To overcome the defects of the standard cubic Heimite interpolating splines, a class of quartic Hermite interpolating splines with parameters was presented in this paper, which inherited the same properties of the standard cubic Hermite interpolating splines. Given the set interpolating conditions, the shape of the proposed splines could be adjusted by changing the values of the parameters. If the parameters were chosen properly, the quartic Hermite interpolating splines could achieve C2 continuity and approximate to the interpolated functions better than the standard cubic Hermite interpolating splines. The proposed new splines further enriched the theories of Hermite interpolating splines, and provided a new method for constructing interpolation curves and surfaces.%为了克服标准三次Hermite插值样条的不足,给出了一种带参数的四次Hermite插值样条,具有标准三次Hermite插值样条完全相同的性质.在插值条件给定时,四次Hermite插值样条的形状可通过改变参数的取值进行调控.通过选择合适的参数,四次Hermite曲线能达到C2连续,而且其整体逼近效果要好于标准三次Hermite插值样条.所提出的新样条进一步丰富了Hermite插值样条理论,也为工程中插值曲线曲面的构造提供了一种新方法.
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