def OA(cls, o, a):
"""
Create SE(3) pure rotation from two vectors
:param o: 3-vector parallel to Y- axis
:type o: array_like
:param a: 3-vector parallel to the Z-axis
:type o: array_like
:return: 4x4 homogeneous transformation matrix
:rtype: SE3 instance
``SE3.OA(O, A)`` is an SE(3) rotation defined in terms of
vectors parallel to the Y- and Z-axes of its reference frame. In robotics these axes are
respectively called the orientation and approach vectors defined such that
R = [N O A] and N = O x A.
Notes:
- The A vector is the only guaranteed to have the same direction in the resulting
rotation matrix
- O and A do not have to be unit-length, they are normalized
- O and A do not have to be orthogonal, so long as they are not parallel
- The vectors O and A are parallel to the Y- and Z-axes of the equivalent coordinate frame.
:seealso: :func:`spatialmath.base.transforms3d.oa2r`
"""
return cls(tr.oa2tr(o, a), check=False)
def OA(cls, o, a):
r"""
Create an SE(3) pure rotation from two vectors
:param o: 3-vector parallel to Y- axis
:type o: array_like
:param a: 3-vector parallel to the Z-axis
:type a: array_like
:return: SE(3) matrix
:rtype: SE3 instance
``SE3.OA(o, a)`` is an SE(3) rotation defined in terms of vectors ``o``
and ``a`` respectively parallel to the Y- and Z-axes of its reference
frame. In robotics these axes are respectively called the *orientation*
and *approach* vectors defined such that :math:`\mathbf{R} = [n, o, a]`
and :math:`n = o \times a`.
.. note::
- The ``a`` vector is the only guaranteed to have the same direction in the resulting
rotation matrix
- ``o`` and ``a`` do not have to be unit-length, they are normalized
- ``o`` and ``a`` do not have to be orthogonal, so long as they are not parallel
``o`` is adjusted to be orthogonal to ``a``.
Example::
>>> SE3.OA([1, 0, 0], [0, 0, -1])
SE3(array([[-0., 1., 0., 0.],
[ 1., 0., 0., 0.],
[ 0., 0., -1., 0.],
[ 0., 0., 0., 1.]]))
:seealso: :func:`~spatialmath.base.transforms3d.oa2r`
"""
return cls(base.oa2tr(o, a), check=False)
