motiontranslations

Motiontranslations is a term used in discussions of kinematics and computer graphics to refer to the translational component of motion. In this sense, it describes the sequence or collection of spatial shifts that accompany the movement of a body, as opposed to its rotation. The concept is often employed to emphasize how an object changes position over time while possibly also changing orientation.

From a mathematical perspective, the motion of a rigid body in three-dimensional space can be described by a rotation and a translation. The translation component, or motion translations, is represented by a vector t that shifts every point x of the body to x + t. In homogeneous coordinates, a rigid-body transformation combines a rotation R and a translation t into a 4x4 transformation matrix [R | t; 0 0 0 1]. The set of all translation vectors forms a subgroup of the Euclidean group E(3) isomorphic to R^3.

Applications of the idea include robotics, where path planning may separate translational movement from rotational maneuvers; computer graphics and animation, where motion can be keyframed as sequences of translations to achieve look and feel; and motion capture, where translation data accompanies rotational motion to reconstruct full body movement. In data representations, motion translations may be stored as time-ordered triples (dx, dy, dz) reflecting incremental position changes.

Note that motiontranslations is not a widely standardized term in published literature. When used, it generally points to the translational aspect of motion rather than to rotation, and its precise meaning can vary by context. See also rigid-body motion, translation, and the Euclidean group.