C~d Hermite interpolations with spatial Pythagorean hodograph B-splines

摘要

Following the recent results of Albrecht et al. (2017, 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.