节点矢量影响NURBS曲线的规律研究与应用  

Research on How the Knot Vector Influences Non-uniform Rational B-spline Curve

作　　者：陈凯云 谢晓芹[2] 

机构地区：[1]哈尔滨工程大学机电工程学院 [2]哈尔滨工程大学计算机科学与技术学院,哈尔滨150001

出　　处：《机械工程学报》2008年第10期294-299,共6页Journal of Mechanical Engineering

基　　金：哈尔滨工程大学基础研究基金资助项目(HEUFT05052)

摘　　要：以非均匀有理B样条(Non uniform rational B-spline,NURBS)曲线理论为基础,证明修改节点矢量对NURBS曲线的影响具有局部性,推导修改节点矢量引起的NURBS曲线变化量的计算式,提出修改节点矢量影响NURBS曲线的一般规律。对计算机辅助图形设计(Computer aided geometric design,CAGD)中曲线局部修改的实例进行试验研究,证明了修改节点矢量可以实现对NURBS曲线的局部修改,实现曲线交互式设计。对NURBS插值曲线节点因子调节法中航空压气机叶片边缘测量的实例进行了试验研究,证明可以获得拟合误差最小的叶片型面测量点NURBS插值曲线。试验研究证明所提出的'节点矢量影响NURBS曲线的一般规律'是正确的和可行的。Based on the non-uniform rational B-spline （NURBS） curve theory, the general rule of how the knot vector affects the shape of the NURBS curve is put forward. The local support property on how a knot affects the NURBS curve is demonstrated. The quantitative computation formula on how a knot affects the NURBS curve is obtained. An experiment performed on the example in computer aided geometric design （CAGD） proves that it is possible that the NURBS curve can be modified locally and be designed interactively by modifying a single knot. And another experiment performed on the measurement of the edge of the vane of the aero-engine compressor proves that the fitting model with the minimum errors can be achieved by the knot factor method （KFM） that is based on the rule. Both experiments prove that the rule proposed here is correct, practical and feasible.

关 键 词：非均匀有理B样条 B样条基函数 节点矢量 节点因子 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]