关键词: 三次Hermite插值样条, 次三角Hermite插值样条, 形状参数, 逼近

Abstract: 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 conditions, the shape of the proposed splines curves can be adjusted by changing the values of the parameters. In proper conditions, 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 [C2] continuous and approximate the interpolated functions better than the standard cubic Hermite interpolating splines curves.

Key words: cubic Hermite interpolating splines, cubic trigonometric Hermite interpolating splines, shape parameters, approximation