Definition
A unit quaternion can be described as:
We can associate a quaternion with a rotation around an axis by the following expression
where α is a simple rotation angle (the value in radians of the angle of rotation) and cos(βx), cos(βy) and cos(βz) are the "direction cosines" locating the axis of rotation (Euler's Theorem).
Read more about this topic: Conversion Between Quaternions And Euler Angles
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