• CN:11-2187/TH
  • ISSN:0577-6686

›› 2006, Vol. 42 ›› Issue (9): 54-60.

• 论文 • 上一篇    下一篇

半正交B样条小波及其在曲线曲面光顺中的应用

纪小刚;龚光容   

  1. 南京理工大学机械工程学院;江南大学机械工程学院
  • 发布日期:2006-09-15

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

JI Xiaogang;GONG Guangrong   

  1. School of Mechanical Engineering, Nanjing University of Science & Technology School of Mechanical Engineering,Southern Yangtze University
  • Published:2006-09-15

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。

关键词: B样条曲线, 多分辨分析, 分解重构, 计算机图形学, 小波

Abstract: 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 semi- orthogonal 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.

Key words: B-Spline curve, Computer graphics, Multiresolution analysis Decomposition and reconstruction, Wavelets

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