双奇次NUAHT样条  

NUAH T-splines of Odd Bi-degree

作　　者：段小娟[1] 汪国昭[1] 

机构地区：[1]浙江大学数学系,杭州310027

出　　处：《计算机辅助设计与图形学学报》2015年第6期1091-1098,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61272300)

摘　　要：针对T样条无法精确表示双曲超越曲面的问题,构造了一种样条曲面——双奇次代数双曲T样条曲面(NUAH T样条),探讨了其细分算法和调配函数的线性无关性.通过将非均匀代数双曲B样条曲面(NUAH B样条曲面)定义在T网上,给出了双奇次NUAH T样条的定义;基于NUAH B样条的节点插入公式,提出NUAH T样条的一种局部细分算法;并证明了NUAH T样条的调配函数线性无关的充要条件,即由NUAH T样条转化为NUAH B样条曲面的过渡矩阵是满秩矩阵.最后,通过实例验证了曲面构建和细分算法的有效性.Since T-splines cannot represent hyperbolic spline surfaces exactly, this paper presents a kind of spline surfaces, called non-uniform algebraic hyperbolic T-spline surfaces （NUAH T-splines for short） of odd bi-degree. The NUAH T-splines are defined by applying the T-spline framework to the non-uniform al- gebraic hyperbolic B-spline surfaces （NUAH B-spline surfaces）. Based on the knot insertion of NUAH B-splines, a local refinement algorithm for NUAH T-splines of odd bi-degree is shown. This paper proves that, for any NUAH T-spline of odd bi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAH T-spline-to-NUAH B-spline transformation matrix. Finally, the examples verify the effectiveness of the local refinement algorithm of NUAH T-splines.

关 键 词：双奇次 非均匀代数双曲T样条 局部细分 调配函数 线性无关 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]