自动满足C^2连续的带参数五次Hermite插值样条

The automatic C^2 continuous quintic Hermite interpolating spline with parameters

为了克服已有的带形状参数的三次或四次Hermite型插值样条不能自动满足C2连续这一不足,提出了一类新的五次Hermite插值样条.该样条除了具有带形状参数Hermite型插值样条的特性外,在插值条件保持不变的情形下可自动满足C2连续且其形状还可通过所带的形状参数进行调控.进一步,给出了一种确定形状参数最优取值的方法,该法可使得五次Hermite插值样条曲线具有最优插值效果.

In order to solve the problem that the cubic or quartic Hermite-type interpolating splines with shape parameters can not automatically satisfy C^2 continuity,a new class of quintic Hermite interpolating spline with shape parameters is presented.The proposed spline not only has the same characteristics as the Hermite-type interpolating spline with shape parameters,but also automatically satisfies C^2 continuity and can be controlled by the shape parameters when the interpolation conditions remain unchanged.Furthermore,a method for determining the optimal value of the shape parameters is given,which can make the quintic Hermite interpolating spline curve with the optimal interpolation effects.