一种显式Hermite曲线插值方法

An Explicit Hermite Curve Interpolation

Hermite曲线插值要求插值曲线不仅严格通过型值点,还要满足型值点处的各阶导数切触条件.针对传统隐式或半显式Hermite曲线插值方法中求解复杂、非严格插值等问题,提出一种显式Hermite曲线插值方法.首先构造了一类基数型Hermite插值基函数,该基函数具有局部支集、对称性、高阶连续等性质;然后将该基函数与给定的Hermite插值条件调配,得到一条严格满足各阶切触条件的k次样条曲线.实验结果表明,利用文中方法得到的插值曲线不仅严格满足插值条件,还具有光滑的曲率与较高的插值精度;与传统方法相比,该方法具有插值过程简单、无需求解方程组的优点.

Hermite curve interpolation requires the result curve interpolating the given points as well as various derivatives at these points. The traditional implicit and semi-explicit methods have the problems on difficult solving and inexact interpolation. With respect to these defects, a novel explicit Hermite curve interpolation method is proposed in this paper. Firstly, we constructed a class of cardinal type Hermite basis functions. Then they will be blended with all the given interpolation conditions, and a spline curve of degree k will be obtained directly which satisfies all-order derivatives. The experimental results show that our result curves have smooth curvature and high interpolation precision. Compared with the traditional methods, our method has a simper interpolation process without solving equations.