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
Inversion in a sphere the radius of the sphere is 1. Then every point can be written in the form "r"v, where "r" is the distance from the point to the origin and v is a unit vector; moreover, for every point apart from the origin this representation is unique. Given such a representation of a point, its image under spherical inversion is defined to be the point "r"v. This defines a homeomorphism from formula_1 to itself. As a map from Euclidean space to itself, the spherical inversion map is not defined at the origin, but we can extend it to formula_2, the one-point