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
Differential geometry of surfaces nearby point. The direction of the geodesic at the base point and the distance uniquely determine the other endpoint. These two bits of data, a direction and a magnitude, thus determine a tangent vector at the base point. The map from tangent vectors to endpoints smoothly sweeps out a neighbourhood of the base point and defines what is called the "exponential map", defining a local coordinate chart at that base point. The neighbourhood swept out has similar properties to balls in Euclidean space, namely any two points in it are joined by a unique geodesic. This property is called "geodesic