def OA(cls, o, a):
"""
Construct a new SO(3) 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: SO(3) rotation
:rtype: SO3 instance
``SO3.OA(O, A)`` is an SO(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::
- Only the ``A`` vector is 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
:seealso: :func:`spatialmath.base.transforms3d.oa2r`
"""
return cls(base.oa2r(o, a), check=False)
def OA(cls, o, a):
"""
Create SO(3) 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: 3x3 rotation matrix
:rtype: SO3 instance
``SO3.OA(O, A)`` is an SO(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(quat.r2q(tr.oa2r(angles, unit=unit)), check=False)
