# Online Encyclopedia

# Translation (geometry)

In Euclidean geometry, **translation** is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. It can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. Each translation is an isometry.

## Matrix representation

A translation cannot be accomplished using a 3-by-3 matrix, so homogeneous coordinates are normally used.

To translate an object by a vector *v* = (*v _{x}, v_{y}, v_{z}*), each homogeneous vector

*p*= (

*p*, 1) would need to be multiplied with this translation matrix:

_{x}, p_{y}, p_{z}As shown below, the multiplication will give the expected result:

The inverse of a translation matrix can be obtained by negating the vector:

## See also

- Translation operator
- Affine transformation
- Translation (physics)

Last updated: 10-24-2004 05:10:45