tfg.geometry.transformation.rotation_matrix_2d.from_euler_with_small_angles_approximation

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

tfg.geometry.transformation.rotation_matrix_2d.from_euler_with_small_angles_approximation(
    angles: type_alias.TensorLike,
    name: str = 'rotation_matrix_2d_from_euler_with_small_angles_approximation'
) -> tf.Tensor

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.