An orthogonal basis for non-uniform algebraic-trigonometric spline space  

作　　者：WEI Yong-wei WANG Guo-zhao 

机构地区：[1]Department of Mathematics, Shanghai Maritime University [2]Department of Mathematics, Zhejiang University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2014年第3期273-282,共10页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(60933008,61272300 and 11226327);the Science&Technology Program of Shanghai Maritime University(20120099)

摘　　要：Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic-trigonometric spline space in order to resolve the theo- retical problem that there is not an explicit orthogonai basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic-trigonometric spline space in order to resolve the theo- retical problem that there is not an explicit orthogonai basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.

关 键 词：CAGD algebraic-trigonometric spline space NUAT B-spline orthogonal spline 

分 类 号：O177[理学—数学]