以节点与权因子修改为基础的4阶NURBS受限形状控制  

Constrained shape modification of cubic NURBS curves based on knots and weights

作　　者：李亚娟[1] 汪国昭[1] 

机构地区：[1]浙江大学数学系浙江大学计算机图形图象研究所,浙江杭州310027

出　　处：《高校应用数学学报（A辑）》2006年第1期118-124,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10371110);国家重点基础研究发展规划项目(2004CB318000)

摘　　要：改变k阶NURBS曲线的节点,会产生一个单参数NURBS曲线族,该曲线族的包络是用相同控制顶点定义的k-a阶NURBS曲线,这里a是所改变的节点的重数.论文运用这项理论结果,提出了几种建立在修改一个节点与两个连续权因子基础上的4阶NURBS形状控制方法,该方法要受一定的位置与切线方向的约束.The modification of a knot of a NURBS curve of order k generates a oneparameter family of curves. This family has an envelope which is also a NURBS curve with the same control polygon and of order k-α, where a is the multiplicity of the modified knot. By applying this theoretical result, several shape control methods are provided for cubic NURBS curves based on the modification of a knot and two consecutive weights. The proposed methods enable local shape modifications to be subjected to position and tangent constraints that can be specified within well defined limits.

关 键 词：NURBS曲线 改变节点 包络 受约束的形状控制 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]