空间曲线的几何Hermite插值问题

摘要

A 3-dimensional quartic Bèzier curve for given GC2 Hermite interpolation conditions is constructed. Study shows that the solution exists locally and possesses one degree of freedom. Moreover, the approximation order of the interpolation is proven to be 6.%在给定的GC2插值条件下,构造了一条空间四次Bèzier 曲线(空间曲线的几何Hermite插值问题)，结果表明了四次GC2-Hermite插值问题的解是局部存在的，并且有一个自由度；文章还讨论了逼近阶，并证明了局部解具有六阶逼近精度.