represents a transformation function that applies geometric and other transformations.


  • TransformationFunction[] objects are generated by constructors such as TranslationTransform, RotationTransform, etc.
  • TransformationFunction[][x] applies the transformation function to a vector x, returning a transformed vector.
  • TransformationFunction[][{x1,x2,}] for a list of vectors applies the transformation to each vector xi, producing a list of transformed vectors.
  • TransformationFunction works with both numerical and symbolic vectors and represents a linear fractional transformation , where AMatrices[{m,n}], bMatrices[{m,1}], cMatrices[{1,n}] and dMatrices[{1,1}].
  • For smaller dimensions, it is typically displayed as an transformation matrix . TransformationMatrix can be used to extract the transformation matrix.
  • Composition[t1,t2] where ti has transformation matrix gives a new TransformationFunction object with transformation matrix .
  • InverseFunction[t] where t has transformation matrix gives a new TransformationFunction object with transformation matrix where is the matrix inverse.
  • GeometricTransformation can be used to represent the effect of applying a TransformationFunction object to geometrical or graphics objects when restricted to affine transformations.
  • TransformationFunction[][prop] gives the transformation property prop. For a transformation function with transformation matrix , properties include:
  • "AffineQ"whether the transformation is affine or not, it gives True if both c and d are zero
    "AffineMatrix"the matrix A
    "AffineVector"the vector b
    "FractionalVector"the vector c
    "FractionalConstant"then constant d
    "ArgumentLength"the length n of the vector x
    "ResultLength"the length m of the result vector


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Basic Examples  (1)

Create a rotation transform:

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This rotates the vector {x,y} by angle θ:

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Scope  (15)

Applications  (2)

Properties & Relations  (1)

Introduced in 2007
Updated in 2019