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 line equation of a line can be given in vector form: Here is the position of a point on the line, and is a unit vector in the direction of the line. Then as scalar "t" varies, gives the locus of the line. The distance of an arbitrary point to this line is given by This formula can be derived as follows: formula_39 is a vector from to the point on the line. Then formula_40 is the projected length onto the line and so is a vector that is the projection of formula_39 onto the line. Thus is the component of