quaternions

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A collection of quaternion libraries for various languages.

Table of Contents

• Table of Contents
• Quaternion Conventions
• Supported Languages
• References

Quaternion Conventions

The chosen conventions for the quaternions were chosen as to match Hamilton's description of a quaternion. All notation and definition is defined as in Joan Solà[1].

Convention	Choice	Example
Components Order	Scalar First	($q_w$ , $q_v$)
Handedness	Right-Handed	$ij=k$
Rotation Function	Passive	$x_{\mathcal{B}}=q_{passive}\otimes x_{\mathcal{A}}\otimes q^*_{passive}$
Rotation Direction	Local-to-Global	$q\triangleq q_{\mathcal{GL}}$ $x_{\mathcal{G}}=q\otimes x_{\mathcal{L}}\otimes q^*$

Note: For rotation direction, $q_{\mathcal{GL}}=q_{[with-respect-to][of]}=q_{[to][from]}$[1].

Supported Languages

     

Click image for that language's library

References

[1] Solà, J. (2017). Quaternion Kinematics for the error-state Kalman filter