### Abstract

Though it may be tempting to smooth orientation data by filtering the Euler angles directly, it is noted that smoothed Euler angles do not necessarily yield a smooth motion. This is caused by the difference between the metric in the rotation group and that in the Euclidean space. The quaternions, which Hamilton discovered in 1853, provide a means for representing rotation. A unit quaternion, represented as a hypersphere in R ^{4}, has the same local topology and geometry as the rotation group. It thus provides a means for interpolating orientations. It is possible to achieve smooth rotation by filtering in quaternions the resulting quaternion may no longer be unitized. Fortunately, a unit quaternion curve, which represents the rotation path, can be derived by integrating the exponential map of the angular velocity. Unity of quaternions is thus maintained by filtering angular velocities. A lowpass filter coupled with an adaptive, mediative filter are employed to achieve smooth rotation motion in real time

Original language | English |
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Pages (from-to) | 191-198 |

Number of pages | 8 |

Journal | CAD Computer Aided Design |

Volume | 30 |

Issue number | 3 |

Publication status | Published - 1998 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering

### Cite this

*CAD Computer Aided Design*,

*30*(3), 191-198.