Representation of 3D Rotations

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


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).


Invariant Measure Real Root Rotation Matrix Euler Angle Stereographic Projection 
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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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