一种类Legendre基及其应用

A quasi-Legendre basis and its application

利用T-Bézier基的优美性质,如对称性质和端点性质,在空间Γn=span{1,t,t2,…,tn-4,sint,cost,sin 2t,cos 2t}中构造了一组正交基,并利用正交性和升阶及求导性质得出了这两组基之间的过渡矩阵,进一步指明了这组类Legendre基在降阶逼近中的应用.另外,在T-Bézier系统中可以充当Legendre基在Bézier系统中的角色.

A new orthogonal basis, called quasi-Legendre basis, is constructed for the space Гn=span { 1 ,t,t^2 , ..., t^n-4 ,sin t,cos 2t,sin 2t,cos 2t}, by using the properties of T-Bézier basis. The transition matrix of the two basises is acquired by the properties of orthogonality, differentiation and degree-elevation. Furthermore, the application of quasi-Legendre basis in degree-reduction approximation is showed. Its application is more, and it can act as Legendre basis in the system of T-Bézier.