A geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation

@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}
}
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