tfg.geometry.transformation.rotation_matrix_3d.from_euler_with_small_angles_approximation

Convert an Euler angle representation to a rotation matrix.

tfg.geometry.transformation.rotation_matrix_3d.from_euler_with_small_angles_approximation(
    angles: type_alias.TensorLike,
    name: str = 'rotation_matrix_3d_from_euler_with_small_angles'
) -> tf.Tensor

The resulting matrix is \(\mathbf{R} = \mathbf{R}_z\mathbf{R}_y\mathbf{R}_x\). 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 \(\cos(x) \approx 1 - \frac{x^2}{2}\). In the current implementation, the smallness of the angles is not verified.

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

Args
angles	A tensor of shape [A1, ..., An, 3], where the last dimension represents the three small Euler angles. [A1, ..., An, 0] is the angle about x in radians, [A1, ..., An, 1] is the angle about y in radians and [A1, ..., An, 2] is the angle about z in radians.
name	A name for this op that defaults to "rotation_matrix_3d_from_euler_with_small_angles".

Returns
A tensor of shape [A1, ..., An, 3, 3], where the last two dimensions represent a 3d rotation matrix.

Raises
ValueError	If the shape of angles is not supported.