摘要
We propose an optimal approach to solve the problem of multi-degree reduction of C-Brzier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Brzier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Brzier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.
本文提出了一种在L_2范数下C-Bézier曲面带约束条件的降多阶逼近最优方法。利用C-Bézier基函数的转换矩阵,得到了降阶曲面控制顶点的显式矩阵表示。结合指定的边界约束条件,该法利用于对分片连续曲面或细分子曲面同时降多阶逼近,所得到的系列降阶曲面整体上保持G^1连续。数值实验表明该方法的优质高效。
作者
Lian ZHOU
Xin-hui LIN
Hong-yan ZHAO
Jin CHEN
Lian ZHOU;Xin-hui LIN;Hong-yan ZHAO;Jun CHEN(Department of Mathematics, Shanghai Maritime University;Zhejiang Institute of Economics and Trade;College of Fundamental Studies, Shanghai University of Engineering Science;Faculty of Science, Ningbo University of Technology)
基金
Project supported by the National Natural Science Foundation of China （Nos. 11401373, 61402281, and 11601322） and the Zhejiang Provincial Natural Science Foundation, China （No. LY16F020020）
