Introducing quaternions

The minimum number of values needed to represent rotations in 3D space is three. The most intuitive and long-applied method for defining rotations, as we’ve seen, is to use these values as the three angles of rotation around the x axis, the y axis, and the z axis. The values of these angles can range from 0 to 360 degrees or 0 to 2 PI radians.

Any object in 3D space can be rotated around these axes that represent either the world axes or the object’s own local access system. Formally, the angles around the world axes are called fixed angles, while the angles around an object’s local axis system are called Euler angles. However, often both sets of angles are referred to as Euler angles. We covered the mathematics to apply rotations around these three axes in Chapter 15, Navigating the View Space, in addition to investigating when these calculations break down and cause gimbal lock.

Quaternions were devised in 1843 by Irish mathematician...