Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 924839, 10 pages
http://dx.doi.org/10.5402/2012/924839
Research Article

A New 5-Point Ternary Interpolating Subdivision Scheme and Its Differentiability

Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Received 25 July 2012; Accepted 18 September 2012

Academic Editors: L. Hajdu, L. Pan, and Q.-W. Wang

Copyright © 2012 Ghulam Mustafa et al. 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.

Linked References

  1. S. Dubuc, “Interpolation through an iterative scheme,” Journal of Mathematical Analysis and Applications, vol. 114, no. 1, pp. 185–204, 1986. View at Google Scholar · View at Scopus
  2. N. Dyn, D. Levin, and J. A. Gregory, “A 4-point interpolatory subdivision scheme for curve design,” Computer Aided Geometric Design, vol. 4, no. 4, pp. 257–268, 1987. View at Google Scholar · View at Scopus
  3. G. Deslauriers and S. Dubuc, “Symmetric iterative interpolation processes,” Constructive Approximation, vol. 5, no. 1, pp. 49–68, 1989. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Weissman, A 6-point interpolatory subdivision scheme for curve design [M.S. thesis], Tel-Aviv University, Tel Aviv, Israel, 1990.
  5. M. F. Hassan, I. P. Ivrissimitzis, N. A. Dodgson, and M. A. Sabin, “An interpolating 4-point C2 ternary stationary subdivision scheme,” Computer Aided Geometric Design, vol. 19, no. 1, pp. 1–18, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. M. F. Hassan and N. A. Dodgson, “Ternary three point univariate subdivision scheme,” in Curve and Surface Fitting: Saint-Malo, A. Cohen, J. Laouis Merrien, and L. L. Schumaker, Eds., pp. 199–208, 2002. View at Google Scholar
  7. M. F. Hassan and N. A. Dodgson, “Further analysis of ternary three point univariate subdivision scheme,” Tech. Rep. 599, University of Cambridge Computer Laboratory, 2004. View at Google Scholar
  8. N. Dyn, Tutorials on Multiresolution in Geometric Modelling, Summer School Lecture Notes Series: Mathematics and Visualization, Springer, Berlin, Germany, 2002.
  9. C. Beccari, G. Casciola, and L. Romani, “An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control,” Computer Aided Geometric Design, vol. 24, no. 4, pp. 210–219, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. C. Beccari, G. Casciola, and L. Romani, “A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics,” Computer Aided Geometric Design, vol. 24, no. 1, pp. 1–9, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. K. P. Ko, A Study on Subdivision Scheme, Dongseo University, Busan, Republic of Korea, 2007.
  12. H. Zheng, H. Zhao, Z. Ye, and M. Zhou, “Differentiability of four point ternary subdivision scheme and its application, LEANG,” International Journal of Computer Science, vol. 36, no. 1, pp. 1–4, 2007. View at Google Scholar
  13. J.-A. Lian, “On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes,” Application and Applied Mathematics, vol. 3, no. 1, pp. 176–187, 2008. View at Google Scholar
  14. C. Conti, L. Gemignani, and L. Romani, “From symmetric subdivision masks of hurwitz type to interpolatory subdivision masks,” Linear Algebra and Its Applications, vol. 431, no. 10, pp. 1971–1987, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. M. A. Sabin, “Eigenanalysis and artifacts of subdivision curves and surfaces,” in Tutorials on Multiresolution in Geometric Modelling, A. Iske, E. Quak, and M. S. Floater, Eds., chapter 4, pp. 69–92, Springer, Berlin, Germany, 2002. View at Google Scholar