def test_affine_points_fit_generic(self): p_start = np.array([[1,.5,-.3], [0,2,4], [-1,0.,-1.5], [1,-4,.5]]) p_end = np.array([[0,1,0], [-1,0,0], [0,0,1], [0,0,0]]) v_test = np.array([1., 2., 3.]) v_exact = np.array([-0.68443497, 0.7249467 , -0.34221748]) transformation = at.affine_points_fit(p_start, p_end) v_trans = transformation(v_test) np.testing.assert_array_almost_equal(v_exact, v_trans)
def test_affine_points_fit_identity_2(self): p_start = np.array([[1,.5,-.3], [0,2,4], [-1,0.,-1.5], [1,-4,.5]]) p_end = p_start v_test = np.array([-1., 2.5, .3]) v_exact = v_test transformation = at.affine_points_fit(p_start, p_end) v_trans = transformation(v_test) np.testing.assert_array_almost_equal(v_exact, v_trans)
def test_affine_points_fit_rotation(self): p_start = np.array([[1,0,0], [0,1,0], [0,0,1], [0,0,0]]) p_end = np.array([[0,1,0], [-1,0,0], [0,0,1], [0,0,0]]) v_test = np.array([1., 2., 3.]) v_exact = np.array([-2., 1., 3.]) transformation = at.affine_points_fit(p_start, p_end) v_trans = transformation(v_test) np.testing.assert_array_almost_equal(v_exact, v_trans)
def test_affine_points_fit_rotation(self):
p_start = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, 0]])
p_end = np.array([[0, 1, 0], [-1, 0, 0], [0, 0, 1], [0, 0, 0]])
v_test = np.array([1., 2., 3.])
v_exact = np.array([-2., 1., 3.])
transformation = at.affine_points_fit(p_start, p_end)
v_trans = transformation(v_test)
np.testing.assert_array_almost_equal(v_exact, v_trans)
def test_affine_points_fit_generic(self):
p_start = np.array([[1, .5, -.3], [0, 2, 4], [-1, 0., -1.5],
[1, -4, .5]])
p_end = np.array([[0, 1, 0], [-1, 0, 0], [0, 0, 1], [0, 0, 0]])
v_test = np.array([1., 2., 3.])
v_exact = np.array([-0.68443497, 0.7249467, -0.34221748])
transformation = at.affine_points_fit(p_start, p_end)
v_trans = transformation(v_test)
np.testing.assert_array_almost_equal(v_exact, v_trans)
def test_affine_points_fit_identity_2(self):
p_start = np.array([[1, .5, -.3], [0, 2, 4], [-1, 0., -1.5],
[1, -4, .5]])
p_end = p_start
v_test = np.array([-1., 2.5, .3])
v_exact = v_test
transformation = at.affine_points_fit(p_start, p_end)
v_trans = transformation(v_test)
np.testing.assert_array_almost_equal(v_exact, v_trans)
def perform(self):
"""
This method performs the deformation on the mesh points. After the execution
it sets `self.modified_mesh_points`.
.. todo::
"""
# translation and then affine transformation
translation = self.parameters.origin_box
physical_frame = np.array([
self.parameters.position_vertex_1 - translation,
self.parameters.position_vertex_2 - translation,
self.parameters.position_vertex_3 - translation, [0, 0, 0]
])
reference_frame = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0,
0]])
transformation = at.affine_points_fit(physical_frame, reference_frame)
inverse_transformation = at.affine_points_fit(reference_frame,
physical_frame)
# apply transformation to original mesh points
reference_frame_mesh_points = self._transform_points(
self.original_mesh_points - translation, transformation)
# select mesh points inside bounding box
mesh_points = reference_frame_mesh_points[
(reference_frame_mesh_points[:, 0] >= 0.)
& (reference_frame_mesh_points[:, 0] <= 1.) &
(reference_frame_mesh_points[:, 1] >= 0.) &
(reference_frame_mesh_points[:, 1] <= 1.) &
(reference_frame_mesh_points[:, 2] >= 0.) &
(reference_frame_mesh_points[:, 2] <= 1.)]
(n_rows_mesh, n_cols_mesh) = mesh_points.shape
# Initialization. In order to exploit the contiguity in memory the following are transposed
(dim_n_mu, dim_m_mu, dim_t_mu) = self.parameters.array_mu_x.shape
bernstein_x = np.zeros((dim_n_mu, n_rows_mesh))
bernstein_y = np.zeros((dim_m_mu, n_rows_mesh))
bernstein_z = np.zeros((dim_t_mu, n_rows_mesh))
shift_mesh_points = np.zeros((n_cols_mesh, n_rows_mesh))
for i in range(0, dim_n_mu):
aux1 = np.power((1 - mesh_points[:, 0]), dim_n_mu - 1 - i)
aux2 = np.power(mesh_points[:, 0], i)
bernstein_x[i, :] = special.binom(dim_n_mu - 1, i) * np.multiply(
aux1, aux2)
for i in range(0, dim_m_mu):
aux1 = np.power((1 - mesh_points[:, 1]), dim_m_mu - 1 - i)
aux2 = np.power(mesh_points[:, 1], i)
bernstein_y[i, :] = special.binom(dim_m_mu - 1, i) * np.multiply(
aux1, aux2)
for i in range(0, dim_t_mu):
aux1 = np.power((1 - mesh_points[:, 2]), dim_t_mu - 1 - i)
aux2 = np.power(mesh_points[:, 2], i)
bernstein_z[i, :] = special.binom(dim_t_mu - 1, i) * np.multiply(
aux1, aux2)
aux_x = 0.
aux_y = 0.
aux_z = 0.
for j in range(0, dim_m_mu):
for k in range(0, dim_t_mu):
bernstein_yz = np.multiply(bernstein_y[j, :],
bernstein_z[k, :])
for i in range(0, dim_n_mu):
aux = np.multiply(bernstein_x[i, :], bernstein_yz)
aux_x += aux * self.parameters.array_mu_x[i, j, k]
aux_y += aux * self.parameters.array_mu_y[i, j, k]
aux_z += aux * self.parameters.array_mu_z[i, j, k]
shift_mesh_points[0, :] += aux_x
shift_mesh_points[1, :] += aux_y
shift_mesh_points[2, :] += aux_z
# shift_mesh_points needs to be transposed to be summed with mesh_points
# apply inverse transformation to shifted mesh points
new_mesh_points = self._transform_points(np.transpose(shift_mesh_points) +
mesh_points, inverse_transformation) + \
translation
# merge non-shifted mesh points with shifted ones
self.modified_mesh_points = np.copy(self.original_mesh_points)
self.modified_mesh_points[(reference_frame_mesh_points[:,0] >= 0.) &
(reference_frame_mesh_points[:,0] <= 1.) &
(reference_frame_mesh_points[:,1] >= 0.) &
(reference_frame_mesh_points[:,1] <= 1.) &
(reference_frame_mesh_points[:,2] >= 0.) &
(reference_frame_mesh_points[:,2] <= 1.)] \
= new_mesh_points
def test_affine_points_fit_under_determined_system_2(self): p_start = np.array([[1,0,0], [0,1,0]]) p_end = np.array([[0,1,0], [-1,0,0]]) with self.assertRaises(RuntimeError): transformation = at.affine_points_fit(p_start, p_end)
def test_affine_points_fit_right_points_size(self): p_start = np.array([[1,0,0], [0,1,0], [0,0,1], [0,0,0]]) p_end = np.array([[0,1,0], [-1,0,0], [0,0,1]]) with self.assertRaises(RuntimeError): transformation = at.affine_points_fit(p_start, p_end)
def perform(self): """ This method performs the deformation on the mesh points. After the execution it sets `self.modified_mesh_points`. .. todo:: In order to improve the performances, we need to perform the FFD only on the points inside the lattice. """ (n_rows_mesh, n_cols_mesh) = self.original_mesh_points.shape # translation and then affine transformation translation = self.parameters.origin_box fisical_frame = np.array([self.parameters.position_vertex_1 - translation, \ self.parameters.position_vertex_2 - translation, \ self.parameters.position_vertex_3 - translation, \ [0, 0, 0]]) reference_frame = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, 0]]) transformation = at.affine_points_fit(fisical_frame, reference_frame) inverse_transformation = at.affine_points_fit(reference_frame, fisical_frame) # Initialization. In order to exploit the contiguity in memory the following are transposed (dim_n_mu, dim_m_mu, dim_t_mu) = self.parameters.array_mu_x.shape bernstein_x = np.zeros((dim_n_mu, n_rows_mesh)) bernstein_y = np.zeros((dim_m_mu, n_rows_mesh)) bernstein_z = np.zeros((dim_t_mu, n_rows_mesh)) shift_mesh_points = np.zeros((n_cols_mesh, n_rows_mesh)) reference_frame_mesh_points = self._transform_points(self.original_mesh_points - translation, \ transformation) for i in range(0, dim_n_mu): aux1 = np.power((1-reference_frame_mesh_points[:, 0]), dim_n_mu-1-i) aux2 = np.power(reference_frame_mesh_points[:, 0], i) bernstein_x[i, :] = special.binom(dim_n_mu-1, i) * np.multiply(aux1, aux2) for i in range(0, dim_m_mu): aux1 = np.power((1-reference_frame_mesh_points[:, 1]), dim_m_mu-1-i) aux2 = np.power(reference_frame_mesh_points[:, 1], i) bernstein_y[i, :] = special.binom(dim_m_mu-1, i) * np.multiply(aux1, aux2) for i in range(0, dim_t_mu): aux1 = np.power((1-reference_frame_mesh_points[:, 2]), dim_t_mu-1-i) aux2 = np.power(reference_frame_mesh_points[:, 2], i) bernstein_z[i, :] = special.binom(dim_t_mu-1, i) * np.multiply(aux1, aux2) aux_x = 0. aux_y = 0. aux_z = 0. for j in range(0, dim_m_mu): for k in range(0, dim_t_mu): bernstein_yz = np.multiply(bernstein_y[j, :], bernstein_z[k, :]) for i in range(0, dim_n_mu): aux = np.multiply(bernstein_x[i, :], bernstein_yz) aux_x += aux * self.parameters.array_mu_x[i, j, k] aux_y += aux * self.parameters.array_mu_y[i, j, k] aux_z += aux * self.parameters.array_mu_z[i, j, k] shift_mesh_points[0, :] += aux_x shift_mesh_points[1, :] += aux_y shift_mesh_points[2, :] += aux_z # Splitting points inside and outside the lattice: TODO not very efficient for i in range(0, n_rows_mesh): if (reference_frame_mesh_points[i, 0] < 0) or (reference_frame_mesh_points[i, 1] < 0) \ or (reference_frame_mesh_points[i, 2] < 0) or (reference_frame_mesh_points[i, 0] > 1) \ or (reference_frame_mesh_points[i, 1] > 1) or (reference_frame_mesh_points[i, 2] > 1): shift_mesh_points[:, i] = 0 # Here shift_mesh_points needs to be transposed to be summed with reference_frame_mesh_points self.modified_mesh_points = self._transform_points(np.transpose(shift_mesh_points) + \ reference_frame_mesh_points, inverse_transformation) + translation
def test_affine_points_fit_under_determined_system_2(self):
p_start = np.array([[1, 0, 0], [0, 1, 0]])
p_end = np.array([[0, 1, 0], [-1, 0, 0]])
with self.assertRaises(RuntimeError):
transformation = at.affine_points_fit(p_start, p_end)
def test_affine_points_fit_right_points_size(self):
p_start = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, 0]])
p_end = np.array([[0, 1, 0], [-1, 0, 0], [0, 0, 1]])
with self.assertRaises(RuntimeError):
transformation = at.affine_points_fit(p_start, p_end)
def perform(self):
"""
This method performs the deformation on the mesh points. After the
execution it sets `self.modified_mesh_points`.
"""
# translation and then affine transformation
translation = self.parameters.box_origin
physical_frame = self.parameters.position_vertices - translation
reference_frame = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]])
transformation = at.affine_points_fit(physical_frame, reference_frame)
inverse_transformation = at.affine_points_fit(reference_frame,
physical_frame)
# apply transformation to original mesh points
reference_frame_mesh_points = self._transform_points(
self.original_mesh_points - translation, transformation)
# select mesh points inside bounding box
mesh_points = reference_frame_mesh_points[
(reference_frame_mesh_points[:, 0] >= 0.)
& (reference_frame_mesh_points[:, 0] <= 1.) &
(reference_frame_mesh_points[:, 1] >= 0.) &
(reference_frame_mesh_points[:, 1] <= 1.) &
(reference_frame_mesh_points[:, 2] >= 0.) &
(reference_frame_mesh_points[:, 2] <= 1.)]
(n_rows_mesh, n_cols_mesh) = mesh_points.shape
# Initialization. In order to exploit the contiguity in memory the
# following are transposed
(dim_n_mu, dim_m_mu, dim_t_mu) = self.parameters.array_mu_x.shape
bernstein_x = np.zeros((dim_n_mu, n_rows_mesh))
bernstein_y = np.zeros((dim_m_mu, n_rows_mesh))
bernstein_z = np.zeros((dim_t_mu, n_rows_mesh))
shift_mesh_points = np.zeros((n_cols_mesh, n_rows_mesh))
for i in range(0, dim_n_mu):
aux1 = np.power((1 - mesh_points[:, 0]), dim_n_mu - 1 - i)
aux2 = np.power(mesh_points[:, 0], i)
bernstein_x[i, :] = special.binom(dim_n_mu - 1, i) * np.multiply(
aux1, aux2)
for i in range(0, dim_m_mu):
aux1 = np.power((1 - mesh_points[:, 1]), dim_m_mu - 1 - i)
aux2 = np.power(mesh_points[:, 1], i)
bernstein_y[i, :] = special.binom(dim_m_mu - 1, i) * np.multiply(
aux1, aux2)
for i in range(0, dim_t_mu):
aux1 = np.power((1 - mesh_points[:, 2]), dim_t_mu - 1 - i)
aux2 = np.power(mesh_points[:, 2], i)
bernstein_z[i, :] = special.binom(dim_t_mu - 1, i) * np.multiply(
aux1, aux2)
aux_x = 0.
aux_y = 0.
aux_z = 0.
for j in range(0, dim_m_mu):
for k in range(0, dim_t_mu):
bernstein_yz = np.multiply(bernstein_y[j, :], bernstein_z[k, :])
for i in range(0, dim_n_mu):
aux = np.multiply(bernstein_x[i, :], bernstein_yz)
aux_x += aux * self.parameters.array_mu_x[i, j, k]
aux_y += aux * self.parameters.array_mu_y[i, j, k]
aux_z += aux * self.parameters.array_mu_z[i, j, k]
shift_mesh_points[0, :] += aux_x
shift_mesh_points[1, :] += aux_y
shift_mesh_points[2, :] += aux_z
# shift_mesh_points needs to be transposed to be summed with mesh_points
# apply inverse transformation to shifted mesh points
new_mesh_points = self._transform_points(
np.transpose(shift_mesh_points) + mesh_points,
inverse_transformation) + translation
# merge non-shifted mesh points with shifted ones
self.modified_mesh_points = np.copy(self.original_mesh_points)
self.modified_mesh_points[(reference_frame_mesh_points[:, 0] >= 0.)
& (reference_frame_mesh_points[:, 0] <= 1.) &
(reference_frame_mesh_points[:, 1] >= 0.) &
(reference_frame_mesh_points[:, 1] <= 1.) &
(reference_frame_mesh_points[:, 2] >= 0.) &
(reference_frame_mesh_points[:, 2] <=
1.)] = new_mesh_points