构造了含参数的分段线性有理插值函数(分子、分母均为一次多项式),通过适当选择形状参数,由此函数产生的曲线一阶连续并且保单调.文中用张量积方法将此结果推广到二元矩形网格上的曲面插值,同时给出了插值函数的误差估计及数值例子.%A piecewise linear rational interpolating function with shape parameters is constructed, which is linear numerator and linear denominator. Through giving appropriate values to the shape parameters, the function is continuity and preserving monotonity. Extenting this result, we construct an interpolatory surface on a rectangular grid. Furthermore, the error analysis of the interpolant and the numerial examples are also given.
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