@article{Perwass2007AGP, title={A geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation}, author={Christian Perwass and Rida T. Farouki and Lyle Noakes}, journal={Computer Aided Geometric Design}, year={2007}, volume={24}, pages={220-237} }

- Published 2007 in Computer Aided Geometric Design
DOI:10.1016/j.cagd.2007.01.002

A novel formulation for spatial Pythagorean–hodograph (PH) curves, based on the geometric product of vectors from Clifford algebra, is proposed. Compared to the established quaternion representation, in which a hodograph is generated by a continuous sequence of scalings/rotations of a fixed unit vector n̂ , the new representation corresponds to a sequence of scalings/reflections of n̂ . The two representations are shown to be equivalent for cubic and quintic PH curves, modulo certain… CONTINUE READING

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