带形状参数的三次三角Hermite插值样条曲线

给出了一种带形状参数的三次三角Hermite插值样条曲线，具有标准三次Hermite插值样条曲线完全相同的性质。给定插值条件时，样条曲线的形状可通过改变形状参数的取值进行调控。在适当条件下，该样条曲线对应的Ferguson曲线可精确表示椭圆、抛物线等工程曲线。通过选择合适的形状参数，该插值样条曲线能达到C 2连续，而且其整体逼近效果要好于标准三次Hermite插值样条曲线。

Cubic trigonometric Hermite interpolating splines curves with shape pa-rameters

A class of cubic trigonometric Hermite interpolating splines curves with shape parameters is presented in this paper, which inherits the same properties of the standard cubic Hermite interpolating splines. For given interpolating con-ditions, the shape of the proposed splines curves can be adjusted by changing the values of the parameters. In proper con-ditions, the corresponding Ferguson curve can be used to represent some engineering curves exactly, such as ellipse and parabola. By selecting proper shape parameters, the proposed interpolating splines curves could satisfy C 2 continuous and approximate the interpolated functions better than the standard cubic Hermite interpolating splines curves.