Jacobi-Bernstein基变换矩阵的一些性质

在计算机辅助设计中,经常需要不同形式的曲线、曲面之间的变换,以完成曲线、曲面的降阶以及不同几何造型系统之间数据交换的操作,而这些变换的误差将依赖于相应变换矩阵的条件数.由于这个原因,我们研究了Jacobi-Bernstein矩阵的与其条件数相关的若干性质,而且通过计算变换矩阵与逆变换矩阵的无穷范数我们以显形式给出了这些条件数的上界.我们还给出了这些条件数在CAGD中的应用实例.

Some Properties of Jacobi-Bernstein Basis Transformation Matrices

In computer-aided design,transformations among different forms of curves and surfaces are often required to carry out operations of degree-reduction of curves and surfaces and data exchanging between different geometric modeling systems.The errors of these transformations would depend on the condition numbers of the corresponding transformation matrices.For this reason,we studied some properties of Jacobi-Bernstein basis transformation matrices related to their condition numbers,and by computing the infinite norms of the transformation matrices and their inverse matrices,we obtained explicit upper bounds to these condition numbers.An example of applications of these condition numbers in CAGD was also provided.