Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 408492, 6 pages
http://dx.doi.org/10.1155/2014/408492
Research Article

The Representation of Circular Arc by Using Rational Cubic Timmer Curve

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

Received 24 June 2013; Accepted 12 December 2013; Published 16 January 2014

Academic Editor: Metin O. Kaya

Copyright © 2014 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. G. Farin, Curves and Surfaces for CAGD: A Practical Guide, Morgan Kaufmann, Boston, Mass, USA, 5th edition, 2002.
  2. I. D. Faux and M. J. Pratt, Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester, UK, 1979.
  3. G.-J. Wang, “Rational cubic circular arcs and their application in CAD,” Computers in Industry, vol. 16, no. 3, pp. 283–288, 1991. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Blanc and C. Schlick, “Accurate parametrization of conics by NURBS,” IEEE Computer Graphics and Applications, vol. 16, no. 6, pp. 64–71, 1996. View at Publisher · View at Google Scholar · View at Scopus
  5. J. J. Chou, “Higher order Bézier circles,” Computer-Aided Design, vol. 27, no. 4, pp. 303–309, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Fang, “A rational quartic Bézier representation for conics,” Computer Aided Geometric Design, vol. 19, no. 5, pp. 297–312, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. G.-J. Wang and G.-Z. Wang, “The rational cubic Bézier representation of conics,” Computer Aided Geometric Design, vol. 9, no. 6, pp. 447–455, 1992. View at Publisher · View at Google Scholar · View at Scopus
  8. Q.-Q. Hu and G.-J. Wang, “Necessary and sufficient conditions for rational quartic representation of conic sections,” Journal of Computational and Applied Mathematics, vol. 203, no. 1, pp. 190–208, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. Q.-Q. Hu, “Approximating conic sections by constrained Bézier curves of arbitrary degree,” Journal of Computational and Applied Mathematics, vol. 236, no. 11, pp. 2813–2821, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. J. Ahn and H. O. Kim, “Approximation of circular arcs by Bézier curves,” Journal of Computational and Applied Mathematics, vol. 81, no. 1, pp. 145–163, 1997. View at Publisher · View at Google Scholar · View at Scopus
  11. S.-H. Kim and Y. J. Ahn, “An approximation of circular arcs by quartic Bézier curves,” Computer-Aided Design, vol. 39, no. 6, pp. 490–493, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. J. Ahn, “Approximation of conic sections by curvature continuous quartic Bézier curves,” Computers and Mathematics with Applications, vol. 60, no. 7, pp. 1986–1993, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. Q.-Q. Hu and G.-J. Wang, “Rational cubic/quartic Said-Ball conics,” Applied Mathematics, vol. 26, no. 2, pp. 198–212, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. H. B. Said, “A generalized Ball curve and its recursive algorithm,” ACM Transactions on Graphics, vol. 8, no. 4, pp. 360–371, 1989. View at Publisher · View at Google Scholar
  15. J. M. Ali, “An alternative derivation of Said basis function,” Sains Malaysiana, vol. 23, no. 3, pp. 42–56, 1994. View at Google Scholar
  16. H. G. Timmer, “Alternative representation for parametric cubic curves and surfaces,” Computer-Aided Design, vol. 12, no. 1, pp. 25–28, 1980. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Sarfraz, “Optimal curve fitting to digital data,” Journal of WSCG, vol. 11, no. 3, 8 pages, 2003. View at Google Scholar