def EulerVec(cls, w):
r"""
Construct a new SO(3) rotation matrix from an Euler rotation vector
:param ω: rotation axis
:type ω: 3-element array_like
:return: SO(3) rotation
:rtype: SO3 instance
``SO3.EulerVec(ω)`` is a unit quaternion that describes the 3D rotation
defined by a rotation of :math:`\theta = \lVert \omega \rVert` about the
unit 3-vector :math:`\omega / \lVert \omega \rVert`.
Example:
.. runblock:: pycon
>>> from spatialmath import SO3
>>> SO3.EulerVec([0.5,0,0])
.. note:: :math:`\theta \eq 0` the result in an identity matrix, otherwise
``V`` must have a finite length, ie. :math:`|V| > 0`.
:seealso: :func:`~spatialmath.pose3d.SE3.angvec`, :func:`~spatialmath.base.transforms3d.angvec2r`
"""
assert base.isvector(w, 3), 'w must be a 3-vector'
w = base.getvector(w)
theta = base.norm(w)
return cls(base.angvec2r(theta, w), check=False)
def AngVec(cls, theta, v, *, unit='rad'):
r"""
Construct a new SO(3) rotation matrix from rotation angle and axis
:param theta: rotation
:type theta: float
:param unit: angular units: 'rad' [default], or 'deg'
:type unit: str
:param v: rotation axis, 3-vector
:type v: array_like
:return: SO(3) rotation
:rtype: SO3 instance
``SO3.AngVec(theta, V)`` is an SO(3) rotation defined by
a rotation of ``THETA`` about the vector ``V``.
.. note:: :math:`\theta \eq 0` the result in an identity matrix, otherwise
``V`` must have a finite length, ie. :math:`|V| > 0`.
:seealso: :func:`~spatialmath.pose3d.SE3.angvec`, :func:`spatialmath.base.transforms3d.angvec2r`
"""
return cls(base.angvec2r(theta, v, unit=unit), check=False)
def AngVec(cls, theta, v, *, unit='rad'):
"""
Create an SO(3) rotation matrix from rotation angle and axis
:param theta: rotation
:type theta: float
:param unit: angular units: 'rad' [default], or 'deg'
:type unit: str
:param v: rotation axis, 3-vector
:type v: array_like
:return: 3x3 rotation matrix
:rtype: SO3 instance
``SO3.AngVec(THETA, V)`` is an SO(3) rotation defined by
a rotation of ``THETA`` about the vector ``V``.
Notes:
- If ``THETA == 0`` then return identity matrix.
- If ``THETA ~= 0`` then ``V`` must have a finite length.
:seealso: :func:`~spatialmath.pose3d.SE3.angvec`, :func:`spatialmath.base.transforms3d.angvec2r`
"""
return cls(quat.r2q(tr.angvec2r(theta, v, unit=unit)), check=False)
def Omega(cls, w):
return cls(quat.r2q(tr.angvec2r(tr.norm(w), tr.unitvec(w))),
check=False)