Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2016, Article ID 4875358, 14 pages
http://dx.doi.org/10.1155/2016/4875358
Research Article

Shape Preserving Interpolation Using Rational Cubic Spline

1Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia
2School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Minden, Penang, Malaysia

Received 18 January 2016; Revised 10 April 2016; Accepted 21 April 2016

Academic Editor: Francisco J. Marcellán

Copyright © 2016 Samsul Ariffin Abdul Karim and Kong Voon Pang. 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. F. N. Fritsch and R. E. Carlson, “Monotone piecewise cubic interpolation,” SIAM Journal on Numerical Analysis, vol. 17, no. 2, pp. 238–246, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. L. Dougherty, A. S. Edelman, and J. M. Hyman, “Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation,” Mathematics of Computation, vol. 52, no. 186, pp. 471–494, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Butt and K. W. Brodlie, “Preserving positivity using piecewise cubic interpolation,” Computers and Graphics, vol. 17, no. 1, pp. 55–64, 1993. View at Publisher · View at Google Scholar · View at Scopus
  4. K. W. Brodlie and S. Butt, “Preserving convexity using piecewise cubic interpolation,” Computers and Graphics, vol. 15, no. 1, pp. 15–23, 1991. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Sarfraz, “Visualization of positive and convex data by a rational cubic spline interpolation,” Information Sciences, vol. 146, no. 1–4, pp. 239–254, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. Sarfraz, S. Butt, and M. Z. Hussain, “Visualization of shaped data by a rational cubic spline interpolation,” Computers & Graphics, vol. 25, no. 5, pp. 833–845, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Sarfraz, M. Z. Hussain, and A. Nisar, “Positive data modeling using spline function,” Applied Mathematics and Computation, vol. 216, no. 7, pp. 2036–2049, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. M. Abbas, Shape preserving data visualization for curves and surfaces using rational cubic functions [Ph.D. thesis], School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia, 2012.
  9. M. Z. Hussain and M. Hussain, “Visualization of data subject to positive constraint,” Journal of Information and Computing Sciences, vol. 1, no. 3, pp. 149–160, 2006. View at Google Scholar
  10. M. Z. Hussain, M. Sarfraz, and T. S. Shaikh, “Shape preserving rational cubic spline for positive and convex data,” Egyptian Informatics Journal, vol. 12, no. 3, pp. 231–236, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Sarfraz, M. Z. Hussain, T. S. Shaikh, and R. Iqbal, “Data visualization using shape preserving C2 rational spline,” in Proceeding of 5th International Conference on Information Visualisation, pp. 528–533, London, UK, July 2011. View at Publisher · View at Google Scholar
  12. M. Abbas, A. A. Majid, M. N. H. Awang, and J. M. Ali, “Positivity-preserving C2 rational cubic spline interpolation,” ScienceAsia, vol. 39, no. 2, pp. 208–213, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. R. Delbourgo, “Accurate C2 rational interpolants in tension,” SIAM Journal on Numerical Analysis, vol. 30, no. 2, pp. 595–607, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J. A. Gregory, “Shape preserving spline interpolation,” Computer-Aided Design, vol. 18, no. 1, pp. 53–57, 1986. View at Publisher · View at Google Scholar · View at Scopus
  15. R. Delbourgo and J. A. Gregory, “C2 rational quadratic spline interpolation to monotonic data,” IMA Journal of Numerical Analysis, vol. 3, no. 2, pp. 141–152, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. S. A. A. Karim and K. V. Pang, “Local control of the curves using rational cubic spline,” Journal of Applied Mathematics, vol. 2014, Article ID 872637, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. S. A. A. Karim and K. V. Pang, “Monotonicity-preserving using rational cubic spline interpolation,” Research Journal of Applied Sciences, vol. 9, no. 4, pp. 214–223, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. S. A. A. Karim and V. P. Kong, “Shape preserving interpolation using rational cubic spline,” Research Journal of Applied Sciences, Engineering and Technology, vol. 8, no. 2, pp. 167–168, 2014. View at Google Scholar
  19. S. A. A. Karim and V. P. Kong, “Convexity-preserving using rational cubic spline interpolation,” Research Journal of Applied Sciences, Engineering and Technology, vol. 8, no. 3, pp. 312–320, 2014. View at Google Scholar · View at Scopus
  20. M. Tian, Y. Zhang, J. Zhu, and Q. Duan, “Convexity-preserving piecewise rational cubic interpolation,” Journal of Information and Computational Science, vol. 2, no. 4, pp. 799–803, 2005. View at Google Scholar · View at Scopus
  21. P. Lamberti and C. Manni, “Shape-preserving C2 functional interpolation via parametric cubics,” Numerical Algorithms, vol. 28, no. 1–4, pp. 229–254, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Q. Duan, L. Wang, and E. H. Twizell, “A new C2 rational interpolation based on function values and constrained control of the interpolant curves,” Applied Mathematics and Computation, vol. 161, no. 1, pp. 311–322, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. F. Bao, Q. Sun, and Q. Duan, “Point control of the interpolating curve with a rational cubic spline,” Journal of Visual Communication and Image Representation, vol. 20, no. 4, pp. 275–280, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. J.-C. Fiorot and J. Tabka, “Shape-preserving C2 cubic polynomial interpolating splines,” Mathematics of Computation, vol. 57, no. 195, pp. 291–298, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  25. M. Dube and P. Tiwari, “Convexity preserving C2 rational quadratic trigonometric spline,” in Proceedings of the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM '12), vol. 1479, pp. 995–998, September 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. Y.-J. Pan and G.-J. Wang, “Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter,” Journal of Zhejiang University SCIENCE A, vol. 8, no. 8, pp. 1199–1209, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. F. Ibraheem, M. Hussain, M. Z. Hussain, and A. A. Bhatti, “Positive data visualization using trigonometric function,” Journal of Applied Mathematics, vol. 2012, Article ID 247120, 19 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. M. Sarfraz, M. Z. Hussain, and F. S. Chaudary, “Shape preserving cubic spline for data visualization,” Computer Graphics and CAD/CAM, vol. 1, pp. 185–193, 2005. View at Google Scholar
  29. R. Delbourgo and J. A. Gregory, “The determination of derivative parameters for a monotonic rational quadratic interpolant,” IMA Journal of Numerical Analysis, vol. 5, no. 4, pp. 397–406, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. J. W. Schmidt and W. Hess, “Positivity of cubic polynomials on intervals and positive spline interpolation,” BIT Numerical Mathematics, vol. 28, no. 2, pp. 340–352, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. M. H. Schultz, Spline Analysis, Prentice-Hall, Englewood-Cliffs, NJ, USA, 1973. View at MathSciNet
  32. M. Z. Hussain and J. M. Ali, “Positivity preserving piecewise rational cubic interpolation,” Matematika, vol. 22, no. 2, pp. 147–153, 2006. View at Google Scholar