tfg.geometry.transformation.rotation_matrix_2d.from_euler_with_small_angles_approximation

Converts an angle to a 2d rotation matrix under the small angle assumption.

Under the small angle assumption, \(\sin(x)\) and \(\cos(x)\) can be approximated by their second order Taylor expansions, where \(\sin(x) \approx x\) and \(\cos(x) \approx 1 - \frac{x^2}{2}\). The 2d rotation matrix will then be approximated as

\[ \mathbf{R} = \begin{bmatrix} 1.0 - 0.5\theta^2 & -\theta \\ \theta & 1.0 - 0.5\theta^2 \end{bmatrix}. \]

In the current implementation, the smallness of the angles is not verified.

The resulting matrix rotates points in the \(xy\)-plane counterclockwise.

In the following, A1 to An are optional batch dimensions.

angles A tensor of shape [A1, ..., An, 1], where the last dimension represents a small angle in radians.
name A name for this op that defaults to "rotation_matrix_2d_from_euler_with_small_angles_approximation".

A tensor of shape [A1, ..., An, 2, 2], where the last dimension represents a 2d rotation matrix.

ValueError If the shape of angle is not supported.