# AffineTransform

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.

# 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 carpet:

Heighway's Dragon:

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

Sierpiński carpet:

Heighway's Dragon:

Hedgehog:

Compute an iterated function system applied to graphics primitives:

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_2023_affinetransform, author="Wolfram Research", title="{AffineTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AffineTransform.html}", note=[Accessed: 24-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_affinetransform, organization={Wolfram Research}, title={AffineTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/AffineTransform.html}, note=[Accessed: 24-September-2023 ]}