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
Distance from a point to a plane the closest point to the origin may be expressed more succinctly using notation from linear algebra. The expression formula_19 in the definition of a plane is a dot product formula_20, and the expression formula_21 appearing in the solution is the squared norm formula_22. Thus, if formula_23 is a given vector, the plane may be described as the set of vectors formula_24 for which formula_25 and the closest point on this plane is the vector Written in Cartesian form, the closest point is given by formula_27 for formula_28 where and the distance from formula_30 to the hyperplane is Thus in formula_32