摘要
为了在CAGD中有效地求解三角域上Bézier曲面的最小平方逼近问题,给出了三角域上双变量Jacobi基和Bernstein基的相互转换矩阵.首先利用Bernstein基构造了三角域上的Jacobi多项式;然后利用单变量Jacobi基和Bernstein基的转换关系,给出了三角域上双变量Bernstein基与Jacobi基的相互转换矩阵.进一步,利用该矩阵得到了在加权L2范数下基于正交基的Bézier曲面最佳降多阶逼近算法,给出了具体的最佳降多阶矩阵以及该降阶逼近的可预报的误差公式.
For solving least squares approximation problem simply and effectively on triangular domains in CAGD, this paper derives the matrices of transformation of the bivariate Bernstein basis form into the Jacobi basis of the same degree and vice versa. A method for constructing bivariate Jacobi-weighted orthogonal polynomials in the Bernstein form on triangular domains is formulated firstly. And then, by using connection coefficients between the univariate Bernstein and Jacobi basis, the transformation matrices between bivariate Jacobi and Bernstein basis are presented. Finally, by using the matrices, an explicit form of the multi-degree reduction matrix for Bezier surface on triangular domains with respect to Jacobi weighted L2 norm is proposed, and the error of the degree reduction is given.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2009年第10期1394-1400,共7页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60873111)
国家"九七三"重点基础研究发展计划项目(2004CB719400)
作者简介
蔡华辉，男，1975年生，博士，主要研究方向为CAGD、计算机图形学等．
王国瑾，男，1944年生，教授，博士生导师，论文通讯作者，主要研究方向为CAGD、几何逼近等（gjwang@hzcnc．com）．
