def test_orient_new_methods():
N = CoordSysCartesian('N')
D = N.orient_new('D', 'Axis', [q4, N.j])
E = N.orient_new('E', 'Space', [q1, q2, q3], '123')
F = N.orient_new('F', 'Quaternion', [q1, q2, q3, q4])
G = N.orient_new('G', 'Body', [q1, q2, q3], '123')
assert D == N.orient_new_axis('D', q4, N.j)
assert E == N.orient_new_space('E', q1, q2, q3, '123')
assert F == N.orient_new_quaternion('F', q1, q2, q3, q4)
assert G == N.orient_new_body('G', q1, q2, q3, '123')
def test_orient_new_methods():
N = CoordSysCartesian('N')
orienter1 = AxisOrienter(q4, N.j)
orienter2 = SpaceOrienter(q1, q2, q3, '123')
orienter3 = QuaternionOrienter(q1, q2, q3, q4)
orienter4 = BodyOrienter(q1, q2, q3, '123')
D = N.orient_new('D', (orienter1, ))
E = N.orient_new('E', (orienter2, ))
F = N.orient_new('F', (orienter3, ))
G = N.orient_new('G', (orienter4, ))
assert D == N.orient_new_axis('D', q4, N.j)
assert E == N.orient_new_space('E', q1, q2, q3, '123')
assert F == N.orient_new_quaternion('F', q1, q2, q3, q4)
assert G == N.orient_new_body('G', q1, q2, q3, '123')
def test_orient_new_methods():
N = CoordSysCartesian("N")
orienter1 = AxisOrienter(q4, N.j)
orienter2 = SpaceOrienter(q1, q2, q3, "123")
orienter3 = QuaternionOrienter(q1, q2, q3, q4)
orienter4 = BodyOrienter(q1, q2, q3, "123")
D = N.orient_new("D", (orienter1,))
E = N.orient_new("E", (orienter2,))
F = N.orient_new("F", (orienter3,))
G = N.orient_new("G", (orienter4,))
assert D == N.orient_new_axis("D", q4, N.j)
assert E == N.orient_new_space("E", q1, q2, q3, "123")
assert F == N.orient_new_quaternion("F", q1, q2, q3, q4)
assert G == N.orient_new_body("G", q1, q2, q3, "123")
def test_orient_new_methods():
N = CoordSysCartesian('N')
orienter1 = AxisOrienter(q4, N.j)
orienter2 = SpaceOrienter(q1, q2, q3, '123')
orienter3 = QuaternionOrienter(q1, q2, q3, q4)
orienter4 = BodyOrienter(q1, q2, q3, '123')
D = N.orient_new('D', (orienter1, ))
E = N.orient_new('E', (orienter2, ))
F = N.orient_new('F', (orienter3, ))
G = N.orient_new('G', (orienter4, ))
assert D == N.orient_new_axis('D', q4, N.j)
assert E == N.orient_new_space('E', q1, q2, q3, '123')
assert F == N.orient_new_quaternion('F', q1, q2, q3, q4)
assert G == N.orient_new_body('G', q1, q2, q3, '123')
def test_rotation_matrix():
N = CoordSysCartesian('N')
A = N.orient_new_axis('A', q1, N.k)
B = A.orient_new_axis('B', q2, A.i)
C = B.orient_new_axis('C', q3, B.j)
D = N.orient_new_axis('D', q4, N.j)
E = N.orient_new_space('E', q1, q2, q3, '123')
F = N.orient_new_quaternion('F', q1, q2, q3, q4)
G = N.orient_new_body('G', q1, q2, q3, '123')
assert N.rotation_matrix(C) == Matrix([
[- sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), - sin(q1) *
cos(q2), sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)], \
[sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), \
cos(q1) * cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * \
cos(q3)], [- sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)]])
test_mat = D.rotation_matrix(C) - Matrix(
[[cos(q1) * cos(q3) * cos(q4) - sin(q3) * (- sin(q4) * cos(q2) +
sin(q1) * sin(q2) * cos(q4)), - sin(q2) * sin(q4) - sin(q1) *
cos(q2) * cos(q4), sin(q3) * cos(q1) * cos(q4) + cos(q3) * \
(- sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4))], \
[sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * \
cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)], \
[sin(q4) * cos(q1) * cos(q3) - sin(q3) * (cos(q2) * cos(q4) + \
sin(q1) * sin(q2) * \
sin(q4)), sin(q2) *
cos(q4) - sin(q1) * sin(q4) * cos(q2), sin(q3) * \
sin(q4) * cos(q1) + cos(q3) * (cos(q2) * cos(q4) + \
sin(q1) * sin(q2) * sin(q4))]])
assert test_mat.expand() == zeros(3, 3)
assert E.rotation_matrix(N) == Matrix(
[[cos(q2)*cos(q3), sin(q3)*cos(q2), -sin(q2)],
[sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1), \
sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q2)], \
[sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3), - \
sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1), cos(q1)*cos(q2)]])
assert F.rotation_matrix(N) == Matrix([[
q1**2 + q2**2 - q3**2 - q4**2,
2*q1*q4 + 2*q2*q3, -2*q1*q3 + 2*q2*q4],[ -2*q1*q4 + 2*q2*q3,
q1**2 - q2**2 + q3**2 - q4**2, 2*q1*q2 + 2*q3*q4],
[2*q1*q3 + 2*q2*q4,
-2*q1*q2 + 2*q3*q4,
q1**2 - q2**2 - q3**2 + q4**2]])
assert G.rotation_matrix(N) == Matrix([[
cos(q2)*cos(q3), sin(q1)*sin(q2)*cos(q3) + sin(q3)*cos(q1),
sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3)], [
-sin(q3)*cos(q2), -sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3),
sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)],[
sin(q2), -sin(q1)*cos(q2), cos(q1)*cos(q2)]])
def test_rotation_matrix():
N = CoordSysCartesian('N')
A = N.orient_new_axis('A', q1, N.k)
B = A.orient_new_axis('B', q2, A.i)
C = B.orient_new_axis('C', q3, B.j)
D = N.orient_new_axis('D', q4, N.j)
E = N.orient_new_space('E', q1, q2, q3, '123')
F = N.orient_new_quaternion('F', q1, q2, q3, q4)
G = N.orient_new_body('G', q1, q2, q3, '123')
assert N.rotation_matrix(C) == Matrix([
[- sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), - sin(q1) *
cos(q2), sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)], \
[sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), \
cos(q1) * cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * \
cos(q3)], [- sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)]])
test_mat = D.rotation_matrix(C) - Matrix(
[[cos(q1) * cos(q3) * cos(q4) - sin(q3) * (- sin(q4) * cos(q2) +
sin(q1) * sin(q2) * cos(q4)), - sin(q2) * sin(q4) - sin(q1) *
cos(q2) * cos(q4), sin(q3) * cos(q1) * cos(q4) + cos(q3) * \
(- sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4))], \
[sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * \
cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)], \
[sin(q4) * cos(q1) * cos(q3) - sin(q3) * (cos(q2) * cos(q4) + \
sin(q1) * sin(q2) * \
sin(q4)), sin(q2) *
cos(q4) - sin(q1) * sin(q4) * cos(q2), sin(q3) * \
sin(q4) * cos(q1) + cos(q3) * (cos(q2) * cos(q4) + \
sin(q1) * sin(q2) * sin(q4))]])
assert test_mat.expand() == zeros(3, 3)
assert E.rotation_matrix(N) == Matrix(
[[cos(q2)*cos(q3), sin(q3)*cos(q2), -sin(q2)],
[sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1), \
sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q2)], \
[sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3), - \
sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1), cos(q1)*cos(q2)]])
assert F.rotation_matrix(N) == Matrix([[
q1**2 + q2**2 - q3**2 - q4**2,
2*q1*q4 + 2*q2*q3, -2*q1*q3 + 2*q2*q4],[ -2*q1*q4 + 2*q2*q3,
q1**2 - q2**2 + q3**2 - q4**2, 2*q1*q2 + 2*q3*q4],
[2*q1*q3 + 2*q2*q4,
-2*q1*q2 + 2*q3*q4,
q1**2 - q2**2 - q3**2 + q4**2]])
assert G.rotation_matrix(N) == Matrix([[
cos(q2)*cos(q3), sin(q1)*sin(q2)*cos(q3) + sin(q3)*cos(q1),
sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3)], [
-sin(q3)*cos(q2), -sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3),
sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)],[
sin(q2), -sin(q1)*cos(q2), cos(q1)*cos(q2)]])
def test_rotation_matrix():
N = CoordSysCartesian("N")
A = N.orient_new_axis("A", q1, N.k)
B = A.orient_new_axis("B", q2, A.i)
C = B.orient_new_axis("C", q3, B.j)
D = N.orient_new_axis("D", q4, N.j)
E = N.orient_new_space("E", q1, q2, q3, "123")
F = N.orient_new_quaternion("F", q1, q2, q3, q4)
G = N.orient_new_body("G", q1, q2, q3, "123")
assert N.rotation_matrix(C) == Matrix(
[
[
-sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3),
-sin(q1) * cos(q2),
sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1),
],
[
sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1),
cos(q1) * cos(q2),
sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3),
],
[-sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)],
]
)
test_mat = D.rotation_matrix(C) - Matrix(
[
[
cos(q1) * cos(q3) * cos(q4) - sin(q3) * (-sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4)),
-sin(q2) * sin(q4) - sin(q1) * cos(q2) * cos(q4),
sin(q3) * cos(q1) * cos(q4) + cos(q3) * (-sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4)),
],
[
sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1),
cos(q1) * cos(q2),
sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3),
],
[
sin(q4) * cos(q1) * cos(q3) - sin(q3) * (cos(q2) * cos(q4) + sin(q1) * sin(q2) * sin(q4)),
sin(q2) * cos(q4) - sin(q1) * sin(q4) * cos(q2),
sin(q3) * sin(q4) * cos(q1) + cos(q3) * (cos(q2) * cos(q4) + sin(q1) * sin(q2) * sin(q4)),
],
]
)
assert test_mat.expand() == zeros(3, 3)
assert E.rotation_matrix(N) == Matrix(
[
[cos(q2) * cos(q3), sin(q3) * cos(q2), -sin(q2)],
[
sin(q1) * sin(q2) * cos(q3) - sin(q3) * cos(q1),
sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3),
sin(q1) * cos(q2),
],
[
sin(q1) * sin(q3) + sin(q2) * cos(q1) * cos(q3),
-sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1),
cos(q1) * cos(q2),
],
]
)
assert F.rotation_matrix(N) == Matrix(
[
[q1 ** 2 + q2 ** 2 - q3 ** 2 - q4 ** 2, 2 * q1 * q4 + 2 * q2 * q3, -2 * q1 * q3 + 2 * q2 * q4],
[-2 * q1 * q4 + 2 * q2 * q3, q1 ** 2 - q2 ** 2 + q3 ** 2 - q4 ** 2, 2 * q1 * q2 + 2 * q3 * q4],
[2 * q1 * q3 + 2 * q2 * q4, -2 * q1 * q2 + 2 * q3 * q4, q1 ** 2 - q2 ** 2 - q3 ** 2 + q4 ** 2],
]
)
assert G.rotation_matrix(N) == Matrix(
[
[
cos(q2) * cos(q3),
sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1),
sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3),
],
[
-sin(q3) * cos(q2),
-sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3),
sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1),
],
[sin(q2), -sin(q1) * cos(q2), cos(q1) * cos(q2)],
]
)
