# scipy.spatial.transform.Rotation.as_dcm¶

Rotation.as_dcm(self)[source]

Represent as direction cosine matrices.

3D rotations can be represented using direction cosine matrices, which are 3 x 3 real orthogonal matrices with determinant equal to +1 [1].

Returns
dcmnumpy.ndarray, shape (3, 3) or (N, 3, 3)

Shape depends on shape of inputs used for initialization.

References

1

Direction Cosine Matrix

Examples

>>> from scipy.spatial.transform import Rotation as R


Represent a single rotation:

>>> r = R.from_rotvec([0, 0, np.pi/2])
>>> r.as_dcm()
array([[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
[ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
[ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])
>>> r.as_dcm().shape
(3, 3)


Represent a stack with a single rotation:

>>> r = R.from_quat([[1, 1, 0, 0]])
>>> r.as_dcm()
array([[[ 0.,  1.,  0.],
[ 1.,  0.,  0.],
[ 0.,  0., -1.]]])
>>> r.as_dcm().shape
(1, 3, 3)


Represent multiple rotations:

>>> r = R.from_rotvec([[np.pi/2, 0, 0], [0, 0, np.pi/2]])
>>> r.as_dcm()
array([[[ 1.00000000e+00,  0.00000000e+00,  0.00000000e+00],
[ 0.00000000e+00,  2.22044605e-16, -1.00000000e+00],
[ 0.00000000e+00,  1.00000000e+00,  2.22044605e-16]],
[[ 2.22044605e-16, -1.00000000e+00,  0.00000000e+00],
[ 1.00000000e+00,  2.22044605e-16,  0.00000000e+00],
[ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]]])
>>> r.as_dcm().shape
(2, 3, 3)