Examples for

# Geometric Transformations

Geometric transformations are bijections preserving certain geometric properties, usually from the xy-plane to itself but can also be of higher dimension. In particular for each linear geometric transformation, there is one unique real matrix representation. Wolfram|Alpha has the ability to compute the transformation matrix for a specific 2D or 3D transformation activity or to return a general transformation calculator for rotations, reflections and shears.

Compute the matrix of a rotation transformation and visualize it.

#### Visualize a rotation and compute its matrix:

#### Rotate a point:

#### Rotate the graph of a function:

#### Visualize a rotation in 3D:

Compute the matrix of a reflection transformation and visualize it.

#### Visualize a reflection and compute its matrix:

#### Reflect a point:

#### Reflect the graph of an implicitly defined function through a line:

#### Visualize a reflection in 3D:

Compute the matrix of a rotation transformation given by a sequence of rolls, yaws and pitches and visualize it.

#### Specify a rotation in 3D using the angles of rolls, pitches and yaws and visualize it:

#### Specify a rotation in 3D using Euler angles:

Compute the matrix of a shear transformation and visualize it.