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 Bezier curves with respect to the weighted L2-norm for the interval [0, 1], using the weight function w(x)=1/4x-4x2. The error of the degree reduction scheme is given, and the degree reduction with continuity conditions is also considered.