Translation (geometry) 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 transformation is a one-to-one correspondence between two sets of points or a mapping from one plane to another. A translation can be described as a rigid motion: the other rigid motions are rotations, reflections and glide reflections. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an
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