Advertisement

Journal of Computer Science and Technology

, Volume 18, Issue 5, pp 592–597 | Cite as

Approaches for constrained parametric curve interpolation

  • Zhang CaiMing Email author
  • Yang XingQiang 
  • Wang JiaYe 
Article

Abstract

The construction of aGC 1 cubic interpolating curve that lies on the same side of a given straight line as the data points is studied. The main task is to choose appropriate approaches to modify tangent vectors at the data points for the desired curve. Three types of approaches for changing the magnitudes of the tangent vectors are presented. The first-type approach modifies the tangent vectors by applying a constraint to the curve segment. The second one does the work by optimization techniques. The third one is a modification of the existing method. Three criteria are presented to compare the three types of approaches with the existing method. The experiments that test the effectiveness of the approaches are included.

Keywords

computer aided geometric design constrained interpolation polynomial curve straight line constraint 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Duan Qi, Djidjeli K, Price W G, Twizell E H. Rational cubic spline based on function values.Computer & Graphics, 1998, 22: 479–486.CrossRefGoogle Scholar
  2. [2]
    Goodman T N T, Ong B H, Unsworth K. Constrained interpolation using rational cubic splines. InNurbs for Curve and Surface Design, Farin G (ed.), SIAM, 1991, pp. 59–74.Google Scholar
  3. [3]
    Nowacki H, Liu D, Lu X. Fairing Bézier-curves with constraints.CAGD, 1990, 7: 43–55.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Ong B H, Unsworth K. On non-parametric constrained interpolation. InMathematical Methods in Computer Aided Geometric Design, Lyche T, Schumaker L L (eds.), 1992, pp.419–430Google Scholar
  5. [5]
    Schmidt J W, Hess W. Positivity of cubic polynomial on intervals and positive spline interpolation.BIT, 1988, 28: 340–352.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    de Boor C. A Practical Guide to Splines. Springer-Verlag, New York, 1978, p.318.zbMATHGoogle Scholar
  7. [7]
    Lee E T Y. Choosing nodes in parametric curve interpolation.CAD, 1989, 21(6): 363–370.zbMATHGoogle Scholar
  8. [8]
    Farin G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press, 1997, Fourth Edition, p.132.Google Scholar
  9. [9]
    Zhang C, Cheng F, Miura K. A method for determining knots in parametric curve interpolation.CAGD, 1998, 15: 399–416.zbMATHMathSciNetGoogle Scholar
  10. [10]
    Zhang C, Cheng F. Constructing parametric quadratic curves.Journal of Computational and Applied Mathematics, 1999, 102: 21–36.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2003

Authors and Affiliations

  • Zhang CaiMing 
    • 1
    Email author
  • Yang XingQiang 
    • 1
  • Wang JiaYe 
    • 1
  1. 1.School of Computer Science and TechnologyShandong UniversityJinanP.R. China

Personalised recommendations