def test_rotate_inertia(self):
"""Are we obtaining the global inertia properly?"""
# Create parameters.
label = "seg1"
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
# This inertia matrix describes two 1kg point masses at (0, 2, 1) and
# (0, -2, -1) in the global reference frame, A.
seg1._rel_inertia = mat([[10.0, 0.0, 0.0], [0.0, 2.0, -4.0], [0.0, -4.0, 8.0]])
# If we want the inertia about a new reference frame, B, such that the
# two masses lie on the yb axis we can rotate about xa through the angle
# arctan(1/2). Note that this function returns R from va = R * vb.
seg1._rot_mat = inertia.rotate_space_123((arctan(1.0 / 2.0), 0.0, 0.0))
seg1.calc_properties()
I_b = seg1.inertia
expected_I_b = mat([[10.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 10.0]])
testing.assert_allclose(I_b, expected_I_b)
def test_rotate_inertia(self):
"""Are we obtaining the global inertia properly?"""
# Create parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
# This inertia matrix describes two 1kg point masses at (0, 2, 1) and
# (0, -2, -1) in the global reference frame, A.
seg1._rel_inertia = mat([[10.0, 0.0, 0.0], [0.0, 2.0, -4.0],
[0.0, -4.0, 8.0]])
# If we want the inertia about a new reference frame, B, such that the
# two masses lie on the yb axis we can rotate about xa through the angle
# arctan(1/2). Note that this function returns R from va = R * vb.
seg1._rot_mat = inertia.rotate_space_123((arctan(1.0 / 2.0), 0.0, 0.0))
seg1.calc_properties()
I_b = seg1.inertia
expected_I_b = mat([[10.0, 0.0, 0.0], [0.0, 0.0, 0.0],
[0.0, 0.0, 10.0]])
testing.assert_allclose(I_b, expected_I_b)
def test_print_properties(self):
"""Ensures the proper printing of segment mass properties. """
# Create parameters.
label = "seg1"
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
# For capturing print.
old_stdout = sys.stdout
sys.stdout = mystdout = StringIO()
# Calling print_properties before calc_properties should still work.
seg1.print_properties()
sys.stdout = old_stdout
des_str = open(os.path.join(os.path.split(__file__)[0], "segment_print_des.txt"), "r").read()
self.assertEquals(mystdout.getvalue(), des_str)
# Use the __str__method.
# It's just a fluke that we need to append an additional newline char.
self.assertEquals(seg1.__str__() + "\n", des_str)
def test_rotate_inertia():
"""Are we obtaining the global inertia properly?"""
density = 1.5
height = 4
height_vec = array([[0], [0], [height]])
# One thickness is 0.
r0 = 5; t0 = 0; r1 = 2; t1 = 2;
stad1 = Stadium('Ls1: umbilicus', 'thicknessradius', t0, r0)
stad2 = Stadium('Lb1: mid-arm', 'thicknessradius', t1, r1)
solidA = StadiumSolid('solid', density, stad1, stad2, height)
# This inertia matrix describes two 1kg point masses at (0, 2, 1) and
# (0, -2, -1) in the global reference frame, A.
solidA._rel_inertia = mat([[10.0, 0.0, 0.0],
[0.0, 2.0, -4.0],
[0.0, -4.0, 8.0]])
# If we want the inertia about a new reference frame, B, such that the
# two masses lie on the yb axis we can rotate about xa through the angle
# arctan(1/2). Note that this function returns R from va = R * vb.
solidA._rot_mat = inertia.rotate_space_123((arctan(1.0 / 2.0), 0.0, 0.0))
solidA.calc_properties()
I_b = solidA.inertia
expected_I_b = mat([[10.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
[0.0, 0.0, 10.0]])
testing.assert_allclose(I_b, expected_I_b)
def test_print_properties(self):
"""Ensures the proper printing of segment mass properties. """
# Create parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
# For capturing print.
old_stdout = sys.stdout
sys.stdout = mystdout = StringIO()
# Calling print_properties before calc_properties should still work.
seg1.print_properties()
sys.stdout = old_stdout
des_str = open(
os.path.join(os.path.split(__file__)[0], 'segment_print_des.txt'),
'r').read()
self.assertEquals(mystdout.getvalue(), des_str)
# Use the __str__method.
# It's just a fluke that we need to append an additional newline char.
self.assertEquals(seg1.__str__() + '\n', des_str)
def test_rotate_inertia():
"""Are we obtaining the global inertia properly?"""
density = 1.5
height = 4
height_vec = array([[0], [0], [height]])
# One thickness is 0.
r0 = 5
t0 = 0
r1 = 2
t1 = 2
stad1 = Stadium('Ls1: umbilicus', 'thicknessradius', t0, r0)
stad2 = Stadium('Lb1: mid-arm', 'thicknessradius', t1, r1)
solidA = StadiumSolid('solid', density, stad1, stad2, height)
# This inertia matrix describes two 1kg point masses at (0, 2, 1) and
# (0, -2, -1) in the global reference frame, A.
solidA._rel_inertia = mat([[10.0, 0.0, 0.0], [0.0, 2.0, -4.0],
[0.0, -4.0, 8.0]])
# If we want the inertia about a new reference frame, B, such that the
# two masses lie on the yb axis we can rotate about xa through the angle
# arctan(1/2). Note that this function returns R from va = R * vb.
solidA._rot_mat = inertia.rotate_space_123((arctan(1.0 / 2.0), 0.0, 0.0))
solidA.calc_properties()
I_b = solidA.inertia
expected_I_b = mat([[10.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 10.0]])
testing.assert_allclose(I_b, expected_I_b)
def test_print_solid_properties(self):
# Create parameters.
label = "seg1"
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
old_stdout = sys.stdout
sys.stdout = mystdout = StringIO()
seg1.print_solid_properties()
sys.stdout = old_stdout
desStr = open(os.path.join(os.path.split(__file__)[0], "segment_print_solid_des.txt"), "r").read()
self.assertEquals(mystdout.getvalue(), desStr)
def test_init_bad_input(self):
"""Ensures only proper constructor arguments get through. Exercises
duck-typing.
"""
# Create default parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Empty position.
self.assertRaises(AttributeError, seg.Segment, label, [], rot, solids,
color)
# Non-numpy position.
self.assertRaises(AttributeError, seg.Segment, label, [0, 0, 0], rot,
solids, color)
# Wrong dimensions.
self.assertRaises(ValueError, seg.Segment, label, pos[1:2,:], rot,
solids, color)
# Empty rotation.
self.assertRaises(ValueError, seg.Segment, label, pos, [], solids,
color)
# Wrong type rot.
self.assertRaises(ValueError, seg.Segment, label, pos, pos, solids,
color)
# Wrong dimensions rot.
self.assertRaises(ValueError, seg.Segment, label, pos, np.mat(pos),
solids, color)
# Empty solids.
self.assertRaises(IndexError, seg.Segment, label, pos, rot, [], color)
# Missing color.
self.assertRaises(TypeError, seg.Segment, label, pos, rot, solids)
# Test just having one solid; make sure we do not depend on a segment
# having multiple solids.
# Should not raise exception.
seg1 = seg.Segment(label, pos, rot, [self.solidAB], color)
# Objects in the solids list are not actually `Solid`'s.
self.assertRaises(AttributeError, seg.Segment, label, pos, rot, ["1",
"2"], color)
def test_init_bad_input(self):
"""Ensures only proper constructor arguments get through. Exercises
duck-typing.
"""
# Create default parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Empty position.
self.assertRaises(AttributeError, seg.Segment, label, [], rot, solids,
color)
# Non-numpy position.
self.assertRaises(AttributeError, seg.Segment, label, [0, 0, 0], rot,
solids, color)
# Wrong dimensions.
self.assertRaises(ValueError, seg.Segment, label, pos[1:2, :], rot,
solids, color)
# Empty rotation.
self.assertRaises(ValueError, seg.Segment, label, pos, [], solids,
color)
# Wrong type rot.
self.assertRaises(ValueError, seg.Segment, label, pos, pos, solids,
color)
# Wrong dimensions rot.
self.assertRaises(ValueError, seg.Segment, label, pos, np.mat(pos),
solids, color)
# Empty solids.
self.assertRaises(IndexError, seg.Segment, label, pos, rot, [], color)
# Missing color.
self.assertRaises(TypeError, seg.Segment, label, pos, rot, solids)
# Test just having one solid; make sure we do not depend on a segment
# having multiple solids.
# Should not raise exception.
seg1 = seg.Segment(label, pos, rot, [self.solidAB], color)
# Objects in the solids list are not actually `Solid`'s.
self.assertRaises(AttributeError, seg.Segment, label, pos, rot,
["1", "2"], color)
def test_calc_properties(self):
"""Ensures proper calculation of global-frame COM and Inertia."""
# Create parameters.
label = "seg1"
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
seg1.calc_properties()
testing.assert_allclose(seg1.center_of_mass, np.array([[seg1.rel_center_of_mass[2, 0] + 1, 2, 3]]).T)
desXInertia = seg1.rel_inertia[2, 2]
desYInertia = seg1.rel_inertia[1, 1]
desZInertia = seg1.rel_inertia[0, 0]
desInertia = np.mat(np.diag(np.array([desXInertia, desYInertia, desZInertia])))
testing.assert_allclose(seg1.inertia, desInertia, atol=1e-10)
def test_print_solid_properties(self):
# Create parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
old_stdout = sys.stdout
sys.stdout = mystdout = StringIO()
seg1.print_solid_properties()
sys.stdout = old_stdout
desStr = open(
os.path.join(
os.path.split(__file__)[0], 'segment_print_solid_des.txt'),
'r').read()
self.assertEquals(mystdout.getvalue(), desStr)
def test_calc_properties(self):
"""Ensures proper calculation of global-frame COM and Inertia."""
# Create parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
seg1.calc_properties()
testing.assert_allclose(
seg1.center_of_mass,
np.array([[seg1.rel_center_of_mass[2, 0] + 1, 2, 3]]).T)
desXInertia = seg1.rel_inertia[2, 2]
desYInertia = seg1.rel_inertia[1, 1]
desZInertia = seg1.rel_inertia[0, 0]
desInertia = np.mat(
np.diag(np.array([desXInertia, desYInertia, desZInertia])))
testing.assert_allclose(seg1.inertia, desInertia, atol=1e-10)
def test_init_real_input(self):
"""Ensures the constructor for valid input makes correct calculations.
"""
# Create parameters.
label = "seg1"
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
# Check that parameters were set.
assert seg1.label == label
assert (seg1.pos == pos).all()
assert (seg1.rot_mat == rot).all()
assert seg1.solids == solids
assert seg1.nSolids == len(solids)
assert seg1.color == color
# -- Check the other constructor actions.
# Setting orientations of all constituent solids.
assert (seg1.solids[0].pos == pos).all()
assert (seg1.solids[0]._rot_mat == rot).all()
pos2 = np.array([[6], [2], [3]])
assert (seg1.solids[0].end_pos == pos2).all()
# 2nd solid in the segment.
assert (seg1.solids[1].pos == pos2).all()
assert (seg1.solids[1]._rot_mat == rot).all()
# See definition of solids in setUp().
pos3 = pos2 + np.array([[6], [0], [0]])
assert (seg1.solids[1].end_pos == pos3).all()
# 3rd solid in the segment.
assert (seg1.solids[2].pos == pos3).all()
assert (seg1.solids[2]._rot_mat == rot).all()
# See definition of solids in setUp().
pos4 = pos3 + np.array([[7], [0], [0]])
assert (seg1.solids[2].end_pos == pos4).all()
# Other segment-wide attributes we define.
assert (seg1.end_pos == pos4).all()
assert (seg1.length == (5 + 6 + 7)).all()
# -- The constructor then calls calc_rel_properties().
desMass = self.solidAB.mass + self.solidBC.mass + self.solidCD.mass
testing.assert_almost_equal(seg1.mass, desMass)
desRelCOM = (
self.solidAB.mass * self.solidAB.rel_center_of_mass
+ self.solidBC.mass * (self.solidBC.rel_center_of_mass + np.array([[0, 0, 5]]).T)
+ self.solidCD.mass * (self.solidCD.rel_center_of_mass + np.array([[0, 0, 11]]).T)
) / desMass
testing.assert_allclose(seg1.rel_center_of_mass, desRelCOM)
# Helper definitions
relCOM_AB = self.solidAB.rel_center_of_mass
relCOM_BC = np.array([[0, 0, self.solidAB.height]]).T + self.solidBC.rel_center_of_mass
relCOM_CD = np.array([[0, 0, self.solidAB.height + self.solidBC.height]]).T + self.solidCD.rel_center_of_mass
# Inertia for each direction.
desXInertia = (
self.solidAB.rel_inertia[0, 0]
+ self.solidAB.mass * (relCOM_AB[2, 0] - seg1.rel_center_of_mass[2, 0]) ** 2
+ self.solidBC.rel_inertia[0, 0]
+ self.solidBC.mass * (relCOM_BC[2, 0] - seg1.rel_center_of_mass[2, 0]) ** 2
+ self.solidCD.rel_inertia[0, 0]
+ self.solidCD.mass * (relCOM_CD[2, 0] - seg1.rel_center_of_mass[2, 0]) ** 2
)
desYInertia = (
self.solidAB.rel_inertia[1, 1]
+ self.solidAB.mass * (relCOM_AB[2, 0] - seg1.rel_center_of_mass[2, 0]) ** 2
+ self.solidBC.rel_inertia[1, 1]
+ self.solidBC.mass * (relCOM_BC[2, 0] - seg1.rel_center_of_mass[2, 0]) ** 2
+ self.solidCD.rel_inertia[1, 1]
+ self.solidCD.mass * (relCOM_CD[2, 0] - seg1.rel_center_of_mass[2, 0]) ** 2
)
desZInertia = self.solidAB.rel_inertia[2, 2] + self.solidBC.rel_inertia[2, 2] + self.solidCD.rel_inertia[2, 2]
# Combine components into array.
desRelInertia = np.diag(np.array([desXInertia, desYInertia, desZInertia]))
# Compare.
testing.assert_allclose(seg1.rel_inertia, desRelInertia)
def test_init_real_input(self):
"""Ensures the constructor for valid input makes correct calculations.
"""
# Create parameters.
label = 'seg1'
pos = np.array([[1], [2], [3]])
rot = inertia.rotate_space_123([pi / 2, pi / 2, pi / 2])
solids = [self.solidAB, self.solidBC, self.solidCD]
color = (1, 0, 0)
# Create the segment.
seg1 = seg.Segment(label, pos, rot, solids, color)
# Check that parameters were set.
assert seg1.label == label
assert (seg1.pos == pos).all()
assert (seg1.rot_mat == rot).all()
assert seg1.solids == solids
assert seg1.nSolids == len(solids)
assert seg1.color == color
# -- Check the other constructor actions.
# Setting orientations of all constituent solids.
assert (seg1.solids[0].pos == pos).all()
assert (seg1.solids[0]._rot_mat == rot).all()
pos2 = np.array([[6], [2], [3]])
assert (seg1.solids[0].end_pos == pos2).all()
# 2nd solid in the segment.
assert (seg1.solids[1].pos == pos2).all()
assert (seg1.solids[1]._rot_mat == rot).all()
# See definition of solids in setUp().
pos3 = pos2 + np.array([[6], [0], [0]])
assert (seg1.solids[1].end_pos == pos3).all()
# 3rd solid in the segment.
assert (seg1.solids[2].pos == pos3).all()
assert (seg1.solids[2]._rot_mat == rot).all()
# See definition of solids in setUp().
pos4 = pos3 + np.array([[7], [0], [0]])
assert (seg1.solids[2].end_pos == pos4).all()
# Other segment-wide attributes we define.
assert (seg1.end_pos == pos4).all()
assert (seg1.length == (5 + 6 + 7)).all()
# -- The constructor then calls calc_rel_properties().
desMass = self.solidAB.mass + self.solidBC.mass + self.solidCD.mass
testing.assert_almost_equal(seg1.mass, desMass)
desRelCOM = (
self.solidAB.mass * self.solidAB.rel_center_of_mass +
self.solidBC.mass *
(self.solidBC.rel_center_of_mass + np.array([[0, 0, 5]]).T) +
self.solidCD.mass *
(self.solidCD.rel_center_of_mass + np.array([[0, 0, 11]]).T)
) / desMass
testing.assert_allclose(seg1.rel_center_of_mass, desRelCOM)
# Helper definitions
relCOM_AB = self.solidAB.rel_center_of_mass
relCOM_BC = (np.array([[0, 0, self.solidAB.height]]).T +
self.solidBC.rel_center_of_mass)
relCOM_CD = (
np.array([[0, 0, self.solidAB.height + self.solidBC.height]]).T +
self.solidCD.rel_center_of_mass)
# Inertia for each direction.
desXInertia = (self.solidAB.rel_inertia[0, 0] + self.solidAB.mass *
(relCOM_AB[2, 0] - seg1.rel_center_of_mass[2, 0])**2 +
self.solidBC.rel_inertia[0, 0] + self.solidBC.mass *
(relCOM_BC[2, 0] - seg1.rel_center_of_mass[2, 0])**2 +
self.solidCD.rel_inertia[0, 0] + self.solidCD.mass *
(relCOM_CD[2, 0] - seg1.rel_center_of_mass[2, 0])**2)
desYInertia = (self.solidAB.rel_inertia[1, 1] + self.solidAB.mass *
(relCOM_AB[2, 0] - seg1.rel_center_of_mass[2, 0])**2 +
self.solidBC.rel_inertia[1, 1] + self.solidBC.mass *
(relCOM_BC[2, 0] - seg1.rel_center_of_mass[2, 0])**2 +
self.solidCD.rel_inertia[1, 1] + self.solidCD.mass *
(relCOM_CD[2, 0] - seg1.rel_center_of_mass[2, 0])**2)
desZInertia = (self.solidAB.rel_inertia[2, 2] +
self.solidBC.rel_inertia[2, 2] +
self.solidCD.rel_inertia[2, 2])
# Combine components into array.
desRelInertia = np.diag(
np.array([desXInertia, desYInertia, desZInertia]))
# Compare.
testing.assert_allclose(seg1.rel_inertia, desRelInertia)