Postrotation

Postrotation is a term used to describe the rotation applied after one or more other transformations in a sequence. It is commonly encountered in fields such as computer graphics, robotics, and kinematics to denote the orientation change that occurs following an initial operation, such as a translation or an earlier rotation. Because rotations do not commute, the order in which transformations are applied matters, and a postrotation can produce a different final pose than applying the same rotation earlier in the sequence.

Mathematically, a postrotation arises when a point or object is transformed by a prior operation and then rotated. For example, if a point p is translated by t and subsequently rotated by a rotation R, the final position can be expressed (depending on the convention) as p' = R(p + t). The rotation R here is the postrotation relative to the translation. Transformation pipelines may implement this with matrices or quaternions, with careful attention to the chosen convention for multiplying transformations.

In practice, postrotations appear in robot arm pose planning, camera orientation in 3D scenes, and animation pipelines, where the final orientation is achieved by applying a rotation after other motions. Handling postrotations robustly often benefits from using quaternions to represent rotations, as they avoid issues such as gimbal lock and allow smooth interpolation between orientations.

See also: pre-rotation, rotation, transformation matrix, quaternion, gimbal lock.