TransformationMatrix

TransformationMatrix[tfun]

gives the homogeneous matrix associated with a TransformationFunction object.

Details

  • For transformations in n dimensions, TransformationMatrix normally gives an × matrix.
  • mat[[1;;n,1;;n]] gives the linear part of the transformation; mat[[1;;n,-1]] gives the displacement vector.

Examples

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Basic Examples  (1)

Here is defined to be a rotation around the axis:

Get the transformation matrix:

The linear part:

The displacement vector:

Scope  (1)

Translation matrix in four dimensions:

Transformation of homogeneous coordinates:

Points at infinity do not change under translation:

Properties & Relations  (1)

The matrix of a general 2D affine transform:

Composition of linear fractional transformations corresponds to the product of their matrices:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_transformationmatrix, author="Wolfram Research", title="{TransformationMatrix}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/TransformationMatrix.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_transformationmatrix, organization={Wolfram Research}, title={TransformationMatrix}, year={2007}, url={https://reference.wolfram.com/language/ref/TransformationMatrix.html}, note=[Accessed: 21-February-2025 ]}