关键词: Hermite 插值样条, 保形插值, 形状可调

Abstract: A method is developed to construct adjustable quartic Hermite interpolating spline curves.
The extra degree of freedom can be used to adjust the quartic curve to a reasonable shape. The
interpolation based on the approximation of derivatives is discussed to make quartic Hermite spline with
similar shape feature of cubic B-spline. The degree freedom is determined by minimizing the proximity,
which is defined by the squared difference of the derivatives of the curves. The shape of the proposed
quartic spline can be adjusted to satisfy the shape-preserving requirement by changing the values of
degree of freedom. Four numerical examples are presented to compare the proposed quartic Hermite
spline with the standard cubic Hermite spline.

Key words: Hermite interpolating spline, shape-preserving interpolation, shape adjustable