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Mathematica > Visualization and Graphics > Computational Geometry > Geometric Transforms > AffineTransform >

Mathematica > Visualization and Graphics > Symbolic Graphics Language > Graphics Transformations > Geometric Transforms > AffineTransform >

BUILT-IN MATHEMATICA SYMBOL

AffineTransform

AffineTransform[m]
gives a TransformationFunction that represents an affine transform that maps r to

AffineTransform

gives an affine transform that maps r to

MORE INFORMATION

AffineTransform gives a TransformationFunction which 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

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Basic Examples (2)

A general affine transformation:

Transform points:

A pure rotation:

A pure translation:

A general affine transformation:

In[1]:=

Out[1]=

Transform points:

In[2]:=

Out[2]=

A pure rotation:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

A pure translation:

In[3]:=

Out[3]=

In[4]:=

Out[4]=

Scope (3)

Affine transform in four dimensions:

The inverse transform:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications (1)

Transforming graphics primitives:

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: