Translation (geometry)

In Euclidean geometry, a translation, or translation operator, is an affine 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. In other words, if v is a fixed vector, then the translation Tv will work as Tv(p) = p + v.

Related Topics:
Euclidean geometry - Affine transformation - Euclidean space - Vector - Origin - Coordinate system

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If T is a translation, then the image of a subset A under the function T is the translate of A by T. The translate of A by Tv is often written A + v.

Related Topics:
Image - Function

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Each translation is an isometry.

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