–6 (1998)MathSciNetGoogle Scholar
  23. 23.
    Iglesias, A., Gálvez, A.: A new artificial intelligence paradigm for computer-aided geometric design. In: Campbell, J., Roanes-Lozano, E. (eds.) AISC 2000. LNCS (LNAI), vol. 1930, pp. 200–213. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  24. 24.
    Les, P.: On NURBS: A Survey. IEEE Computer Graphics and Applications 11(1), 55–71 (1991)CrossRefGoogle Scholar
  25. 25.
    Rogers David, F., Earnshaw, R.A. (eds.): State of the Art in Computer Graphics - Visualization and Modeling, pp. 225–269. Springer, New York (1991)zbMATHGoogle Scholar
  26. 26.
    de Boor, C.: A Practical Guide to Splines. Springer, New York (1978)zbMATHGoogle Scholar
  27. 27.
    Alan, W., Mark, W.: Advanced Animation and Rendering Techniques. AMC press Addision-Wesley, New York (1992)Google Scholar
  28. 28.
    Foley James, D., et al.: Introduction to Computer Graphics. Addision-Wesley, London (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Erkan Ülker
    • 1
  • Ahmet Arslan
    • 1
  1. 1.Computer Engineering DepartmentSelçuk UniversityKonyaTurkey

Personalised recommendations