半正交B样条小波及其在曲线曲面光顺中的应用  

SEMI-ORTHOGONAL B-SPLINE WAVELETS AND ITS APPLICATION TO CURVE AND SURFACE FAIRING

作　　者：纪小刚[1,2] 龚光容[1] 

机构地区：[1]南京理工大学机械工程学院 [2]江南大学机械工程学院 无锡 214122

出　　处：《机械工程学报》2006年第9期54-60,共7页Journal of Mechanical Engineering

基　　金：国防'十五'预先研究资助项目(41318.1.1.7)

摘　　要：基于B样条基函数及其对应的小波不具有平移正交性,因而不能用现有Mallat快速算法进行小波分析的特点,从B样条基函数以及多分辨分析的定义出发,用严格的数学推导实现半正交B样条小波的分解重构算法。详细阐述该算法在准均匀三次B样条曲线中的运用,并给出一条复杂曲线及一个复杂曲面的分解重构实例,表明该方法能够在复杂曲线曲面的光顺中取得良好效果。Because B-Spline basis functions and corresponding wavelets are lack of translation orthogonality, rapid Mallat algorithm does not work for this kind of wavelets analysis. Decomposition and reconstruction algorithm of semiorthogonal B-Spline wavelets is obtained by strict mathematical deduction based on definition of B-Spline basis function and multiresolution analysis. And its application to Quadi-Uniform Cubic B-Spline is expatiated in details. This algorithm is applied to decomposition and reconstruction of complicated curve and surface and proved to be practicable to fairing of complicated curve and surface.

关 键 词：B样条曲线 多分辨分析 分解重构 小波 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]