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

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## Abstract

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.

## Keywords

Rational Bézier curves Piecewise polynomial approximation Jacobi wavelets Guass–Jacobi quadrature## Mathematics Subject Classification

65T60 65D17 41A29## Notes

### Acknowledgements

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

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