In view of the deficiency of the piecewise cubic Hermite interpolating splines in shape adjustment and continuity, theC3 piecewise seventh-degree Hermite interpolating splines with two parameters are pre-sented in this paper. First, a class of seventh-degree Hermite basis functions with two parameters is con-structed. Then, the piecewise seventh-degree Hermite parametric spline curves are defined on base of the proposed basis functions, and the parameter selection of the spline curves is discussed. Finally, the piecewise seventh-degree Hermite spline interpolation function is studied, and the interpolation error and the method for determining the optimal interpolation function are given. Example results show that, when the interpola-tion conditions remain unchanged, piecewise seventh-degree Hermite parametric spline curves not only achieveC3 continuity, but also can realize shape control through the two parameters. By determining the op-timal values of the two parameters, the piecewise seventh-degree Hermite spline interpolation function can obtain better interpolation results.%针对分段三次Hermite插值样条在形状调控与连续性方面的不足,提出带2个参数的C3连续分段七次Hermite插值样条.首先构造一组带2个参数的七次Hermite基函数;然后基于该组基函数定义分段七次Hermite参数样条曲线,并讨论样条曲线所带参数的选取方案;最后研究对应的分段七次Hermite样条插值函数,并给出其插值余项及最佳插值函数的确定方法.实例结果表明,当插值条件保持不变时,分段七次Hermite参数样条曲线不仅达到C3连续,而且还可利用所带的参数实现对曲线形状的调控;通过确定所带参数的最佳取值,可使得分段七次Hermite样条插值函数获得较好的插值效果.
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