局部形状可调插值曲线曲面及其参数选取方案

以形状可调插值曲线曲面为研究主题的文献多数侧重于分析曲线曲面性质，少有文献介绍可调插值曲线曲面的构造方法，以及调节参数的选取方案。这里以3次Hermite插值曲线为基础，通过在导矢中引入参数来构造形状可调插值曲线，将曲线按照插值数据进行整理，即可得到含参数的插值基函数，进而由之构造张量积插值曲面。为了帮助设计者寻找合适的参数，提供了4种用于确定曲线中形状参数的准则，其中的3种还推广应用于曲面，每种准则都提供了可以直接使用的公式。所给可调插值曲线曲面的构造方法以及参数选取方案具有一般性，数值实例验证了方案的有效性。

Parameter selection scheme of local shape adjustable interpolation curve and surface

Most of the literatures with the theme of shape adjustable interpolation curve and surface focus on analyzing the properties of curve and surface. Few literatures introduce the construction method of the adjustable interpolation curve and surface, as well as the selection scheme of the parameter. Based on the cubic Hermite interpolation curve, this paper constructs shape adjustable interpolation curve by introducing parameter in the derivative vector. Rearranging the expressing of the curve according to interpolation data, we can obtain the interpolation basis functions with parameter. Then we can construct tensor product interpolation surface. To help the designer to find suitable parameter, four criteria used to determine the shape parameter of the curve are provided and three of them are applied in surface. Each criterion provides a formula can be used directly. The construction method and the parameter selection scheme of the interpolation curve and surface is common, and the numerical examples demonstrate the effectiveness of the scheme.