def orientation_matrix(euler1, euler2, euler3):
"""Input: Three Euler angles (Bunge convention), expressed in degrees
Output: Cartesian coordinates of the orientation direction"""
e1, e2, e3 = np.eye(3) #standard basis (sample coord system)
sample_basis = np.array([e1, e2, e3])
deg2rad = np.pi / 180.0 #degree to radian conversion factor
#rot1 = affine.rotation_matrix(euler1*deg2rad,axis=e3) @ sample_basis
#rot2 = affine.rotation_matrix(euler2*deg2rad,axis=rot1.T[0]) @ rot1
#rot3 = affine.rotation_matrix(euler3*deg2rad,axis=rot2.T[2]) @ rot2
rot1 = affine.rotation_matrix(euler1 * deg2rad, axis=e3)
rot2 = rot1 @ affine.rotation_matrix(euler2 * deg2rad, axis=e1)
rot3 = rot2 @ affine.rotation_matrix(euler3 * deg2rad, axis=e3)
return rot3
def test_random(self):
""" Test that rotation_matrix() returns a valid rotation matrix
for random axes and angles """
axis = np.random.random((3,))
angle = np.random.random()
mat = tr.rotation_matrix(angle, axis)
self.assertTrue(tr.is_rotation_matrix(mat))
def test_change_of_basis(self):
""" Test that change_of_basis() returns a correct change-of-basis matrix"""
b1 = np.array([[0, 0, 1], [1, 0, 0], [0, 1, 0]])
# Generate a new basis as a rotation of pi/3 around z-axis
b2 = np.dot(tr.rotation_matrix(np.pi / 3, axis=[0, 0, 1]), b1)
cob = tr.change_of_basis(b1, b2)
self.assertTrue(np.allclose(np.dot(cob, b1), b2))
def test_random(self):
""" Test that translation_rotation_matrix() produces a matrix that correctly
transforms a random point """
pt = np.random.random((3,))
axis = np.random.random((3,))
angle = np.random.random()
translation = np.random.random((3,))
trmat = tr.translation_rotation_matrix(angle, axis, translation=translation)
v1 = tr.transform(trmat, pt) # translated rotated point
# Transform the point once operator at a time
v2 = tr.transform(tr.rotation_matrix(angle, axis), pt)
v2 += translation
self.assertTrue(np.allclose(v1, v2))
def test_from_rotation_matrix(self):
""" test that the rotated identity operator is
a rotation matrix"""
self.assertTrue(
tr.is_rotation_matrix(tr.rotation_matrix(np.pi / 3, axis=[0, 0, 1]))
)