准均匀三次B样条曲线的任意分辨率光顺  

Arbitrary Resolution Fairing of Quasi-Uniform Cubic B-Spline Curve

作　　者：纪小刚 龚光容[2] 

机构地区：[1]江南大学机械工程学院 [2]南京理工大学机械工程学院

出　　处：《机械科学与技术》2009年第11期1477-1481,共5页Mechanical Science and Technology for Aerospace Engineering

基　　金：国防十五预研项目(41318.1.1.7)资助

摘　　要：小波分析应用于逆向工程时,对控制顶点有特殊要求,只能处理2j+r个控制顶点的图形。笔者根据多分辨分析的思想,提出了一种任意分辨率下的曲线光顺新方法。该方法以准均匀三次B样条曲线为研究对象,构造出相应的曲线光顺滤波器组,并推导了相应的快速算法,最后对B样条基函数及滤波器组的归一化进行了详细的阐述。该算法成功应用于具有任意控制顶点数的B样条曲线的光顺。When wavelets analysis is used to reverse engineering, it asks for specific number of control vertices, as a result, it can only treat the curve with 2j ＋ r control vertices. According to thread of multiresolution analysis （MRA）, a new arbitrary resolution fairing algorithm to curve with any amount of control vertices is put forward. And corresponding curve fairing filter bank and rapid algorithm on quasi-uniform cubic B-Spline curve is deduced. Finally, the standardizations of B-Spline basis functions and filter bank are expounded in details. This new algorithm is applied to a quasi-uniform cubic B-Spline curve with any amount of control vertices successfully and proved to be accurate, stable, and efficient by the given examples.

关 键 词：准均匀三次B样条曲线 多分辨分析 光顺 计算机图形学 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]