# Exponentials and motions in geometric algebra

### Reference:

Simpson, L. and Mullineux, G., 2009. Exponentials and motions in geometric algebra. *In*: Skala, V. and Hildenbrand, D., eds. *International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) 2009*, 2009-09-01. Plzen, CZ: Vaclav Skala/ University of West Bohemia, pp. 9-16.

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### Official URL:

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

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### Abstract

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.

### Details

Item Type | Conference or Workshop Items (UNSPECIFIED) | ||||

Creators | Simpson, L.and Mullineux, G. | ||||

Editors | Skala, V.and Hildenbrand, D. | ||||

Related URLs |
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Departments | Faculty of Engineering & Design > Mechanical Engineering | ||||

Research Centres | Innovative Design & Manufacturing Research Centre (IdMRC) | ||||

Status | Published | ||||

ID Code | 20039 |

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