Quaternions

Quaternions are an alternate way to describe orientation or rotations in 3d space using an ordered set of four numbers. They have the ability to uniquely describe any 3d rotation about an arbitrary axis and do not suffer from a problem using euler angles called gimbal lock.

The basics of rotation in 2d and 3d for computer graphics with a focus on 3d rotation about cardinal axes and 3d rotation with quaternions.

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Quaternions are a set of 4-dimensional vectors that are used to represent rotations in computer graphics, they were discovered by William Hamilton as an extension of 2d complex numbers to a 3d equivalent.

This article covers the definition of a quaternion, its notation and operations.