Translation (geometry)

The parallel displacement or translation is a geometric figure, which moves each point on the plane of the drawing or the space in the same direction by the same distance. It can be characterized by a vector, the so-called motion vector.

Parallel shifts among the movements, as lengths and angles are preserved in their application. As movements, they are - especially the parallel shifts in the plane - also numbered among the Kongruenzabbildungen.


In the axiomatic built affine geometry ( synthetic geometry) is called a collineation a translation, if both the following conditions are met:

  • Straight lines are mapped to parallel lines.
  • If any one point is varied, the Figure does not have a fixed point.

(The set of all points, the set of all lines, see incidence). These translations can be used, for example, an affine translation level position vectors of the points.

Again, a translation is always an affinity in the sense of synthetic geometry. The continuation of a translation in the projective completion of the affine space is a projective perspectivity and therefore a projectivity.

Parallel shift in the optical

In optics is referred to as a parallel shift to the effect that a light beam that passes through an optically denser medium than center beam to be constant, i.e. without changing the direction of propagation continues its travel, but on a parallel to the extension of the incident beam.