CAJ | 학술논문

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.
재계산궤보조설계중,경상수요불동형식적곡선、곡면지간적변환,이완성곡선、곡면적강계이급불동궤하조형계통지간수거교환적조작,이저사변환적오차장의뢰우상응변환구진적조건수.유우저개원인,아문연구료Jacobi-Bernstein구진적여기조건수상관적약간성질,이차통과계산변환구진여역변환구진적무궁범수아문이현형식급출료저사조건수적상계.아문환급출료저사조건수재CAGD중적응용실례.
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.