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 = (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
- Translation operator
- Affine transformation
- Translation (physics)
Last updated: 10-24-2004 05:10:45