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AffineTransform[m]

gives a TransformationFunction that represents an affine transform that maps r to m.r.

AffineTransform[{m,v}]

gives an affine transform that maps r to m.r+v.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Iterated Function Systems  
Image Transformations  
Properties & Relations  
Neat Examples  
See Also
Related Guides
History
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AffineTransform

AffineTransform[m]

gives a TransformationFunction that represents an affine transform that maps r to m.r.

AffineTransform[{m,v}]

gives an affine transform that maps r to m.r+v.

Details

Examples

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Basic Examples  (2)

A general affine transformation:

Transform points:

A pure rotation:

A pure translation:

Scope  (3)

Affine transform in four dimensions:

The inverse transform:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications  (5)

Iterated Function Systems  (3)

Define an iterated function system (IFS) and iterate it on point sets, by computing in each iteration:

Sierpiński gasket:

Sierpiński carpet:

Heighway's Dragon:

Compute an iterated function system's (IFS) fixed points efficiently by randomly picking subparts of point sets:

Sierpiński gasket:

Sierpiński carpet:

Heighway's Dragon:

Hedgehog:

Compute an iterated function system applied to graphics primitives:

Sierpiński gasket:

Sierpiński carpet:

Hedgehog:

Image Transformations  (2)

Use an AffineTransform to rotate an image:

Affine transform of a 3D image with no translation:

Properties & Relations  (3)

Many other geometric transformations are a special case of affine transform:

In turn, an affine transformation is a special case of a linear-fractional transformation:

The composition of affine transforms is an affine transform:

Neat Examples  (1)

Nested transformations of a circle:

Wolfram Research (2007), AffineTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/AffineTransform.html.

Text

Wolfram Research (2007), AffineTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/AffineTransform.html.

CMS

Wolfram Language. 2007. "AffineTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AffineTransform.html.

APA

Wolfram Language. (2007). AffineTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AffineTransform.html

BibTeX

@misc{reference.wolfram_2025_affinetransform, author="Wolfram Research", title="{AffineTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AffineTransform.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_affinetransform, organization={Wolfram Research}, title={AffineTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/AffineTransform.html}, note=[Accessed: 08-August-2025]}