Translation (geometry) of the object. The translation vector formula_8 common to all points of the object describes a particular type of displacement of the object, usually called a "linear" displacement to distinguish it from displacements involving rotation, called "angular" displacements. When considering spacetime, a change of time coordinate is considered to be a translation. For example, the Galilean group and the Poincaré group include translations with respect to time. 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
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