def test_error_drop_curvature_quadric(self):
""" Asserts the error drops when the mesh resolution is increased"""
out = []
for j in range(3):
K = [1, 1]
# Increase of the number of points
quadric = sgps.generate_quadric(K,
nstep=[20 + 10 * j, 20 + 10 * j],
ax=3,
ay=1,
random_sampling=False,
ratio=0.3,
random_distribution_type='gamma')
# Computation of estimated curvatures
p_curv, d1, d2 = scurv.curvatures_and_derivatives(quadric)
k1_estim, k2_estim = p_curv[0, :], p_curv[1, :]
# k_gauss_estim = k1_estim * k2_estim
k_mean_estim = .5 * (k1_estim + k2_estim)
# Computation of analytical curvatures
k_mean_analytic = sgps.quadric_curv_mean(K)(np.array(
quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1]))
k_gauss_analytic = sgps.quadric_curv_gauss(K)(np.array(
quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1]))
k1_analytic = np.zeros((len(k_mean_analytic)))
k2_analytic = np.zeros((len(k_mean_analytic)))
for i in range(len(k_mean_analytic)):
a, b = np.roots(
(1, -2 * k_mean_analytic[i], k_gauss_analytic[i]))
k1_analytic[i] = min(a, b)
k2_analytic[i] = max(a, b)
# /// STATS
# k_mean_relative_change = abs(
# (k_mean_analytic - k_mean_estim) / k_mean_analytic)
k_mean_absolute_change = abs((k_mean_analytic - k_mean_estim))
# k1_relative_change = abs((k1_analytic - k1_estim) / k1_analytic)
# k1_absolute_change = abs((k1_analytic - k1_estim))
out += [np.round(np.mean(k_mean_absolute_change), 6)]
# Assert the absolute mean error decreases as we increase the number of
# points
assert (sorted(out, reverse=True) == out)
def test_correctness_decomposition_quadric(self):
# Precision on the shapeIndex calculation
precisionA = 0.000001
# Precision on the curvedness calculation
precisionB = 0.000001
set_of_tests = [
# Set = [K, correct shapeIndex, correct curvedness]
# For example, on a quadric generated by K=[1,1], the shapeIndex
# is +-1 at the center and the curvedness is +-2
[[1, 1], 1, 2],
[[-1, -1], 1, 2],
[[.5, .5], 1, 1],
[[1, 0], .5, np.sqrt(2)],
]
for i in range(len(set_of_tests)):
current_test = set_of_tests[i]
K = current_test[0]
# Correct values of shapeIndex and curvedness on the vertex at the
# center of the mesh
correct_shape_index = current_test[1]
correct_curvedness = current_test[2]
with self.subTest(i):
# Generate quadric
quadric = sgps.generate_quadric(
K,
nstep=[20, 20],
ax=3,
ay=1,
random_sampling=False,
ratio=0.3,
)
# Computation of analytical k_mean, k_gauss, k_1 and k_2
k_mean_analytic = sgps.quadric_curv_mean(K)(np.array(
quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1]))
k_gauss_analytic = sgps.quadric_curv_gauss(K)(np.array(
quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1]))
k1_analytic = np.zeros((len(k_mean_analytic)))
k2_analytic = np.zeros((len(k_mean_analytic)))
for i in range(len(k_mean_analytic)):
a, b = np.roots(
(1, -2 * k_mean_analytic[i], k_gauss_analytic[i]))
k1_analytic[i] = min(a, b)
k2_analytic[i] = max(a, b)
# Decomposition of the curvature
shapeIndex, curvedness = scurv.decompose_curvature(
np.array((k1_analytic, k2_analytic)))
# Find the index of the vertex which is the closest to the
# center
def mag(p):
"""Distance to the center for the point p, not considering
the z axis"""
x = p[0]
y = p[1]
return np.sqrt(x * x + y * y)
min_i = 0
min_m = mag(quadric.vertices[0])
for i, v in enumerate(quadric.vertices):
mg = mag(v)
if mg < min_m:
min_i = i
min_m = mg
# Correctness
computed_shapeIndex = shapeIndex[min_i]
computed_curvedness = curvedness[min_i]
assert (np.isclose(computed_shapeIndex, correct_shape_index,
precisionA)
| np.isclose(computed_shapeIndex, -correct_shape_index,
precisionA))
assert (np.isclose(computed_curvedness, correct_curvedness,
precisionB)
| np.isclose(computed_curvedness, -correct_curvedness,
precisionB))
import slam.plot as splt
import numpy as np
###############################################################################
# Generating a quadrix surface
K = [1, 1]
quadric = sgps.generate_quadric(K,
nstep=20,
ax=3,
ay=1,
random_sampling=True,
ratio=0.3,
random_distribution_type='gamma')
quadric_mean_curv = \
sgps.quadric_curv_mean(K)(np.array(quadric.vertices[:, 0]),
np.array(quadric.vertices[:, 1]))
visb_sc = splt.visbrain_plot(mesh=quadric,
tex=quadric_mean_curv,
caption='quadric',
cblabel='mean curvature')
visb_sc.preview()
###############################################################################
# Generating an ellipsiods
nstep = 50
randomSampling = True
a = 2
b = 1
def test_correctness_curvature_quadric(self):
K = [1, 1]
quadric = sgps.generate_quadric(K,
nstep=[20, 20],
ax=3,
ay=1,
random_sampling=True,
ratio=0.3,
random_distribution_type='gamma')
# Computation of estimated curvatures
p_curv, d1, d2 = scurv.curvatures_and_derivatives(quadric)
k1_estim, k2_estim = p_curv[0, :], p_curv[1, :]
# k_gauss_estim = k1_estim * k2_estim
k_mean_estim = .5 * (k1_estim + k2_estim)
# Computation of analytical curvatures
k_mean_analytic = sgps.quadric_curv_mean(K)(np.array(
quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1]))
k_gauss_analytic = sgps.quadric_curv_gauss(K)(np.array(
quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1]))
k1_analytic = np.zeros((len(k_mean_analytic)))
k2_analytic = np.zeros((len(k_mean_analytic)))
for i in range(len(k_mean_analytic)):
a, b = np.roots((1, -2 * k_mean_analytic[i], k_gauss_analytic[i]))
k1_analytic[i] = min(a, b)
k2_analytic[i] = max(a, b)
# /// STATS
k_mean_relative_change = abs(
(k_mean_analytic - k_mean_estim) / k_mean_analytic)
k_mean_absolute_change = abs((k_mean_analytic - k_mean_estim))
k1_relative_change = abs((k1_analytic - k1_estim) / k1_analytic)
# k1_absolute_change = abs((k1_analytic - k1_estim))
a = []
a += [
[
"K_MEAN", "mean", "relative change",
np.mean(k_mean_relative_change * 100), "%"
],
("K_MEAN", "std", "relative change",
np.std(k_mean_relative_change * 100), "%"),
("K_MEAN", "max", "relative change",
np.max(k_mean_relative_change * 100), "%"),
[
"K_MEAN", "mean", "absolute change",
np.mean(k_mean_absolute_change)
],
[
"K_MEAN", "std", "absolute change",
np.std(k_mean_absolute_change)
],
[
"K_MEAN", "max", "absolute change",
np.max(k_mean_absolute_change)
],
(" K1", "mean", "relative change",
np.mean(k1_relative_change * 100), "%"),
(" K1", "std", "relative change", np.std(k1_relative_change * 100),
"%"),
(" K1", "max", "relative change", np.max(k1_relative_change * 100),
"%"),
(" K1", "mean", "absolute change",
np.mean(k_mean_absolute_change)),
(" K1", "std", "absolute change", np.std(k_mean_absolute_change)),
(" K1", "max", "absolute change", np.max(k_mean_absolute_change)),
]
# PRINT STATS
print("----------------------------------------")
for i, v in enumerate(a):
numeric_value = np.round(v[3], decimals=3)
if i == 6:
print("----------------------------------------")
if len(v) > 4:
print('{0:10} {1:5} {2:16} {3:2} {4} {5}'.format(
v[0], v[1], v[2], "=", numeric_value, v[4]))
else:
print('{0:10} {1:5} {2:16} {3:2} {4}'.format(
v[0], v[1], v[2], "=", numeric_value))
print("----------------------------------------")
'Dong'] #, 'Peyre', 'fem', 'boix', 'bary']
curv_types_leg = curv_types.copy()
curv_types_leg.append('analytic')
meshes = list()
curv_mean = list()
Ks = [[-1, 1], [1, 1], [0, 1]]
for K in Ks:
meshes.append('hex_quad_k1_' + str(K[0]) + '_k2_' + str(K[1]) + '_100')
os.chdir(
r"/hpc/meca/users/souani.a/curvature/Compute_curvatures/Quadrics")
tmp_m = sio.load_mesh('hex_quad_k1_' + str(K[0]) + '_k2_' + str(K[1]) +
'_100.gii')
mesh_coords = tmp_m.vertices
print(np.shape(mesh_coords))
curv_mean.append(
gp.quadric_curv_mean(K[0], K[1])(mesh_coords[:, 0],
mesh_coords[:, 1]))
#meshes.append('FSsphere.ico7')
#meshes.append('KKI2009_113_MR1.lh.white')
for mesh_type, curv_ref in zip(meshes, curv_mean):
print(mesh_type)
print("Shaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaape", np.shape(curv_ref))
file_fig = os.path.join(main_folder,
mesh_type + '_curv_mean_comparison_hist.png')
curvatures = list()
integral = list()
for curv_type in curv_types:
print('----' + curv_type)
curv_tex_gii = nb.load(
os.path.join(
