A simple matrix form for degree reduction of Bezier 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 Bezier curves with respect to the weighted L-2-norm for the interval [0, 1], using the weight function w(x) = 1/root 4x-4x(2). The error of the degree reduction scheme is given, and the degree reduction with continuity conditions is also considered. (c) 2006 Elsevier Inc. All rights reserved.