一种有理插值曲面的有界性质和点的控制

Bounded property and point control of a bivariate rational interpolation surface

文章介绍了一种分母为二次的仅基于函数值的二元有理插值曲面,研究了这种插值曲面的有界性质和点的控制方法;证明了在插值区域内,无论参数如何选择,插值的函数值都是有界的,得到了该插值不依赖于参数的估计表达式;更重要的是,在插值数据不变的情况下,可以通过选择合适的参数来修改插值区域内任一点插值函数的值;在特殊情况下,可将4个参数化为2个参数,研究了"中点-均值"控制方法,并给出了数值例子。

A bivariate parametric rational interpolation surface with quadratic denominator, which is based on function values only, is introduced and the bounded property and the point control method of this interpolation surface are discussed. It is proved that the values of the interpolating function are bounded in the interpolating region no matter what the parameters might be. Also the estimates of the interpolation are derived, which are shown to be independent of the parameters. Moreover, the inter polating function at any point of the interpolating region can be modified by selecting suitable parame- ters under the condition that the interpolating data is invariant. In the special case, the four parameters can be changed into only two parameters. The method of‘Central Point-Mean Value＇ control is studied and an numerical example is given to demonstrate the control.