摘要
样条基的几乎严格全正性和曲线插值适定性关系密切,是几何造型中一个基本且重要的问题.文中证明了代数双曲B样条基具有几乎严格全正性:首先引入代数双曲B样条函数,通过嵌入节点算法推导出函数的零点数和变差数之间的关系;进一步,利用数学归纳法证明了该基具有几乎严格全正性.文中的证明方法直观且具有几何性,为造型中使用代数双曲B样条基奠定了更为完备的理论基础.
Almost strictly total positivity is highly related with the poisedness of curve interpolation problem. It is living a basic status in the bases theory, A geometrical approach is proposed to prove the collection matrices of AH B-spline bases are almost strictly totally positive matrices. Firstly, AH B-spline function is introduced. Using knot inserted algorithm, the relationship between the number of zero points and the number of coefficient variations can be deduced. Finally, using mathematical induction, almost strictly total positivity of AH B-spline bases can be proved. The approach is intuitive and geometrical.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2014年第2期258-262,271,共6页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(61272300
60933008)
关键词
嵌入节点算法
几乎严格全正性
系数变差
代数双曲B样条基
knot inserted algorithm
almost strictly total positivity
coefficient variation
AH B-spline bases
