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TranslationTransform
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TranslationTransform

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gives a TransformationFunction that represents translation of points by a vector v.

Details

Examples

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Basic Examples  (1)Summary of the most common use cases

Generate a function representing a translation by the vector {a,b}:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-mo6trh
Out[1]=1

Apply the transformation function to a vector:

In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-nkdph
Out[2]=2

Scope  (3)Survey of the scope of standard use cases

Translation in four dimensions:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-fq81dh
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-jlmuf
Out[2]=2

The inverse transform:

In[3]:=3
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https://wolfram.com/xid/0cpr5ikhdote9u-d5qnvo
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0cpr5ikhdote9u-kt9dh
Out[4]=4

Apply the transform five times:

In[5]:=5
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https://wolfram.com/xid/0cpr5ikhdote9u-cfjj56
Out[5]=5

Use matrix operations and homogeneous coordinates:

In[6]:=6
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https://wolfram.com/xid/0cpr5ikhdote9u-bdfjsd
Out[6]=6

Transformation applied to a 2D shape:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-g7xt0l
In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-crv30x
Out[2]=2

Transformation applied to a 3D shape:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-gc95ov
In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-c1y145
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Transforming graphics primitives:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-bbbawc
Out[1]=1

A random translation walk:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-pjnau
Out[1]=1

Properties & Relations  (4)Properties of the function, and connections to other functions

The translation transformation is an isometric transform, i.e. preserves distances:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-0xq8b
In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-ciyzpc
In[4]:=4
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https://wolfram.com/xid/0cpr5ikhdote9u-g592dc
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-ditc8h
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-gyzsfg
Out[1]=1

For geometric transformations, use Translate directly:

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-c8bc5i
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-g91fk3
Out[2]=2

Neat Examples  (1)Surprising or curious use cases

Scale a 3D object about a point :

In[1]:=1
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https://wolfram.com/xid/0cpr5ikhdote9u-jiaf3
In[2]:=2
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https://wolfram.com/xid/0cpr5ikhdote9u-c62ncu

Translate along the axis:

In[3]:=3
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https://wolfram.com/xid/0cpr5ikhdote9u-dlteha
Out[3]=3

Translate along the axis:

In[4]:=4
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https://wolfram.com/xid/0cpr5ikhdote9u-nezgnq
Out[4]=4

Translate along the axis:

In[5]:=5
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https://wolfram.com/xid/0cpr5ikhdote9u-brlyrs
Out[5]=5
Wolfram Research (2007), TranslationTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/TranslationTransform.html.
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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.

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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 ]}

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@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 ]}

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@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 ]}