代数双曲空间中拟Legendre基的应用

摘要

鉴于Legendre基等正交基在代数多项式空间中的广泛应用,论文在深入研究代数双曲空间的拟Legendre基性质的基础上,给出了其在反函数逼近和等距曲线逼近上的应用.利用多项式和双曲函数的混合多项式序列来逼近反函数,并通过实例证明给出方法的有效性;对基曲线的法矢曲线进行逼近,构造H-Bézier曲线的等距曲线的最佳逼近,这种方法直接求得逼近曲线的控制顶点,计算简单,截断误差小.%In view of the wide usage of the orthogonal basis such as Legendre basis in the algebra polynomial space, the applications of the quasi-Legendre basis in inversion and offsetting approximations are given in this paper. Inversion approximation is constructed by using the blending of polynomial and hyperbolic functions, and the experimental results show that the approximation method is effective. An approach to approximate the offset curves of the H-Bezier curve based on the ideal approximation for the normal curve is presented. The algebraic approximation algorithms which can obtain the control points of the approximation curves directly are simple and more precise.