Computational and Applied Mathematics

, Volume 37, Issue 3, pp 3951–3966 | Cite as

The use of Jacobi wavelets for constrained approximation of rational Bézier curves

  • M. R. EslahchiEmail author
  • Marzieh Kavoosi


This paper presents an efficient method to solve the approximation problem of the rational Bézier curve by continuous piecewise polynomial curve in \( L_{2} \)-norm. For this purpose, extended Jacobi wavelets together with the Gauss–Jacobi quadrature rules are employed. The proposed technique has some advantages such as: simplicity, high accuracy and fast computation. Also, the method in the paper performs multi-degree reduction at one time and does not need the stepwise computing. Several examples are given to illustrate the effectiveness of the algorithm.


Rational Bézier curves Piecewise polynomial approximation Jacobi wavelets Guass–Jacobi quadrature 

Mathematics Subject Classification

65T60 65D17 41A29 



The authors are very grateful to all reviewers for carefully reading the paper and for their useful comments and suggestions.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran

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