- 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
- Submit a Manuscript
- Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 197383, 14 pages
A Family of Even-Point Ternary Approximating Schemes
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
Received 27 July 2012; Accepted 8 September 2012
Academic Editors: L. Ju, F. Lamnabhi-Lagarrigue, G. Psihoyios, H. C. So, and X. Yang
Copyright © 2012 Abdul Ghaffar and Ghulam Mustafa. 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.
- M. F. Hassan and N. A. Dodgson, “Ternary and three-point univariate subdivision schemes,” in Curve and Surface Fitting: Saint-Malo, 2002, A. Cohen, J. L. Marrien, and L. L. Schumaker, Eds., pp. 199–208, Nashboro Press, Brentwood, Calif, USA, 2003.
- M. F. Hassan, I. P. Ivrissimitzis, N. A. Dodgson, and M. A. Sabin, “An interpolating 4-point ternary stationary subdivision scheme,” Computer Aided Geometric Design, vol. 19, no. 1, pp. 1–18, 2002.
- C. Beccari, G. Casciola, and L. Romani, “An interpolating 4-point ternary non-stationary subdivision scheme with tension control,” Computer Aided Geometric Design, vol. 24, no. 4, pp. 210–219, 2007.
- C. Beccari, G. Casciola, and L. Romani, “Shape controlled interpolatory ternary subdivision,” Applied Mathematics and Computation, vol. 215, no. 3, pp. 916–927, 2009.
- G. Deslauriers and S. Dubuc, “Symmetric iterative interpolation processes,” Constructive Approximation, vol. 5, no. 1, pp. 49–68, 1989.
- F. Khan and G. Mustafa, “Ternary six-point interpolating subdivision scheme,” Lobachevskii Journal of Mathematics, vol. 29, no. 3, pp. 153–163, 2008.
- K. P. Ko, B.-G. Lee, and G. J. Yoon, “A ternary 4-point approximating subdivision scheme,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1563–1573, 2007.
- G. Mustafa and F. Khan, “A new 4-point quaternary approximating subdivision scheme,” Abstract and Applied Analysis, vol. 2009, Article ID 301967, 14 pages, 2009.
- J.-A. Lian, “On a-ary subdivision for curve design. I. 4-point and 6-point interpolatory schemes,” Applications and Applied Mathematics, vol. 3, no. 1, pp. 18–29, 2008.
- J.-A. Lian, “On a subdivision for curve design. II. 3-point and 5-point interpolatory schemes,” Applications and Applied Mathematics, vol. 3, no. 2, pp. 176–187, 2008.
- J.-a. Lian, “On a-ary subdivision for curve design. III. 2m-point and -point interpolatory schemes,” Applications and Applied Mathematics, vol. 4, no. 2, pp. 434–444, 2009.
- H. Zheng, M. Hu, and G. Peng, “Constructing 2n-1-point ternary interpolatory subdivision schemes by using variation of constants,” in Proceedings of the International Conference on Computational Intelligence and Software Engineering (CISE '09).
- H. Zheng, M. Hu, and G. Peng, “Ternary even symmetric 2n-point subdivision,” in Proceedings of the International Conference on Computational Intelligence and Software Engineering (CISE '09).
- H. Zheng, M. Hu, and G. Peng, “P-ary subdivision seneralizing B-splines,” in Proceedings of the 2nd International Conference on Computer and Electrical Engineering (ICCEE '09), 2009.
- G. Mustafa and N. A. Rehman, “The mask of -point n-ary subdivision scheme,” Computing. Archives for Scientific Computing, vol. 90, no. 1-2, pp. 1–14, 2010.
- M. A. Sabin and N. A. Dodgson, “A circle-preserving variant of the four-point subdivision scheme,” in Mathematical Methods for Curve and Surfaces. Troms 2004, M. Dhlen, K. Mrken, Schumaker, and L, Eds., Modern Methods in Mathematics, pp. 275–286, Nashboro Press, Brentwood, Calif, USA, 2005.