均匀二重混合双曲多项式B样条曲线  

Uniform duplicate mixed hyperbolic polynomial B-spline curves

作　　者：严春[1] 

机构地区：[1]浙江广播电视大学信息与工程学院,杭州310030

出　　处：《计算机辅助工程》2009年第3期67-72,共6页Computer Aided Engineering

摘　　要：为扩展B样条曲线,提出1种均匀二重混合双曲多项式B样条曲线.该样条曲线在span{sinh t,cosht,tsinh t,tcosh t,1,t,…,tk-6,tk-5}空间上均匀产生,其中k是大于等于5的整数.证明k阶二重混合双曲多项式B样条基的性质和二重混合双曲多项式B样条曲线的性质.二重混合双曲多项式B样条曲线精确地包含双曲多项式B样条曲线.给出这种新样条曲线的细分公式并证明其有变差缩减性质和细分控制多边形逼近性质.该性质使得通过递归细分得到曲线成为可能.To extend B-spline curves, a kind of uniform duplicate mixed hyperbolic polynomial B-spline curves is proposed. The curves are generated uniformly over the space span {sinh t,cosh t,tsinh t,tcosh t,1,t,…,t^k-6,t^k-5} where k is an arbitrary integer which is larger than or equal to 5. The properties of the basis and curves of duplicate mixed hyperbolic polynomial B-spline are proved. The duplicate mixed hyperbolic polynomial B-spline curves include accurately the hyperbolic polynomial B-spline curves. The subdivision formula of these new kind of curves are given. Further, the existence of the variation diminishing property and the approximation property of the subdivision control polygon is proved. The approximation property makes it possible for generating the curves by reeursive subdivision.

关 键 词：均匀B样条 C—B-样条 超越曲线 二重混合双曲多项式 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]