三次Hermite参数曲线与曲面的扩展

Extensions of cubic Hermite parametric curve and surface

在给定插值条件时,标准三次Hermite参数曲线与曲面的形状无法调整。为克服标准三次Hermite参数曲线与曲面的不足,首先通过提高基函数次数的方法给出了一种带形状参数的四次Hermite基函数,然后生成了相应的带形状参数的四次Hermite参数曲线与曲面。所生成的曲线与曲面是标准三次Hermite参数曲线与曲面的扩展,不仅与标准三次Hermite曲线与曲面具有完全相同的性质,而且当插值条件给定时,其形状可通过修改形状参数的取值进行局部或整体调节,为插值曲线与曲面的构造提供了一种新方法。

The shapes of the standard cubic parametric Hermite curve and surface are hard to be ad- justed when the interpolation conditions are given. For solving this problem, a class of quartic Hermite basis functions is presented through increasing the degree of basis functions. And then, the correspond- ing quartic Hermite parametric curve and surface with shape parameters are presented. The proposed curve and surface are extensions of the corresponding standard cubic Hermite parametric curve and sur- face. They not only inherit the interpolation properties of the standard cubic Hermite parametric curve and surface, but also can be local or global adjusted by using the shape parameters when the interpola- tion conditions are fixed, which offers a new method for constructing interpolation curve and surface.