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A closed-form solution to the inverse problem in interpolation by a Bézier-spline curve

  • Le Phuong Quan
  • Thái Anh NhanEmail author
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Abstract

A geometric construction of a Bézier curve is presented by a unifiable way from the mentioned literature with some modification. A closed-form solution to the inverse problem in cubic Bézier-spline interpolation will be obtained. Calculations in the given examples are performed by a Maple procedure using this solution.

Mathematics Subject Classification

41A05 41A10 41A15 65D05 

Notes

Acknowledgements

The authors gratefully acknowledge the valuable comments and suggestions from the anonymous referees.

References

  1. 1.
    de Boor, C.: A Practical Guide to Splines. Revised Edition (1978). Springer, New York (2001)zbMATHGoogle Scholar
  2. 2.
    Burden, R.L.; Faires, J.D.: Numerical Analysis, 9th edn. Brooks/Cole, Boston (2011)zbMATHGoogle Scholar
  3. 3.
    Elaydi, S.N.: An Introduction to Difference Equations, 3rd edn. Springer, New York (2005)zbMATHGoogle Scholar
  4. 4.
    Mortenson, M.E.: Mathematics for Computer Graphics Applications, 2nd edn. Industrial Press Inc., New York (1999)Google Scholar
  5. 5.
    Phillips, G.M.: Interpolation and Approximation by Polynomials. Springer, New York (2003)CrossRefGoogle Scholar
  6. 6.
    Schumaker, L.L.: Spline Functions: Basic Theory, 3rd edn. Cambridge University Press, Cambridge (2007)CrossRefGoogle Scholar
  7. 7.
    Sharpe, M.: Cubic B-splines using PSTricks, a guiding document for the package pst-bspline from the website http://ctan.org/pkg (Version 1.62, 21/04/2016). Accessed 18 May 2017

Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, College of Natural SciencesCan Tho UniversityCan ThoVietnam
  2. 2.Department of Mathematics and ScienceHoly Names UniversityOaklandUSA

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