单节点3次样条空间上的正交基

Orthogonal Basis with Signal Node over Cubic Spline Space

正交基在许多问题中有重要的应用。在计算机辅助设计中所常用的B样条基不是正交基。尝试构造三次样条空间中的一组正交基。给定区间[a,b]上的一个节点向量a=t0<t1<t2<…<tm<tm+1=b,从三次B样条基出发,利用B样条基的定义及其性质在三次样条空间中构造了一组正交基{Ji(t)}m+3i=0,并且研究了这组基在降阶逼近中的应用。

The B-spline basis is not orthogonal,construct an orthogonal basis over cubic spline space is attempt to.Given a knot vector a=t0t1t2…tmtm＋1=b on the interval [a,b],the cubic B-spline basis is started,and constructed an orthogonal basis {Ji（t）}m＋3i=0,by using the properties of B-spline basis.Furthermore,the properties of the orthogonal basis and its application to degree reduction and approximating are studied.