Quartic Hermite interpolating splines with parameters

To overcome the defects of the standard cubic Hermite 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.