def volume_curvature_normal_smooth(triangles, vertices, nb_iter=1,
diffusion_step=1.0, area_weighted=False,
backward_step=False, flow_file=None):
if isinstance(diffusion_step, (int, float)):
diffusion_step = diffusion_step * np.ones(len(vertices))
if flow_file is not None:
mem_map = np.memmap(flow_file, dtype=G_DTYPE, mode='w+',
shape=(nb_iter, vertices.shape[0], vertices.shape[1]))
for i in range(nb_iter):
stdout.write("\r step %d on %d done" % (i, nb_iter))
stdout.flush()
if flow_file is not None:
mem_map[i] = vertices
# get curvature_normal_matrix
# todo not optimal, because operation done twice etc
curvature_normal_mtx = mean_curvature_normal_matrix(
triangles, vertices, area_weighted=area_weighted)
# do the first step
next_vertices = euler_step(curvature_normal_mtx, csc_matrix(
vertices), diffusion_step, backward_step).toarray()
# test if direction is positive
direction = next_vertices - vertices
normal_dir = vertices_cotan_normal(triangles, vertices, normalize=True)
dotv = dot(normalize_vectors(direction), normal_dir, keepdims=True)
vertices += direction * np.maximum(0.0, -dotv)
stdout.write("\r step %d on %d done \n" % (nb_iter, nb_iter))
return vertices
def vertices_normal(triangles, vertices, normalize=True, area_weighted=True):
tri_normal = triangles_normal(triangles, vertices, normalize=area_weighted)
tv_matrix = triangle_vertex_map(triangles, vertices)
vts_normal = tv_matrix.T.dot(tri_normal)
if normalize:
return normalize_vectors(vts_normal)
return vts_normal
def triangles_normal(triangles, vertices, normalize=True):
if scipy.sparse.__name__ in type(vertices).__module__:
vertices = vertices.toarray()
e1 = vertices[triangles[:, 1]] - vertices[triangles[:, 0]]
e2 = vertices[triangles[:, 2]] - vertices[triangles[:, 0]]
normal = np.cross(e1, e2)
if normalize:
return normalize_vectors(normal)
return normal
def vertices_cotan_direction(triangles,
vertices,
normalize=True,
area_weighted=True):
from trimeshpy.math.matrix import mean_curvature_normal_matrix
curvature_normal_mtx = mean_curvature_normal_matrix(
triangles, vertices, area_weighted=area_weighted)
cotan_normal = curvature_normal_mtx.dot(vertices)
if normalize:
return normalize_vectors(cotan_normal)
return cotan_normal
def volume_mass_stiffness_smooth(triangles,
vertices,
nb_iter=1,
diffusion_step=1.0,
flow_file=None):
vertices_csc = csc_matrix(vertices)
curvature_normal_mtx = mean_curvature_normal_matrix(triangles,
vertices,
area_weighted=False)
if isinstance(diffusion_step, (int, long, float)):
diffusion_step = diffusion_step * np.ones(len(vertices))
if flow_file is not None:
mem_map = np.memmap(flow_file,
dtype=G_DTYPE,
mode='w+',
shape=(nb_iter, vertices.shape[0],
vertices.shape[1]))
for i in range(nb_iter):
stdout.write("\r step %d on %d done" % (i, nb_iter))
stdout.flush()
if flow_file is not None:
mem_map[i] = vertices_csc.toarray()
# get curvature_normal_matrix
mass_mtx = mass_matrix(triangles, vertices)
raise NotImplementedError()
# (D - d*L)*y = D*x = b
A_matrix = mass_mtx - \
diags(diffusion_step, 0).dot(curvature_normal_mtx)
b_matrix = mass_mtx.dot(csc_matrix(vertices_csc))
next_vertices = spsolve(A_matrix, b_matrix)
# test if direction is positive
direction = next_vertices.toarray() - vertices_csc
normal_dir = vertices_cotan_normal(triangles,
next_vertices,
normalize=True)
dotv = normalize_vectors(direction).multiply(normal_dir)
vertices_csc += direction * np.maximum(0.0, -dotv)
# vertices_csc += direction * sigmoid(-np.arctan(dotv)*np.pi - np.pi)
# vertices_csc += direction * softplus(-dotv)
stdout.write("\r step %d on %d done \n" % (nb_iter, nb_iter))
return vertices_csc.toarray()
def vertices_cotan_normal(triangles,
vertices,
normalize=True,
area_weighted=True):
from trimeshpy.math.curvature import vertices_cotan_direction
if scipy.sparse.__name__ in type(vertices).__module__:
vertices = vertices.toarray()
cotan_normal = vertices_cotan_direction(triangles,
vertices,
normalize=False,
area_weighted=area_weighted)
vts_normal = vertices_normal(triangles,
vertices,
normalize=False,
area_weighted=area_weighted)
# inverse inverted cotan_normal direction
cotan_normal = np.sign(dot(cotan_normal, vts_normal,
keepdims=True)) * cotan_normal
if normalize:
return normalize_vectors(cotan_normal)
return cotan_normal