The Translation (geometry) reference article from the English Wikipedia on 24-Jul-2004
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Translation (geometry)

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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 = (vx, vy, vz), each homogeneous vector p = (px, py, pz, 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