| 半正交B样条小波及其在曲线曲面光顺中的应用 |
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| 引用本文： | 纪小刚,龚光容.半正交B样条小波及其在曲线曲面光顺中的应用[J].机械工程学报,2006,42(9):54-60. |
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| 作者姓名： | 纪小刚 龚光容 |
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| 作者单位： | 南京理工大学机械工程学院;江南大学机械工程学院 |
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| 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。
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| 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 |
| 修稿时间： | 2005年12月7日 |
SEMI-ORTHOGONAL B-SPLINE WAVELETS AND ITS APPLICATION TO CURVE AND SURFACE FAIRING |
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| JI Xiaogang,GONG Guangrong.SEMI-ORTHOGONAL B-SPLINE WAVELETS AND ITS APPLICATION TO CURVE AND SURFACE FAIRING[J].Chinese Journal of Mechanical Engineering,2006,42(9):54-60. |
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| Authors: | JI Xiaogang GONG Guangrong |
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| Affiliation: | School of Mechanical Engineering, Nanjing University of Science & Technology School of Mechanical Engineering,Southern Yangtze University |
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| 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. |
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| Keywords: | B-Spline curve Multiresolution analysis Decomposition and reconstruction Wavelets Computer graphics |
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