Real time motion fairing with unit quaternions

Y. C. Fang, C. C. Hsieh, M. J. Kim, J. J. Chang, T. C. Woo

Research output: Contribution to journalArticle

46 Citations (Scopus)


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 languageEnglish
Pages (from-to)191-198
Number of pages8
JournalCAD Computer Aided Design
Issue number3
Publication statusPublished - 1998 Dec 1


All Science Journal Classification (ASJC) codes

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

Cite this

Fang, Y. C., Hsieh, C. C., Kim, M. J., Chang, J. J., & Woo, T. C. (1998). Real time motion fairing with unit quaternions. CAD Computer Aided Design, 30(3), 191-198.