Gravitational Search Algorithm for NURBS Curve Fitting
Abstract
By providing great flexibility non-uniform rational B-spline (NURBS) curves and surfaces are reason of preferability on areas like computer aided design, medical imaging and computer graphics. Knots, control points and weights provide this flexibility. Computation of these parameters makes the problem as a non-linear combinational optimization problem on a process of reverse engineering. The ability of solving these problems using meta-heuristics instead of conventional methods attracts researchers. In this paper, NURBS curve estimation is carried out by a novel optimization method namely gravitational search algorithm. Both knots and knots together weights simultaneous optimization process is implemented by using research agents. The high performance of the proposed method on NURBS curve fitting is showed by obtained results.
Keywords: Non-uniform rational B-spline, gravitational search algorithm, meta-heuristic
References
[1] Prochazkova, J., Prochazka, D., ” An Influence of Parameters on the Shape of NURBS Surfaces”, p. xxx, 2005.
[2] Leal, N.E., Lobo, O.O., Branch, J.W., ”Improving NURBS Surface Sharp Feature Representation”, Int. J. of Computational Intelligence Research, Vol 3(2), pp. 131-138, 2007.
[3] Hoffman, M., Varady, L., “Free-form curve design by neural networks”, Acta Acad. Paed. Agriensis, 24, pp. 99-104, 1997.
[4] Hoffmann, M., “Modified Kohonen Neural Network for Surface Reconstruction”, Publ. Math., 54 suppl., 857-764., 1999.
[5] Hoffmann, M., “Numerical control of Kohonen neural network for scattered data approximation”, Numerical Algorithms, Vol. 39, pp. 175-186, (2005).
[6] Fernand S. Cohen, Walid Ibrahim, Chuchart Pintavirooj, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22, No. 6, pp. 642-648, 2000.
[7] Juhász, I., “Weight-based shape modification of NURBS curves”, Computer Aided Geometric Design, Vol. 16, pp. 377-383, 1999.
[8] Piegl, L., Tiller, W., “The NURBS Book”, Springer-Verlag, Berlin, 1995.
[9] Piegl, L.A., Tiller, W., “Reducing Control Points in Surface Interpolation”, IEEE Computer Graphics and Applications, Vol. 20(5), pp. 70-74, 2000.
[10] Prahasto, T., Bedi, S., “Optimization of Knots for the Multi Curve B-spline Approximation”, IEEE conference on geometric modeling and processing, Hong Kong, China, 2000.
[11] Pottman, H., Leopoldseder, S., Hofer, M., “Approximation with Active B-spline curves and surfaces”, Proc. of 10th Pasific Conf. On Computer Graphics and Applications (PG’02), pp. 8-25, 2002.
[12] Lee, S.-M., Abbott, A.L., Clark, N.A., Araman, P.A., “Cpline curve matching with sparse knot sets: Applications to deformable shape detection and recognition”, Proc. of the 29th Annual Conf. Of the IEEE Industrial Electronics Society, Virginia, USA, pp. 1808-1813, 2003.
[13] Hongwei, L., Guojin, W., Chenshi, D., “Constructing Iterative Non-Uniform B-spline Curve and Surface to Fit Data Points”, Science In China Series F: Information Sciences, Vol.47 No.3, pp.315-331, 2004.
[14] Sarfraz, M., Raza, S.A., and Baig, M.H., “Computing Optimized Curves with NURBS Using Evolutionary Intelligence”, Lecture Notes in Computer Science, Volume 3480, pp. 806-815, 2005.
[15] Sarfraz, M., Raza, S.A.,”Capturing Outline of Fonts using Genetic Algorithm and Splines”, The Proc. of IEEE Int. Conf. On Information Visualization-IV’2001-UK, IEEE Computer Society Press, USA, pp. 738-743, 2001.
[16] Ibrahim, A. R., Shamsuddin, A. M., Ali, A., ”Improving Non-Uniform Rational B- splines’ Knot Removal with Particle Swarm Optimization”, Proc. of Sixth Interna- tional Conference on Computer Graphics, Imaging and Visualization, p. 24-27, 2009.
[17] Kim, T.W., Lee, K., ”Weight Control and Knot Placement for Rational B-spline Curve Interpolation”, KSME International Journal, Vol. 15(2), pp. 192-198, 2001.
[18] Goldenthal, R., Bercovier, M., “Spline Curve Approximation and Design by Optimal Control Over the Knots”, Computing Vol. 72, pp 53-64, 2004.
[19] Sarfraz, M. and Riyazuddin, M., “Curve Fitting with NURBS using Simulated Annealing”, Applied Soft Computing Technologies: The Challenge of Complexity, Series: Advances in Soft Computing, A. Abraham, B. De Baets, M. Köppen and B. Nickolay (Eds.), ISBN 3-540-31649-3, XXXIII, Springer Verlag, 2006.
[20] Sarfraz, M., Riyazuddin, M., Baig, M.H., “Capturing Planar Shapes by Approximating their Outlines”, Journal of Computational and Applied Mathematics, Vol. 189, pp. 494-512, 2006.
[21] Sarfraz, M., Riyazuddin, M., Baig, M.H., “Evolutionary Approach For Data Visualiza- tion”, Book series: Computational Imaging and Vision, Vol. 32, pp. 1094-1099, 2006.
[22] Jing, Z., Shaowei, F., Hanguo, C., ” Optimized NURBS Curve and Surface Fitting using Simulated Annealing”, Proc. of Second International Symposium on Computational Intelligence and Design (ISCID), p. 324-329, 2009.
[23] Adi, D.I.S., Shamsuddin, S.M., Ali, A., ” Particle Swarm Optimization for NURBS Curve fitting”, Proc. of Sixth International Conference on Computer Graphics, Imaging and Visualization (CGIV), p. 259-263, 2009.
[24] Sarfraz, M., “Computer-Aided Reverse Engineering using Simulated Evolution on NURBS”, International Journal of Virtual & Physical Prototyping, Taylor & Francis, Vol. 1(4), pp. 243 – 257, 2006.
[25] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, “GSA: A gravitational search algo- rithm”, Information Sciences, vol. 179, pp. 2232-2248, 2009.