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中文摘要：
为了在CAGD中有效地求解三角域上Bezier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Bezier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．
英文摘要：
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.
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同项目期刊论文
Optimal constrained multi-degree reduction of B,zier curves with explicit expressions based on divid
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