# Motion Interpolation in Lie Subgroups and Symmetric Subspaces

Conference item

Selig, JM, Wu, Y and Carricato, M (2017). Motion Interpolation in Lie Subgroups and Symmetric Subspaces.

*7th IFToMM International Workshop of Computational Kinematics.*Futurescope, Poitiers, France 22 - 24 May 2017 London South Bank University. doi:http://doi.org/10.1007/978-3-319-60867-9_53

Authors | Selig, JM, Wu, Y and Carricato, M |
---|---|

Abstract | We show that a map defined by Pfurner, Schrocker and Husty, mapping points in 7-dimensional projective space to the Study quadric, is equivalent to the composition of an extended inverse Cayley map with the direct Cayley map, where the Cayley map in question is associated to the adjoint representation of the group SE(3). We also verify that subgroups and symmetric subspaces of SE(3) lie on linear spaces in dual quaternion representation of the group. These two ideas are combined with the observation that the Pfurner-Schrocker-Husty map preserves these linear subspaces. This means that the interpolation method proposed by Pfurner et al can be restricted to subgroups and symmetric subspaces of SE(3). |

Keywords | Motion interpolation; Lie triple systems; Symmetric subspaces; Cayley maps |

Year | 2017 |

Publisher | London South Bank University |

Digital Object Identifier (DOI) | doi:http://doi.org/10.1007/978-3-319-60867-9_53 |

Accepted author manuscript | License CC BY 4.0 |

Publication dates | |

Print | 05 Jul 2017 |

Publication process dates | |

Deposited | 03 Apr 2017 |

Accepted | 28 Feb 2017 |

https://openresearch.lsbu.ac.uk/item/86yvv

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