def _with_rotation_to_minimize_angle(
self: _T,
start: np.ndarray,
target: np.ndarray,
axis: np.ndarray,
origin: np.ndarray,
) -> _T:
# If the vector being rotated is not finite, exit. This is
# probably due to a planar molecule.
if not all(np.isfinite(x) for x in start):
return self
if np.allclose(target, [0, 0, 0], atol=1e-15):
raise ValueError(
'target has a magnitude of 0. It is therefore not '
'possible to calculate an angle.')
self._with_displacement(-origin)
# 1. Remove any component of the start and target vectors long
# the axis. This puts them both on the same plane.
# 2. Calculate the angle between them.
# 3. Apply the rotation.
tstart = start - np.dot(start, axis) * axis
# If `tstart` is 0, it is parallel to the rotation axis, stop.
if np.allclose(tstart, [0, 0, 0], 1e-8):
self._with_displacement(origin)
return self
tend = target - np.dot(target, axis) * axis
# If `tend` is 0, it is parallel to the rotation axis, stop.
if np.allclose(tend, [0, 0, 0], 1e-8):
self._with_displacement(origin)
return self
angle = _utilities.vector_angle(tstart, tend)
projection = tstart @ np.cross(axis, tend)
if projection > 0:
angle = 2 * np.pi - angle
rotation_matrix = _utilities.rotation_matrix_arbitrary_axis(
angle=angle,
axis=axis,
)
self._position_matrix = rotation_matrix @ self._position_matrix
self._with_displacement(origin)
return self
def _get_angle(self, item):
"""
Get the angle of `vector` relative to `reference`.
Parameters
----------
item : :class:`object`
The item being sorted.
Returns
-------
:class:`float`
The angle between `item` and the reference vector.
"""
vector = self._get_vector(item)
theta = vector_angle(self._reference, vector)
projection = vector @ self._axis
if theta > 0 and projection < 0:
return 2 * np.pi - theta
return theta