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.
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
- AffineTransform gives a TransformationFunction that can be applied to vectors.
- For ordinary affine transforms in dimensions, m is an × matrix.
- AffineTransform in general supports × matrices for transformations in dimensions.
Examples
open all close allBasic 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:
Related Guides
History
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: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_affinetransform, organization={Wolfram Research}, title={AffineTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/AffineTransform.html}, note=[Accessed: 04-January-2026]}