Translate
In Euclidean geometry, a translation is a function that moves every point a constant distance in a specified direction. (Also in Euclidean geometry a transformation is a one to one correspondence between two sets of points or a mapping from one plane to another.(master math Geometry, Debra Anne, Ross) A translation can be described as a rigid motion: other rigid motions include rotations and 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 operator such that If v is a fixed vector, then the translation Tv will work as Tv(p) = p + v. If T is a translation, then the image of a subset A under the function T is the translate of A by T. The translate of A by Tv is often written A + v. In a Euclidean space, any translation is an isometry. The set of all translations forms the translation group T, which is isomorphic to the space itself, and a normal subgroup of Euclidean group E(n ). The quotient group of E(n ) by T is isomorphic to the orthogonal group O(n ): E(n ) / T ≅ O(n ).
