def test_rodriguesToRotationMatrix():
RES = np.array([[0.50017235, -0.80049871, 0.33019604],
[0.80739289, 0.56894174, 0.15627544],
[-0.3129606, 0.18843328, 0.9308859]])
R = gtr._rodriguesToRotationMatrix(TEST_UVEC, TEST_ANGLE)
# assess rotation matrix properties:
# detR = +=1
nt.assert_almost_equal(np.linalg.det(R), 1.)
# R.T = R^-1
nt.assert_true(np.allclose(np.linalg.inv(R), R.transpose()))
# check against calculated matrix
nt.assert_true(np.allclose(R, RES))
# check if opposite sign generates inverse
Rinv = gtr._rodriguesToRotationMatrix(TEST_UVEC, -TEST_ANGLE)
nt.assert_true(np.allclose(np.dot(Rinv, R), np.identity(3)))
# check basic rotations with a range of angles
for angle in np.linspace(0., 2. * np.pi, 10):
Rx = gtr._rodriguesToRotationMatrix(np.array([1., 0., 0.]), angle)
Ry = gtr._rodriguesToRotationMatrix(np.array([0., 1., 0.]), angle)
Rz = gtr._rodriguesToRotationMatrix(np.array([0., 0., 1.]), angle)
nt.assert_true(np.allclose(Rx, _Rx(angle)))
nt.assert_true(np.allclose(Ry, _Ry(angle)))
nt.assert_true(np.allclose(Rz, _Rz(angle)))
def test_affineTransformPoint():
point = TREE.value[:COLS.R]
# rotate 180 and translate, translate back and rotate 180
# change origin as well
m = copy(point)
R = gtr._rodriguesToRotationMatrix(TEST_UVEC, 2. * np.pi)
gtr._affineTransformPoint(m, R, np.zeros(3))
nt.assert_true(np.allclose(point, m))
new_orig = np.array([10. , 45., 50.])
t = np.array([0.1, - 0.1, 40.3])
R = gtr._rodriguesToRotationMatrix(TEST_UVEC, np.pi)
m = copy(point)
# change origin, rotate 180 and translate
gtr._affineTransformPoint(m, R, t, origin=new_orig)
# translate back
gtr._affineTransformPoint(m, np.identity(3), -t, origin=np.zeros(3))
# rotate back
gtr._affineTransformPoint(m, R, np.zeros(3), origin=new_orig)
nt.assert_true(np.allclose(point, m))
def test_affineTransformNeuron():
# rotate 180 and translate, translate back and rotate 180
# change origin as well
new_orig = np.array([10. , 45., 50.])
t = np.array([0.1, - 0.1, 40.3])
R = gtr._rodriguesToRotationMatrix(TEST_UVEC, np.pi)
m = NEURON.copy()
# change origin, rotate 180 and translate
gtr._affineTransformNeuron(m, R, t, origin=new_orig)
# translate back
gtr._affineTransformNeuron(m, np.identity(3), -t, origin=np.zeros(3))
# rotate back
gtr._affineTransformNeuron(m, R, np.zeros(3), origin=new_orig)
nt.assert_true(np.allclose(list(m.soma.iter()), list(NEURON.soma.iter())))
for neu1, neu2 in izip(NEURON.neurites, m.neurites):
_evaluate(neu1, neu2, lambda x, y: np.allclose(x, y))
def test_rotate_tree():
m = gtr.rotate(TREE, TEST_UVEC, TEST_ANGLE)
R = gtr._rodriguesToRotationMatrix(TEST_UVEC, TEST_ANGLE)
# rotation matrix inverse equals its transpose
Rinv = R.transpose()
# check that if the inverse rotation on the rotated result returns
# the initial coordinates
_evaluate(TREE, m, lambda x, y: np.allclose(np.dot(Rinv, y), x) )
# check with origin
new_orig = np.array([-50., 45., 30.])
m = gtr.rotate(TREE, TEST_UVEC, TEST_ANGLE, origin=new_orig)
m = gtr.rotate(m, TEST_UVEC, -TEST_ANGLE, origin=new_orig)
_evaluate(TREE, m, lambda x, y: np.allclose(x, y) )
def test_affineTransformTree():
# rotate 180 and translate, translate back and rotate 180
# change origin as well
new_orig = np.array([10. , 45., 50.])
t = np.array([0.1, - 0.1, 40.3])
R = gtr._rodriguesToRotationMatrix(TEST_UVEC, np.pi)
# change origin, rotate 180 and translate
m = make_copy(TREE)
gtr._affineTransformTree(m, R, t, origin=new_orig)
# translate back
gtr._affineTransformTree(m, np.identity(3), -t, origin=np.zeros(3))
# rotate back
gtr._affineTransformTree(m, R, np.zeros(3), origin=new_orig)
_evaluate(TREE, m, lambda x, y: np.allclose(x, y))