def test4_1():
"""
This functions builds a planar mesh and checks that the weights of the
middle vertex is correct. Here is the mesh (with the non-zero weights):
________________
|\ | /|
| \ 0.5 / |
| \ | / |
|_0.5__\|/__0.5_| sum(wi) = 2
| /|\ |
| / | \ |
| / 0.5 \ |
|/______|______\|
It also checks that the Laplace-Beltrami operator is correctly defined
"""
# create vertices
x = np.array([0., 1., 2.])
x = np.repeat(x, 3)
y = np.array([0., 1., 2.])
y = np.tile(y ,3)
z = np.zeros(9)
vertices = np.vstack((x, y, z)).T
# create polygons
polygons = np.array([[0, 3, 4], [0, 4, 1], [1, 4, 2], [2, 4, 5],
[3, 6, 4], [4, 6, 7], [4, 7, 8], [4, 8, 5]])
# get edges
nb_edges = 3 * polygons.shape[0]
edges = np.zeros((nb_edges, 2))
# get the polygons edges as tuples
permutator = np.array([(0,0,1),(1,0,0),(0,1,0)], dtype=int)
edges[:,0] = np.ravel(polygons)
edges[:,1] = np.ravel(np.dot(polygons, permutator))
ind = np.lexsort((edges[:,1], edges[:,0]))
edges = edges[ind]
weights_matrix = smooth.compute_weights_matrix(polygons, vertices, edges)
LB_operator = smooth.define_LB_operator(weights_matrix)
assert (LB_operator[4,0] == 0. and LB_operator[4,2] == 0. and
LB_operator[4,6] == 0. and LB_operator[4,8] == 0.)
assert (LB_operator[4,1] == 0.5 and LB_operator[4,3] == 0.5 and
LB_operator[4,5] == 0.5 and LB_operator[4,7] == 0.5)
assert (LB_operator[4,4] == -2.)
### Get information from input texture
# /!\ fixme : check that input_tex corresponds to the mesh
print " * Getting information from input texture"
sys.stdout.flush()
input_tex = tio.Texture(orig_tex_path).read(orig_tex_path)
activation_data = input_tex.data
activation_data[np.isnan(activation_data)] = 0
### Construct the weights matrix
print " * Computing the weights matrix"
sys.stdout.flush()
weights_matrix = smooth.compute_weights_matrix(polygons, vertices, edges)
### Define the Laplace-Beltrami operator
LB_operator = smooth.define_LB_operator(weights_matrix)
### Compute the number of iterations needed
N, dt = smooth.compute_smoothing_parameters(weights_matrix, FWHM)
### Apply smoothing
print " * Smoothing...(FWHM = %g)" %FWHM
sys.stdout.flush()
smoothed_activation_data = smooth.diffusion_smoothing(
activation_data, LB_operator, N, dt)
### Write smoothed data into a new texture file
print " * Writing output texture"
sys.stdout.flush()
output_tex = tio.Texture(smoothed_tex_path, data=smoothed_activation_data)
output_tex.write()
