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Convert an Euler angle representation to a rotation matrix.
tfg.geometry.transformation.rotation_matrix_3d.from_euler_with_small_angles_approximation(
angles, name=None
)
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". |
Returns | |
---|---|
A tensor of shape [A1, ..., An, 3, 3] , where the last two dimensions
represent a 3d rotation matrix.
|
Raises | |
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ValueError
|
If the shape of angles is not supported.
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