均匀B样条曲线的高效细分公式  

A new efficient subdivision rule for producing the uniform B-spline curve

作　　者：管晓鹤[1] 章仁江[2] 

机构地区：[1]中国计量学院理学院,浙江杭州310018 [2]浙江工商大学统计学院,浙江杭州310018

出　　处：《中国计量学院学报》2009年第4期362-366,共5页Journal of China Jiliang University

摘　　要：主要研究在n次均匀B样条初始节点序列中每两个节点间一次性地均匀插入m-1个新节点的算法,导出了原始n次均匀B样条基函数与插入新节点后的基函数之间的明确关系式,进一步得到了原始B样条曲线的新旧控制顶点之间的明确关系式.该结果几何直观性强,新旧控制顶点对应明确,丰富了绘制均匀B样条曲线的方法.An algorithm about how to insert m-1 new knots evenly between every two adjacent knots in the initial uniform B-spline of degree n was preseuted.An explicit expression between the original basis functions of the n degree uniform B-spline curves and the new ones after inserting new knots was obtained.Furthermore,a new efficient subdivision rule for producing the uniform B-spline curve is derived based on the new expression between the old and new control points.

关 键 词：均匀B样条 细分公式 基函数 控制顶点 卷积 

分 类 号：O174.41[理学—数学]