The Translation (geometry) reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Translation (geometry)

In Euclidean geometry, translation is an isometry 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.

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_x, p_y, p_z, 1) would need to be multiplied with this translation matrix:

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

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