Module: tfg.geometry.transformation.rotation_matrix_2d

This module implements 2d rotation matrix functionalities.

Given an angle of rotation \(\theta\) a 2d rotation matrix can be expressed as

\[ \mathbf{R} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix}. \]

More details rotation matrices can be found on this page.

Note: This matrix rotates points in the \(xy\)-plane counterclockwise.

Functions

from_euler(...): Converts an angle to a 2d rotation matrix.

from_euler_with_small_angles_approximation(...): Converts an angle to a 2d rotation matrix under the small angle assumption.

inverse(...): Computes the inverse of a 2D rotation matrix.

is_valid(...): Determines if a matrix is a valid rotation matrix.

rotate(...): Rotates a 2d point using a 2d rotation matrix.