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Representation of 3D Rotations

  • Kenichi Kanatani
Chapter
Part of the Springer Series in Information Sciences book series (SSINF, volume 20)

Abstract

In this chapter, we study various aspects of 3D rotations. We first prove Euler’s theorem and show how to parametrize a 3D rotation and how to compute compositions and inverses. For this purpose, we present many different representations of 3D rotations—by a rotation matrix, an angle and an axis, the Euler angles, the Cayley—Klein parameters, and a quaternion. We also discuss topological aspects of SO(3). Finally, we derive invariant measures of SO(3).

Keywords

Invariant Measure Real Root Rotation Matrix Euler Angle Stereographic Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

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Copyright information

© Spring-verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Kenichi Kanatani
    • 1
  1. 1.Department of Computer ScienceGunma University KiryuJapan

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