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based on an earlier version of the Wolfram Language.
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represents a transformation function that applies geometric and other transformations.
  • TransformationFunction[...][vec] applies the transformation function to a vector, returning a transformed vector.
Create a rotation transform:
This rotates the vector by angle :
Create a rotation transform:
Click for copyable input
This rotates the vector by angle :
Click for copyable input
A translation by the vector :
A rotation around the axis:
Scaling along the coordinate axes:
Shearing in the direction by an angle :
Reflecting in the plane:
Rescaling the box to the unit square:
A linear transformation:
An affine transformation:
A linear fractional transformation:
Here is a rotation of around the axis:
This transforms the axis:
This transforms a list of vectors:
Composing two transformations:
Computing the inverse:
This shows they are inverses:
Computing the partial derivative :
This defines a general transform:
This is the corresponding formula:
A derivative:
A limit:
An integral:
A plot:
TransformationFunction can be used as an argument to GeometricTransformation:
Integrate a function over a rhombic region:
defines a change of variables that maps the unit square to the integration region:
The integrand in the new coordinates:
The Jacobian:
Find the ^(th) power of a transformation:
Apply five times:
Apply :
Find the ^(th) iteration using RSolve:
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