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

Abstract

This paper presents an efficient method to solve the approximation problem of the rational Bezier 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.