TranslationTransform
✖
TranslationTransform
Details

- TranslationTransform gives a TransformationFunction that can be applied to vectors.
- TranslationTransform[{x1,…,xn}] gives a transformation for vectors with dimension n.
- TranslationTransform[v][r] for vectors v and r is equivalent to r+v.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
Scope (3)Survey of the scope of standard use cases
Translation in four dimensions:

https://wolfram.com/xid/0cpr5ikhdote9u-fq81dh


https://wolfram.com/xid/0cpr5ikhdote9u-jlmuf


https://wolfram.com/xid/0cpr5ikhdote9u-d5qnvo


https://wolfram.com/xid/0cpr5ikhdote9u-kt9dh

Apply the transform five times:

https://wolfram.com/xid/0cpr5ikhdote9u-cfjj56

Use matrix operations and homogeneous coordinates:

https://wolfram.com/xid/0cpr5ikhdote9u-bdfjsd

Transformation applied to a 2D shape:

https://wolfram.com/xid/0cpr5ikhdote9u-g7xt0l

https://wolfram.com/xid/0cpr5ikhdote9u-crv30x

Transformation applied to a 3D shape:

https://wolfram.com/xid/0cpr5ikhdote9u-gc95ov

https://wolfram.com/xid/0cpr5ikhdote9u-c1y145

Applications (2)Sample problems that can be solved with this function
Properties & Relations (4)Properties of the function, and connections to other functions
The translation transformation is an isometric transform, i.e. preserves distances:

https://wolfram.com/xid/0cpr5ikhdote9u-0xq8b

https://wolfram.com/xid/0cpr5ikhdote9u-ciyzpc

https://wolfram.com/xid/0cpr5ikhdote9u-g592dc

Translating by and then by
is the same as translating by
:

https://wolfram.com/xid/0cpr5ikhdote9u-ditc8h

The inverse of translating by is the same as translating by
:

https://wolfram.com/xid/0cpr5ikhdote9u-gyzsfg

For geometric transformations, use Translate directly:

https://wolfram.com/xid/0cpr5ikhdote9u-c8bc5i


https://wolfram.com/xid/0cpr5ikhdote9u-g91fk3

Neat Examples (1)Surprising or curious use cases
Scale a 3D object about a point :

https://wolfram.com/xid/0cpr5ikhdote9u-jiaf3

https://wolfram.com/xid/0cpr5ikhdote9u-c62ncu

https://wolfram.com/xid/0cpr5ikhdote9u-dlteha


https://wolfram.com/xid/0cpr5ikhdote9u-nezgnq


https://wolfram.com/xid/0cpr5ikhdote9u-brlyrs

Wolfram Research (2007), TranslationTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/TranslationTransform.html.
Text
Wolfram Research (2007), TranslationTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/TranslationTransform.html.
Wolfram Research (2007), TranslationTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/TranslationTransform.html.
CMS
Wolfram Language. 2007. "TranslationTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TranslationTransform.html.
Wolfram Language. 2007. "TranslationTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TranslationTransform.html.
APA
Wolfram Language. (2007). TranslationTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TranslationTransform.html
Wolfram Language. (2007). TranslationTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TranslationTransform.html
BibTeX
@misc{reference.wolfram_2025_translationtransform, author="Wolfram Research", title="{TranslationTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/TranslationTransform.html}", note=[Accessed: 09-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_translationtransform, organization={Wolfram Research}, title={TranslationTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/TranslationTransform.html}, note=[Accessed: 09-May-2025
]}