## Abstract

Traditional rational motion design describes separately the translation of a reference point in a body and the rotation of the body about it. This means that there is dependence upon the choice of reference point. When considering the derivative of a motion, some approaches require the transform to be unitary. This paper resolves these issues by establishing means for constructing free-form motions from specified control poses using multiplicative and additive approaches. It also establishes the derivative of a motion in the more general non-unitary case. This leads to a characterization of the motion at the end of a motion segment in terms of the end pose and the linear and angular velocity and this, in turn, leads to the ability to join motion segments together with either C^{1}- or G^{1}-continuity.

Original language | English |
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Article number | 114280 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 412 |

Early online date | 29 Mar 2022 |

DOIs | |

Publication status | Published - 1 Oct 2022 |

## Keywords

- Dual quaternions
- Geometric algebra
- Geometric continuity
- Motion design
- Quaternions
- Rational motion

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

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