A simple matrix form for degree reduction of Bézier curves using Chebyshev-Bernstein basis transformations

We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L2-norm for the interval [0,1], using the weight function wðxÞ 1⁄4 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4x 4x2 p . The error of the degree reduction scheme is given, and the degree reduction with continuity conditions is also considered. 2006 Elsevier Inc. All rights reserved.