A simple matrix form for degree reduction of Bézier curves using Chebyshev-Bernstein basis transformations
A simple matrix form for degree reduction of Bézier curves using Chebyshev-Bernstein basis transformations
复制标题
DOI：
10.1016/j.amc.2006.01.034
复制
发表时间：
2006-10
期刊：
影响因子：
--
通讯作者：
A. Rababah;Byung-Gook Lee;Jaechil Yoo
中科院分区：
文献类型：
--
作者：
A. Rababah;Byung-Gook Lee;Jaechil Yoo
我们利用Chebyshev基和Bernstein基之间的变换矩阵和Chebyshev多项式的高程和降阶矩阵，给出了区间[0,1]的bsamzier曲线相对于加权l2 -范数的r次高程和最优r次降阶的简单有效的方法，使用权函数w(x)=1/4x-4x2。给出了降阶方案的误差，并考虑了具有连续性条件的降阶方案。
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.