Built-in Mathematica Symbol

TransformationFunction

TransformationFunction[data]
represents a transformation function that applies geometric and other transformations.

MORE INFORMATION

TransformationFunction works like Function.

TransformationFunction[...][vec] applies the transformation function to a vector, returning a transformed vector.

TransformationFunction works with both numerical and symbolic vectors.

For purposes of display, a -dimensional TransformationFunction is typically shown with a homogenous matrix.

Composition and InverseFunction can be used with TransformationFunction.

When possible, matrix forms for transformations can be obtained from TransformationFunction objects using TransformationMatrix.

GeometricTransformation can be used to represent the effect of applying a TransformationFunction object to geometrical or graphics objects.

EXAMPLES

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Basic Examples (1)

Create a rotation transform:

This rotates the vector {x, y} by angle

:

Create a rotation transform:

In[1]:=

Out[1]=

This rotates the vector {x, y} by angle

:

In[2]:=

Out[2]=

Scope (15)

A translation by the vector {qx, qy, qz}:

A rotation around the z axis:

Scaling along the coordinate axes:

Shearing in the x direction by an angle

:

Reflecting in the x, y plane:

Rescaling the box [xmin, xmax]

[ymin, ymax] to the unit square:

A general TransformationFunction:

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:

Applications (2)

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:

Properties & Relations (1)

Find the

power of a transformation:

Apply

five times:

Apply tt[5]:

Find the

iteration using RSolve: