Following the recent results of Albrecht et al., 2017, Albrecht et al., 2020, the problem of Hermite interpolation by clamped spatial Pythagorean hodograph (PH) B-spline curves is thoroughly investigated in this paper. The constructed interpolants are obtained by using beneficial properties of B-spline basis functions and via solving special quadratic and linear equations in quaternion algebra. All the designed procedures are purely symbolic and the main contribution lies in the unifying approach to the formulated problem. The results are confirmed by several computed examples.

中文翻译：

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带勾股勾线图B样条的C ^d Hermite插值

根据Albrecht等人（2017），Albrecht等人（2020）的最新研究结果，本文对夹紧空间勾股勾线图（PH）B样条曲线的Hermite插值问题进行了深入研究。利用B样条基函数的有益性质，并通过求解四元数代数中的特殊二次方程和线性方程，可以获得构造的插值。所有设计的程序均纯粹是象征性的，其主要贡献在于对提出的问题采取了统一的方法。通过几个计算例证实了该结果。