Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 327457, 12 pages
http://dx.doi.org/10.1155/2009/327457
Research Article

Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received 25 February 2009; Revised 13 June 2009; Accepted 10 September 2009

Academic Editor: Alexander P. Seyranian

Copyright © 2009 Xiaolei Zhang and Jinming Wu. 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. L. Vehlo and J. Gomes, “Approximate conversion from parametric to implicit surfaces,” Computer Graphics Forum, vol. 15, pp. 327–337, 1996. View at Publisher · View at Google Scholar
  2. T. W. Sederberg, J. Zheng, K. Klimaszewski, and T. Dokken, “Approximate implicit using monoid curves and surfaces,” Graphical Model and Image Processing, vol. 61, pp. 177–198, 1999. View at Publisher · View at Google Scholar
  3. T. Dokken, “Approximate implicitization,” in Mathematical Methods for Curves and Surfaces, Oslo 2000, T. Lyche and L. Schumaker, Eds., pp. 81–102, Vanderbilt University Press, Nashville, Tenn, USA, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. Dokken and J. B. Thomassen, “Overview of approximate implicitization,” in Topics in Algebraic Geometry and Geometric Modeling, vol. 334, pp. 169–184, American Mathmatics Society Contemporary Mathematics, Providence, RI, USA, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Yalcin, M. Unel, and W. A. Wolovich, “Implicitization of parametric curves by matrix annihilation,” International Journal of Computer Vision, vol. 54, pp. 105–115, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. Chen and L. Deng, “Interval implicitization of rational curves,” Computer Aided Geometric Design, vol. 21, no. 4, pp. 401–415, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Li, X. S. Gao, and S. C. Chou, “Quadratic approximation to plane parametric curves and its application in approximate implicitization,” Visual Computers, vol. 22, pp. 906–917, 2006. View at Publisher · View at Google Scholar
  8. R. Wang and J. Wu, “Approximate implicitization based on RBF networks and MQ quasi-interpolation,” Journal of Computational Mathematics, vol. 25, no. 1, pp. 97–103, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. M. Wu and R. H. Wang, “Approximate implicitization of parametric surfaces by using compactly supported radial basis functions,” Computers and Mathematics with Applications, vol. 56, pp. 3064–3069, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. M. Wu, Y. S. Lai, and X. L. Zhang, “Approximate implicitization of parametric curves by using quadratic algebraic splines,” Journal of Information and Computational Science, vol. 5, pp. 2181–2186, 2008. View at Google Scholar
  11. T. Sederberg, “Planar piecewise algebraic curves,” Computer Aided Geometric Design, vol. 1, pp. C241–C255, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. G. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, Academic Press, Boston, Mass, USA, 4th edition, 1996.
  13. G. Xu, C. L. Bajaj, and W. Xue, “Regular algebraic curve segments(I)—definitions and characteristics,” Computer Aided Geometric Design, vol. 17, no. 6, pp. 485–501, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. Goldman, “Curvature formulas for implicit curves and surfaces,” Computer Aided Geometric Design, vol. 22, no. 7, pp. 632–658, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Paluszny and R. Patterson, “A family of tangent continuous algebraic splines,” ACM Transaction on Graphics, vol. 12, pp. 209–232, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. M. Paluszny and R. Patterson, “Geometric control of G2-cubic A-splines,” Computer Aided Geometric Design, vol. 15, no. 3, pp. 261–287, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  17. R. H. Wang, Numerical Approximation, Higher Education Press, Beijing, China, 1999.