def test_get_rotation_displacement(self):
# 180 degrees around z moves both x and y components by the *length* * 2
# Use a tiny value so the cross product is not zero
d_0 = (-1, 1e-9, 0) * q.dimensionless
d_1 = (1, 0, 0) * q.dimensionless
length = 5 * q.m
gt = np.array((length * 2, length * 2, 0)) * q.m
displ = geom.get_rotation_displacement(d_0, d_1, length)
np.testing.assert_almost_equal(gt, displ)
# 90 degrees around z moves both x and y components by the *length* * sqrt(2)
# and not *length*!
d_0 = (1, 0, 0) * q.dimensionless
d_1 = (0, 1, 0) * q.dimensionless
length = 5 * q.m
gt = np.array((length * np.sqrt(2), length * np.sqrt(2), 0)) * q.m
displ = geom.get_rotation_displacement(d_0, d_1, length)
np.testing.assert_almost_equal(gt, displ)
def test_get_rotation_displacement(self):
# 180 degrees around z moves both x and y components by the *length* * 2
# Use a tiny value so the cross product is not zero
d_0 = (-1, 1e-9, 0) * q.dimensionless
d_1 = (1, 0, 0) * q.dimensionless
length = 5 * q.m
gt = np.array((length * 2, length * 2, 0)) * q.m
displ = geom.get_rotation_displacement(d_0, d_1, length)
np.testing.assert_almost_equal(gt, displ)
# 90 degrees around z moves both x and y components by the *length* * sqrt(2)
# and not *length*!
d_0 = (1, 0, 0) * q.dimensionless
d_1 = (0, 1, 0) * q.dimensionless
length = 5 * q.m
gt = np.array((length * np.sqrt(2), length * np.sqrt(2), 0)) * q.m
displ = geom.get_rotation_displacement(d_0, d_1, length)
np.testing.assert_almost_equal(gt, displ)
def get_distance(self, t_0, t_1):
"""Return the translational and rotational travelled distance in time interval
*t_0*, *t_1*.
"""
if not self.trajectory.bound:
raise ValueError("Trajectory not bound")
# Place the point for computing the derivative very close
dt = (t_1 - t_0) * 1e-7
def move_and_save(abs_time):
"""Move primitive bodies to time *abs_time* and return
their positions.
"""
primitive = self.primitive_bodies
self.clear_transformation()
self.move(abs_time)
positions = np.zeros((len(primitive), 3))
for i in range(len(primitive)):
positions[i] = primitive[i].position.simplified.magnitude
return positions
self.save_transformation_matrices()
p_0 = move_and_save(t_0)
p_1 = move_and_save(t_1)
if t_0 + dt < self.time:
d_0 = move_and_save(t_0 + dt) - p_0
else:
d_0 = p_0 - move_and_save(t_0 - dt)
if t_1 + dt < self.time:
d_1 = move_and_save(t_1 + dt) - p_1
else:
d_1 = p_1 - move_and_save(t_1 - dt)
self.restore_transformation_matrices()
trans = np.abs(p_1 - p_0) * q.m
rot = []
for i in range(len(self.primitive_bodies)):
rot.append(
geom.get_rotation_displacement(
d_0[i], d_1[i], self.primitive_bodies[i].furthest_point.
simplified.magnitude))
rot = np.array(rot) * q.m
return np.max(trans) + np.max(rot)
def get_distance(self, t_0, t_1):
"""Return the translational and rotational travelled distance in time interval
*t_0*, *t_1*.
"""
if not self.trajectory.bound:
raise ValueError('Trajectory not bound')
# Place the point for computing the derivative very close
dt = (t_1 - t_0) * 1e-7
def move_and_save(abs_time):
"""Move primitive bodies to time *abs_time* and return
their positions.
"""
primitive = self.primitive_bodies
self.clear_transformation()
self.move(abs_time)
positions = np.zeros((len(primitive), 3))
for i in range(len(primitive)):
positions[i] = primitive[i].position.simplified.magnitude
return positions
self.save_transformation_matrices()
p_0 = move_and_save(t_0)
p_1 = move_and_save(t_1)
if t_0 + dt < self.time:
d_0 = move_and_save(t_0 + dt) - p_0
else:
d_0 = p_0 - move_and_save(t_0 - dt)
if t_1 + dt < self.time:
d_1 = move_and_save(t_1 + dt) - p_1
else:
d_1 = p_1 - move_and_save(t_1 - dt)
self.restore_transformation_matrices()
trans = np.abs(p_1 - p_0) * q.m
rot = []
for i in range(len(self.primitive_bodies)):
rot.append(geom.get_rotation_displacement(d_0[i], d_1[i],
self.primitive_bodies[i].
furthest_point.simplified.magnitude))
rot = np.array(rot) * q.m
return np.max(trans) + np.max(rot)
def test_get_distances(self):
"""Compare analytically computed distances with the ones obtained from trajectory."""
points = make_circle(n=128)
x, y, z = zip(*points)
furthest = 3 * q.mm
ps = 10 * q.um
tr = Trajectory(points, ps, furthest, velocity=1 * q.mm / q.s)
d_points = np.abs(tr.points[:, 0][:, np.newaxis] - tr.points)
t = np.linspace(0, 2 * np.pi, tr.points.shape[1])
x, y, z = zip(*make_circle(n=tr.points.shape[1]))
dx = -np.sin(t)
dy = np.cos(t)
dz = z
derivatives = np.array(zip(dx, dy, dz)).T.copy()
d_derivatives = get_rotation_displacement(derivatives[:, 0], derivatives, furthest)
distances = (d_points + d_derivatives).simplified.magnitude
np.testing.assert_almost_equal(distances, tr.get_distances())
def moved(self, t_0, t_1, pixel_size, bind=True):
"""
Return True if the body moves more than *pixel_size* in time interval *t_0*, *t_1*. If
*bind* is True bind the trajectory to the specified *pixel_size*, otherwise use the
trajectory as-is to compute an estimate.
"""
if bind or not self.trajectory.bound:
self.bind_trajectory(pixel_size)
p_0 = self.trajectory.get_point(t_0)
p_1 = self.trajectory.get_point(t_1)
trans_displacement = np.abs(p_1 - p_0)
d_0 = self.trajectory.get_direction(t_0, norm=False)
d_1 = self.trajectory.get_direction(t_1, norm=False)
rot_displacement = geom.get_rotation_displacement(d_0, d_1, self.furthest_point)
total_displacement = trans_displacement + rot_displacement
return max(total_displacement) > pixel_size
def moved(self, t_0, t_1, pixel_size, bind=True):
"""
Return True if the body moves more than *pixel_size* in time interval *t_0*, *t_1*. If
*bind* is True bind the trajectory to the specified *pixel_size*, otherwise use the
trajectory as-is to compute an estimate.
"""
if bind or not self.trajectory.bound:
self.bind_trajectory(pixel_size)
p_0 = self.trajectory.get_point(t_0)
p_1 = self.trajectory.get_point(t_1)
trans_displacement = np.abs(p_1 - p_0)
d_0 = self.trajectory.get_direction(t_0, norm=False)
d_1 = self.trajectory.get_direction(t_1, norm=False)
rot_displacement = geom.get_rotation_displacement(
d_0, d_1, self.furthest_point)
total_displacement = trans_displacement + rot_displacement
return max(total_displacement) > pixel_size
def test_get_distances(self):
"""Compare analytically computed distances with the ones obtained from trajectory."""
points = make_circle(n=128)
x, y, z = list(zip(*points))
furthest = 3 * q.mm
ps = 10 * q.um
tr = Trajectory(points, ps, furthest, velocity=1 * q.mm / q.s)
d_points = np.abs(tr.points[:, 0][:, np.newaxis] - tr.points)
t = np.linspace(0, 2 * np.pi, tr.points.shape[1])
x, y, z = list(zip(*make_circle(n=tr.points.shape[1])))
dx = -np.sin(t)
dy = np.cos(t)
dz = z
derivatives = np.array(list(zip(dx, dy, dz))).T.copy()
d_derivatives = get_rotation_displacement(derivatives[:, 0],
derivatives, furthest)
distances = (d_points + d_derivatives).simplified.magnitude
np.testing.assert_almost_equal(distances, tr.get_distances())