Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is an isometry.^[1]

As a function

Note:This is a translation.

translation graphic — A translation moves every point of a figure or a space by the same amount in a given direction.

See also: Displacement (geometry)

If $\mathbf {v}$ is a fixed vector, known as the translation vector, and $\mathbf {p}$ is the initial position of some object, then the translation function $T_{\mathbf {v} }$ will work as $T_{\mathbf {v} }(\mathbf {p} )=\mathbf {p} +\mathbf {v}$ .

If Failed to parse (Conversion error. 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The translate of Failed to parse (Conversion error. 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Horizontal and vertical translations

In geometry, a vertical translation (also known as vertical shift) is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.

Drawio

Attachments

External links

Translation Transform
Geometric Translation (Interactive Animation) at Math Is Fun
Understanding 2D Translation and Understanding 3D Translation by Roger Germundsson, The Wolfram Dmonstrations Project.

References

↑ Zazkis, R., Liljedahl, P., & Gadowsky, K. Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22, 437-450. Retrieved April 29, 2014, from www.elsevier.com/locate/jmath

[1] Zazkis, R., Liljedahl, P., & Gadowsky, K. Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22, 437-450. Retrieved April 29, 2014, from www.elsevier.com/locate/jmath

[1]