About this Journal Submit a Manuscript Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 174048, 14 pages
http://dx.doi.org/10.5402/2012/174048
Research Article

Local Convexity Shape-Preserving Data Visualization by Spline Function

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
3School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 16 November 2011; Accepted 21 December 2011

Academic Editor: R. Barrio

Copyright © 2012 Muhammad Abbas 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. F. Bao, Q. Sun, J. Pan, and Q. Duan, “Point control of rational interpolating curves using parameters,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 143–151, 2010. View at Publisher · View at Google Scholar
  2. M. Abbas, A. A. Majid, M. N. H. Awang, and J. M. Ali, “Monotonicity preserving interpolation using rational spline,” in Proceedings of the International MultiConference of Engineers and Computer Scientists (IMECS '11), vol. 1, pp. 278–282, Hong Kong, March 2011.
  3. S. Asaturyan, P. Costantini, and C. Manni, “Local shape-preserving interpolation by space curves,” IMA Journal of Numerical Analysis, vol. 21, no. 1, pp. 301–325, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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 Scopus
  5. J. M. Carnicer, M. Garcia-Esnaola, and J. M. Peña, “Convexity of rational curves and total positivity,” Journal of Computational and Applied Mathematics, vol. 71, no. 2, pp. 365–382, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. C. Clements, “A convexity-preserving C2 parametric rational cubic interpolation,” Numerische Mathematik, vol. 63, no. 2, pp. 165–171, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. P. Costantini, “On monotone and convex spline interpolation,” Mathematics of Computation, vol. 46, no. 173, pp. 203–214, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. P. Costantini and F. Fontanella, “Shape-preserving bivariate interpolation,” SIAM Journal on Numerical Analysis, vol. 27, no. 2, pp. 488–506, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R. Delbourgo and J. A. Gregory, “Shape preserving piecewise rational interpolation,” SIAM Journal on Scientific and Statistical Computing, vol. 6, no. 4, pp. 967–976, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. J. A. Gregory, “Shape preserving spline interpolation,” Computer-Aided Design, vol. 18, no. 1, pp. 53–57, 1986. View at Scopus
  11. M. Tian and S. L. Li, “Convexity-preserving piecewise rational cubic interpolation,” Journal of Shandong University, vol. 42, no. 10, pp. 1–5, 2007. View at Zentralblatt MATH
  12. D. F. McAllister and J. A. Roulier, “An algorithm for computing a shape-preserving osculatory quadratic spline,” ACM Transactions on Mathematical Software, vol. 7, no. 3, pp. 331–347, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. E. Passow and J. A. Roulier, “Monotone and convex spline interpolation,” SIAM Journal on Numerical Analysis, vol. 14, no. 5, pp. 904–909, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. A. Roulier, “A convexity preserving grid refinement algorithm for interpolation of bivariate functions,” IEEE Computer Graphics and Applications, vol. 7, no. 1, pp. 57–62, 1987. View at Scopus
  15. L. L. Schumaker, “On shape preserving quadratic spline interpolation,” SIAM Journal on Numerical Analysis, vol. 20, no. 4, pp. 854–864, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. M. H. Schultz, Spline Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1973.
  17. M. Sarfraz and M. Z. Hussain, “Data visualization using rational spline interpolation,” Journal of Computational and Applied Mathematics, vol. 189, no. 1-2, pp. 513–525, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. 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 Zentralblatt MATH
  19. M. Sarfraz, M. Hussain, and Z. Habib, “Local convexity preserving rational cubic spline curves,” in Proceedings of the IEEE Conference on Information Visualization (IV '97), pp. 211–218, 1997.
  20. M. Sarfraz, “Convexity preserving piecewise rational interpolation for planar curves,” Bulletin of the Korean Mathematical Society, vol. 29, no. 2, pp. 193–200, 1992. View at Zentralblatt MATH
  21. M. Sarfraz, “Interpolatory rational cubic spline with biased, point and interval tension,” Computers and Graphics, vol. 16, no. 4, pp. 427–430, 1992. View at Scopus