Constructing a quasi-Legendre basis based on the C-Bézier basis  

作　　者：HUANGYu WANGGuozhao 

机构地区：[1]DepartmentofMathematics,ZhejiangUniversity,Hangzhou310027,China

出　　处：《Progress in Natural Science:Materials International》2005年第6期559-563,共5页自然科学进展·国际材料（英文版）

基　　金：SupportedbytheNationalNaturalScienceFoundationofChina(GrantNo.60473130)

摘　　要：In the space Γ_n = span { sint, cost, 1, t, t^2, ···, t^(n-2)}, aC-Bezier basis is constructed by an integral approach. Howev- er, the C-Bezier basis is notorthogonal. For some applications, we construct an orthogonal basis based on the C-Bezier basis,which has remarkable properties similar to that of the Legendre basis. Then we derive thetransformation matrices that convert the C-Bezier basis and the orthogonal basis into each other. Asan example of application, we apply this orthogonal basis to the degree reduction approximation ofthe C-Bezier curves.In the space Γ_n=span｛sint,cost,1,t,t2,…,t n-2 ｝, a C-Bézier basis is constructed by an integral approach. However, the C-Bézier basis is not orthogonal. For some applications, we construct an orthogonal basis based on the C-Bézier basis, which has remarkable properties similar to that of the Legendre basis. Then we derive the transformation matrices that convert the C-Bézier basis and the orthogonal basis into each other. As an example of application, we apply this orthogonal basis to the degree reduction approximation of the C-Bézier curves.

关 键 词：C-Bezier basis orthogonal basis basis transformations degree reduction 

分 类 号：O17[理学—数学]