Quaternions and spatial rotation

Uncommon card · No. 102640

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space (3D rotations). This is a generalization of the use of unit complex numbers for 2D rotations. Specifically, quaternions encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis. When used to represent rotation, unit quaternions are also called rotation quaternions as they represent the 3D rotation group. When used to represent an orientation or attitude (body rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions. A spatial rotation in the amount of θ {\displaystyle \theta } radians...

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