逼近三次B样条导矢曲线的四次Hermite插值样条

Quartic Hermite Interpolation Spline Determined by Approximating the Derivative of Cubic B-Spline Curve

给出了形状可调的四次Hermite插值样条曲线的构造方法。四次样条曲线可提供额外的自由度用于调整曲线具有合理形状。利用导矢逼近使得四次Hermite样条曲线具有与三次B样条曲线相似的形状。通过最小化曲线间的导矢误差给出了确定自由度的方法,提出了四次Hermite插值样条曲线的构造方法。该方法增加了自由度控制曲线形状能更好满足保形要求。最后以实例对构造的四次Hermite样条曲线和标准三次Hermite插值样条曲线进行了比较。

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.