Multiple degree reduction and elevation of Bezier curves using Jacobi-Bernstein basis transformations

作者：Rababah Abedallah^*; Lee Byung Gook; Yoo Jaechil

来源：Numerical Functional Analysis and Optimization, 2007, 28(9-10): 1179-1196.

DOI：10.1080/01630560701564139

• basis transformation
• Bernstein polynomials
• Bezier curves
• degree reduction
• Jacobi polynomials
• least-squares approximation
• orthogonal polynomials

In this article, we find the optimal r times degree reduction of Bezier curves with respect to the Jacobi-weighted L-2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L-1, L-2, and L-infinity-norms. We give some examples and figures to demonstrate thes e methods.

• 出版日期2007