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中文摘要：
提高插值曲线曲面的逼近性是计算辅助几何设计中的一个重要问题.本文构建了一种带单参数的分段有理三次Hermite插值样条.讨论了该样条的逼近性,给出了一种提高插值曲线曲面逼近性的方法,并且给出数值例子.结果表明,对于给定的插值条件,通过选择合适的参数,依本文方法所生成的插值曲线曲面在逼近效果上好于标准三次Hermite插值曲线曲面.
英文摘要：
Improving the approximability of interpolating curves/surfaces is an important issue in the computer aided geometric design.A piecewise rational cubic Hermite interpolating spline with a single parameter is constructed in this paper.The approximation properties of the interpolating spline are studied and a method for improving the approximability of the curves/surfaces is introduced.Examples are given to illustrate the advantages of our method.The results show that,for given interpolating conditions,if the parameters are chosen properly,the introduced interpolating curves/surfaces can approximate the interpolated functions better than the standard cubic Hermite interpolating curves/surfaces.
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