History of Quaternions - Quaternions As Rotations

Quaternions As Rotations

Quaternions are a concise method of representing the automorphisms of three- and four-dimensional spaces. They have the technical advantage that unit quaternions form the simply connected cover of the space of three-dimensional rotations.

For this reason, quaternions are used in computer graphics, control theory, signal processing, attitude control, physics, bioinformatics, and orbital mechanics. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions. Tomb Raider (1996) is often cited as the first mass-market computer game to have used quaternions to achieve smooth 3D rotation. Quaternions have received another boost from number theory because of their relation to quadratic forms.