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中文摘要：
文[19]中，作者构造了一种基于函数值的带参数的分子为双三次、分母为双二次的二元有理插值样条．本文进一步研究该种二元有理插值样条的有界性，给出插值的逼近表达式，讨论插值曲面形状的点控制问题．在插值条件不变的情况下，插值区域内任一点插值函数的值可以根据设计的需要通过对参数的选取修改，从而达到插值曲面局部修改的目的．
英文摘要：
A bivariate rational interpolation method with parameters was created in an earlier work which was based on function values only, and this spline is with bicubic numerator and biquadratic denominators. This paper will deal with the bounded property, approximation property and the point control method of the interpolating surface. It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be. Also, the approximation expression of the interpolation are derived. More important is that the values of the interpolating function at point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters, so the interpolation surface can be modified for the given interpolation data when needed in practical design.
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