【作者】 魏炜立； 汪国昭；

【Author】 Wei Weili,Wang Guozhao (Department of Mathematics,Zhejiang University, Hangzhou 310027,China)

【机构】 浙江大学数学系；

【摘要】 本文通过嵌入节点的方法证明了NUAHTB-样条基具有全正性。嵌入节点算法是样条理论中基本而重要的算法之一。在曲线造型技术中,基的全正性与曲线的凸包性、变差缩减性和保形性等性质是密切相关的。本文的工作不仅完善了NUAHT B-样条的理论,并且可以作为代数理论中全正性的补充。更多还原

【Abstract】 In this paper,we presented the proof of total positivity of NUAHT B-spline basis,using knot inserted algorithm,which is the basic and significant algorithm in spline basis theory.Total positivity is an important property for spline basis,it is highly related with variation diminishing property as well as shape preserving property,both of which is necessary in curve design.Our work not only make complement to the NUAHT B-spline basis theory,but also can be treated as supplement to the total positivity in algebraic sense.更多还原