Quaternions and Gibbs Vectors

  • Thomas HaslwanterEmail author


Quaternions are a more elegant and more efficient way to characterize rotations than rotation matrices. They allow us to represent every 3D orientation with a 3D vector. This chapter explains quaternions, their properties, and how they relate to rotation matrices. Gibbs vectors (sometimes also referred to as “rotation vectors”) are introduced. And practical examples show how to work efficiently with quaternions.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Medical Engineering and Applied Social SciencesUniversity of Applied Sciences Upper AustriaLinz, Upper AustriaAustria

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