- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Numerical Analysis
Volume 2013 (2013), Article ID 858279, 8 pages
Modified Bézier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm
Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh
Received 27 October 2012; Accepted 6 February 2013
Academic Editor: William J. Layton
Copyright © 2013 Mohammad Asif Zaman and Shuvro Chowdhury. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- F. Curtis Gerald and O. Patrick Wheatley, Applied Numerical Analysis, Pearson, 7th edition.
- K. Anastasiou and C. T. Chan, “Automatic triangular mesh generation scheme for curved surfaces,” Communications in Numerical Methods in Engineering, vol. 12, no. 3, pp. 197–208, 1996.
- M. A. Scott, M. J. Borden, C. V. Verhoosel, T. W. Sederberg, and T. J. R. Hughes, “Isogeometric finite element data structures based on Bézier extraction of T-splines,” International Journal for Numerical Methods in Engineering, vol. 88, no. 2, pp. 126–156, 2011.
- W. Wen-tao and W. Guo-zhao, “Bézier curves with shape parameter,” Journal of Zhejiang University Science A, vol. 6, no. 6, pp. 497–501, 2005.
- Q.-B. Wu and F.-H. Xia, “Shape modification of Bézier curves by constrained optimization,” Journal of Zhejiang University Science, vol. 6, no. 1, pp. 124–127, 2005.
- F. A. Sohel, G. C. Karmakar, and L. S. Dooley, “An improved shape descriptor using bezier curves,” in Pattern Recognition and Machine Intelligence, vol. 3776 of Lecture Notes in Computer Science, pp. 401–406, Springer, Berlin, Germany, 2005.
- M. I. Grigor'cprimeev, V. N. Malozemov, and A. N. Sergeev, “Bernstein polynomials and composite Bézier curves,” Journal of Computational Mathematics and Mathematical Physics, vol. 46, no. 11, pp. 1962–1971, 2006.
- G. T. Tachev, “Approximation of a continuous curve by its Bernstein-Bézier operator,” Mediterranean Journal of Mathematics, vol. 8, no. 3, pp. 369–381, 2011.
- L. Yang and X.-M. Zeng, “Bézier curves and surfaces with shape parameters,” International Journal of Computer Mathematics, vol. 86, no. 7, pp. 1253–1263, 2009.
- Q. Chen and G. Wang, “A class of Bézier-like curves,” Computer Aided Geometric Design, vol. 20, no. 1, pp. 29–39, 2003.
- N. F. Fijasri, S. H. Yahaya, and J. M. Ali, “Bézier-like quartic curve with shape control,” in 2nd IMT-GT Regional Conference on Mathematics, Statistics and Applications, pp. 1–6, June 2006.
- W.-Q. Shen and G.-Z. Wang, “A class of quasi Bézier curves based on hyperbolic polynomials,” Journal of Zhejiang University Science, vol. 6, no. 1, pp. 116–123, 2005.
- Ç. Dişibüyük and H. Oruç, “A generalization of rational Bernstein-Bézier curves,” BIT. Numerical Mathematics, vol. 47, no. 2, pp. 313–323, 2007.
- R. Storn and K. Price, “Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.
- K. V. Price, R. M. Storn, and J. A. Lampinen, Differential Evolution—A Practical Approach to Global Optimization, Springer, 2005.
- P. Pandunata and S. M. H. Shamsuddin, “Differential evolution optimization for Bézier curve fitting,” in Proceedings of the 7th International Conference on Computer Graphics, Imaging and Visualization (CGIV '10), pp. 68–72, August 2010.
- T. Rogalsky, “Bézier parameterization for optimal control by differential evolution,” in International Conference on Genetic and Evolutionary Methods, pp. 28–34, July 2011.