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 positive_curvature_normal_smooth(triangles, vertices, nb_iter=1,
diffusion_step=1.0, area_weighted=False,
backward_step=False, flow_file=None):
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]))
if isinstance(diffusion_step, (int, float)):
diffusion_step = diffusion_step * np.ones(len(vertices))
curvature_normal_mtx = mean_curvature_normal_matrix(
triangles, vertices, area_weighted=area_weighted)
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
# 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_normal(triangles, next_vertices, normalize=False)
pos_curv = dot(direction, normal_dir, keepdims=True) < 0
vertices += direction * pos_curv
stdout.write("\r step %d on %d done \n" % (nb_iter, nb_iter))
return vertices
def positive_curvature_normal_matrix(triangles, vertices, area_weighted=False):
from trimeshpy.math.normal import vertices_normal
curvature_normal_mtx = mean_curvature_normal_matrix(
triangles, vertices, area_weighted)
# get flow vector and normal vector
direction = curvature_normal_mtx.dot(vertices)
normal_dir = vertices_normal(triangles, vertices, normalize=False)
# positive curvature goes opposite to the normal
pos_curv = (dot(direction, normal_dir, axis=1) < 0).astype(G_DTYPE)
curvature_normal_mtx = diags(pos_curv, 0).dot(curvature_normal_mtx)
return curvature_normal_mtx
def vertices_cotan_curvature(triangles, vertices, area_weighted=True):
from trimeshpy.math.normal import vertices_normal
vts_dir = vertices_cotan_direction(triangles,
vertices,
normalize=False,
area_weighted=area_weighted)
vts_normal = vertices_normal(triangles,
vertices,
normalize=False,
area_weighted=area_weighted)
curvature_sign = -np.sign(dot(vts_dir, vts_normal))
curvature = length(vts_dir)
return curvature * curvature_sign
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