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

Built-in Mathematica Symbol

TransformationMatrix

TransformationMatrix[tfun]
gives the homogeneous matrix associated with a TransformationFunction object.

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.

Here t is defined to be a rotation around the z axis:

Get the transformation matrix:

The linear part:

The displacement vector:

Here t is defined to be a rotation around the z axis:

Get the transformation matrix:

The linear part:

The displacement vector:

Translation matrix in four dimensions:

Transformation of homogenous coordinates:

Points at infinity do not change under translation:

The matrix of a general 2D affine transform:

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