### Abstract

Original language | English |
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Title of host publication | GraVisMa 2009: Workshop Proceedings |

Subtitle of host publication | International Workshop on Computer Graphics, Computer Vision and Mathematics in co-operation with EUROGRAPHICS |

Editors | V Skala, D Hildenbrand |

Place of Publication | Plzen, CZ |

Publisher | Vaclav Skala/ University of West Bohemia |

Pages | 9-16 |

Number of pages | 8 |

ISBN (Print) | 9788086943909 |

Publication status | Published - 2009 |

Event | International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) 2009 - University of West Bohemia, Plzen, Czech Republic Duration: 1 Sep 2009 → … |

### Conference

Conference | International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) 2009 |
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Country | Czech Republic |

City | University of West Bohemia, Plzen |

Period | 1/09/09 → … |

### Fingerprint

### Cite this

*GraVisMa 2009: Workshop Proceedings: International Workshop on Computer Graphics, Computer Vision and Mathematics in co-operation with EUROGRAPHICS*(pp. 9-16). Plzen, CZ: Vaclav Skala/ University of West Bohemia.

**Exponentials and motions in geometric algebra.** / Simpson, L; Mullineux, Glen.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*GraVisMa 2009: Workshop Proceedings: International Workshop on Computer Graphics, Computer Vision and Mathematics in co-operation with EUROGRAPHICS.*Vaclav Skala/ University of West Bohemia, Plzen, CZ, pp. 9-16, International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) 2009, University of West Bohemia, Plzen, Czech Republic, 1/09/09.

}

TY - GEN

T1 - Exponentials and motions in geometric algebra

AU - Simpson, L

AU - Mullineux, Glen

PY - 2009

Y1 - 2009

N2 - The use of geometric algebra to define and manipulate rigid-body motions is investigated. An algebra with four basis elements of grade 1 is used in which the square of one of these elements is regarded as being infinite. This gives a representation of projective space and allows rotations and translations to be defined exactly. By smoothly interpolating between such transforms, smooth motions can be created using techniques such as spherical linear interpolation (Slerp). This requires the ability to handle the exponential function within the algebra. A closed form expression for the exponential is derived in the general case when the square of the special basis element is any real number. Taking this to be infinite allows smooth motions to be created and some examples are presented.

AB - The use of geometric algebra to define and manipulate rigid-body motions is investigated. An algebra with four basis elements of grade 1 is used in which the square of one of these elements is regarded as being infinite. This gives a representation of projective space and allows rotations and translations to be defined exactly. By smoothly interpolating between such transforms, smooth motions can be created using techniques such as spherical linear interpolation (Slerp). This requires the ability to handle the exponential function within the algebra. A closed form expression for the exponential is derived in the general case when the square of the special basis element is any real number. Taking this to be infinite allows smooth motions to be created and some examples are presented.

UR - http://gravisma.zcu.cz/GraVisMa-2009/GraVisMa-2009.htm

UR - http://gravisma.zcu.cz/GraVisMa-2009/Papers_2009/!_2009_GraVisMa_proceedings-FINAL.pdf

M3 - Conference contribution

SN - 9788086943909

SP - 9

EP - 16

BT - GraVisMa 2009: Workshop Proceedings

A2 - Skala, V

A2 - Hildenbrand, D

PB - Vaclav Skala/ University of West Bohemia

CY - Plzen, CZ

ER -