Translation (geometry)
A translation moves every point of a figure or a space by the same amount in a given direction. A reflection against an axis followed by a reflection against a second axis parallel to the first one results in a total motion which is a translation. 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. [1] 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 operator Tδ {displaystyle T_{mathbf {delta } }} such that Tδ f(v)=f(v+δ ).{displaystyle T_{mathbf {delta } }f(mathbf {v} )=f(mathbf {v} +mathbf {delta } )....