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

摘要

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 w(x)=1/4x-4x2. The error of the degree reduction scheme is given, and the degree reduction with continuity conditions is also considered.