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.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
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)
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
B-Spline curve Multiresolution analysis Decomposition and reconstruction Wavelets Computer graphics
