| 4阶均匀代数三角样条空间的拟Legendre基 |
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| 引用本文： | 魏永伟,汪国昭.4阶均匀代数三角样条空间的拟Legendre基[J].计算机辅助设计与图形学学报,2012,24(7):858-863. |
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| 作者姓名： | 魏永伟 汪国昭 |
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| 作者单位： | 1. 浙江大学数学系计算机图像图形研究所 杭州310027;上海海事大学应用数学系 上海201306
2. 浙江大学数学系计算机图像图形研究所 杭州310027 |
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| 摘 要： | 为解决代数三角样条空间上正交基的理论问题,提出了4阶均匀代数三角样条空间上构造正交基的方法.该方法利用6阶C-B样条基函数构造一组辅助函数,并以这组辅助函数的二阶导数形式定义样条空间上的一组正交基,称为拟Legendre基.实例结果表明,使用这组正交基可以简化内积计算,便于最佳平方逼近问题求解.
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| 关 键 词： | 代数三角样条空间 代数三角B样条 Legendre基 正交基 |
Legendre-like Basis for the Uniform Four-order Algebraic Trigonometric Spline Space |
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| Wei Yongwei
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Wang Guozhao.Legendre-like Basis for the Uniform Four-order Algebraic Trigonometric Spline Space[J].Journal of Computer-Aided Design & Computer Graphics,2012,24(7):858-863. |
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| Authors: | Wei Yongwei Wang Guozhao |
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| Affiliation: | 1) 1)(Institute of Computer Graphics and Image Processing,Department of Mathematics,Zhejiang University,Hangzhou 310027) 2)(Department of Applied Mathematics,Shanghai Maritime University,Shanghai 201306) |
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| Abstract: | In order to develop the theory of orthogonal basis for algebraic-trigonometric spline space,a novel approach is presented to construct an orthogonal basis for the uniform four-order algebraic trigonometric spline space.Based on the C-B spline functions of order six,a set of auxiliary functions is constructed.And the proposed orthogonal splines are given as the second-order derivatives of these auxiliary functions.This orthogonal basis is also called Legendre-like basis.The result of the practical examples shows that using this basis can simplify inner product computation and facilitate solving least-squares approximation. |
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| Keywords: | algebraic trigonometric spline space algebraic trigonometric B-spline Legendre basis orthogonal basis |
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