Translation (geometry) of the object. The translation vector formula_8 common to all points of the object describes a particular type of displacement of the object, usually called a "linear" displacement to distinguish it from displacements involving rotation, called "angular" displacements. When considering spacetime, a change of time coordinate is considered to be a translation. For example, the Galilean group and the Poincaré group include translations with respect to time. Translation (geometry) In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. In Euclidean geometry a
Motion (geometry) or inproper motions are motions like reflections, glide reflections and Improper rotations that invert the orientation of a chiral shape. Some geometers define motion in such a way that only direct motions are motions. In differential geometry, a diffeomorphism is called a motion if it induces an isometry between the tangent space at a manifold point and the tangent space at the image of that point. Given a geometry, the set of motions forms a group under composition of mappings. This group of motions is noted for its properties. For example, the Euclidean group is noted for the normal subgroup