def centre_of_mass(geometry, vertices='throat.offset_vertices', **kwargs):
r"""
Calculate the centre of mass of the throat from the voronoi vertices.
"""
Nt = geometry.num_throats()
outer_verts = geometry['throat.vertices']
offset_verts = geometry[vertices]
normal = geometry['throat.normal']
z_axis = [0, 0, 1]
value = _sp.ndarray([Nt, 3])
for i in range(Nt):
if len(offset_verts[i]) > 2:
verts = offset_verts[i]
elif len(outer_verts[i]) > 2:
verts = outer_verts[i]
else:
verts = []
if len(verts) > 0:
# For boundaries some facets will already be aligned with the axis -
# if this is the case a rotation is unnecessary and could also cause
# problems
angle = tr.angle_between_vectors(normal[i], z_axis)
if angle == 0.0 or angle == _sp.pi:
"We are already aligned"
rotate_input = False
facet = verts
else:
rotate_input = True
M = tr.rotation_matrix(
tr.angle_between_vectors(normal[i], z_axis),
tr.vector_product(normal[i], z_axis))
facet = _sp.dot(verts, M[:3, :3].T)
# Now we have a rotated facet aligned with the z axis - make 2D
facet_2D = _sp.column_stack((facet[:, 0], facet[:, 1]))
z = _sp.unique(_sp.around(facet[:, 2], 10))
if len(z) == 1:
# We need the vertices arranged in order so perform a convex hull
hull = ConvexHull(facet_2D)
ordered_facet_2D = facet_2D[hull.vertices]
# Call the routine to calculate an area wighted centroid from the
# 2D polygon
COM_2D = vo.PolyWeightedCentroid2D(ordered_facet_2D)
COM_3D = _sp.hstack((COM_2D, z))
# If we performed a rotation we need to rotate back
if (rotate_input):
MI = tr.inverse_matrix(M)
# Unrotate the offset coordinates using the inverse of the
# original rotation matrix
value[i] = _sp.dot(COM_3D, MI[:3, :3].T)
else:
value[i] = COM_3D
else:
logger.error('Rotation Failed: ' +
str(_sp.unique(facet[:, 2])))
return value
def centre_of_mass(geometry, vertices='throat.offset_vertices', **kwargs):
r"""
Calculate the centre of mass of the throat from the voronoi vertices.
"""
Nt = geometry.num_throats()
outer_verts = geometry['throat.vertices']
offset_verts = geometry[vertices]
normal = geometry['throat.normal']
z_axis = [0, 0, 1]
value = _sp.ndarray([Nt, 3])
for i in range(Nt):
if len(offset_verts[i]) > 2:
verts = offset_verts[i]
elif len(outer_verts[i]) > 2:
verts = outer_verts[i]
else:
verts = []
if len(verts) > 0:
# For boundaries some facets will already be aligned with the axis -
# if this is the case a rotation is unnecessary and could also cause
# problems
angle = tr.angle_between_vectors(normal[i], z_axis)
if angle == 0.0 or angle == _sp.pi:
"We are already aligned"
rotate_input = False
facet = verts
else:
rotate_input = True
M = tr.rotation_matrix(tr.angle_between_vectors(normal[i], z_axis),
tr.vector_product(normal[i], z_axis))
facet = _sp.dot(verts, M[:3, :3].T)
# Now we have a rotated facet aligned with the z axis - make 2D
facet_2D = _sp.column_stack((facet[:, 0], facet[:, 1]))
z = _sp.unique(_sp.around(facet[:, 2], 10))
if len(z) == 1:
# We need the vertices arranged in order so perform a convex hull
hull = ConvexHull(facet_2D)
ordered_facet_2D = facet_2D[hull.vertices]
# Call the routine to calculate an area wighted centroid from the
# 2D polygon
COM_2D = vo.PolyWeightedCentroid2D(ordered_facet_2D)
COM_3D = _sp.hstack((COM_2D, z))
# If we performed a rotation we need to rotate back
if (rotate_input):
MI = tr.inverse_matrix(M)
# Unrotate the offset coordinates using the inverse of the
# original rotation matrix
value[i] = _sp.dot(COM_3D, MI[:3, :3].T)
else:
value[i] = COM_3D
else:
logger.error('Rotation Failed: ' + str(_sp.unique(facet[:, 2])))
return value
def rotate_and_chop(verts, normal, axis=[0, 0, 1]):
r"""
Method to rotate a set of vertices (or coords) to align with an axis
points must be coplanar and normal must be given
Chops axis coord to give vertices back in 2D
Used to prepare verts for printing or calculating convex hull in order to arrange
them in hull order for calculations and printing
"""
xaxis = [1, 0, 0]
yaxis = [0, 1, 0]
zaxis = [0, 0, 1]
angle = tr.angle_between_vectors(normal, axis)
if angle == 0.0 or angle == np.pi:
# We are already aligned
facet = verts
else:
M = tr.rotation_matrix(tr.angle_between_vectors(normal, axis),
tr.vector_product(normal, axis))
try:
facet = np.dot(verts, M[:3, :3].T)
except ValueError:
pass
try:
x = facet[:, 0]
y = facet[:, 1]
z = facet[:, 2]
except IndexError:
x = facet[0]
y = facet[1]
z = facet[2]
# Work out span of points and set axes scales to cover this and be
# equal in both dimensions
if axis == xaxis:
output = np.column_stack((y, z))
elif axis == yaxis:
output = np.column_stack((x, z))
elif axis == zaxis:
output = np.column_stack((x, y))
else:
output = facet
return output
def rotate_and_chop(verts, normal, axis=[0, 0, 1]):
r"""
Method to rotate a set of vertices (or coords) to align with an axis
points must be coplanar and normal must be given
Chops axis coord to give vertices back in 2D
Used to prepare verts for printing or calculating convex hull in order to arrange
them in hull order for calculations and printing
"""
xaxis = [1, 0, 0]
yaxis = [0, 1, 0]
zaxis = [0, 0, 1]
angle = tr.angle_between_vectors(normal, axis)
if angle == 0.0 or angle == np.pi:
# We are already aligned
facet = verts
else:
M = tr.rotation_matrix(tr.angle_between_vectors(normal, axis),
tr.vector_product(normal, axis))
try:
facet = np.dot(verts, M[:3, :3].T)
except ValueError:
pass
try:
x = facet[:, 0]
y = facet[:, 1]
z = facet[:, 2]
except IndexError:
x = facet[0]
y = facet[1]
z = facet[2]
# Work out span of points and set axes scales to cover this and be
# equal in both dimensions
if axis == xaxis:
output = np.column_stack((y, z))
elif axis == yaxis:
output = np.column_stack((x, z))
elif axis == zaxis:
output = np.column_stack((x, y))
else:
output = facet
return output
def _rotation(self, direction, angle):
# type: (Vector3D, Union[int, np.float]) -> Transformation
return Transformation(rotation_matrix(angle, direction))
def distance_transform(network, geometry, offset, **kwargs):
r"""
Use the Voronoi vertices and perform image analysis to obtain throat properties
"""
import math
import numpy as np
from skimage.morphology import convex_hull_image
from skimage.measure import regionprops
from scipy import ndimage
Nt = geometry.num_throats()
area = sp.zeros(Nt)
perimeter = sp.zeros(Nt)
centroid = sp.zeros([Nt, 3])
incentre = sp.zeros([Nt, 3])
inradius = sp.zeros(Nt)
equiv_diameter = sp.zeros(Nt)
eroded_verts = sp.ndarray(Nt, dtype=object)
res = 200
vertices = geometry['throat.vertices']
normals = geometry['throat.normal']
z_axis = [0, 0, 1]
for i in range(Nt):
logger.info("Processing throat " + str(i+1)+" of "+str(Nt))
# For boundaries some facets will already be aligned with the axis - if this
# is the case a rotation is unnecessary and could also cause problems
angle = tr.angle_between_vectors(normals[i], z_axis)
if angle == 0.0 or angle == np.pi:
# We are already aligned
rotate_facet = False
facet = vertices[i]
else:
rotate_facet = True
M = tr.rotation_matrix(tr.angle_between_vectors(normals[i], z_axis),
tr.vector_product(normals[i], z_axis))
facet = np.dot(vertices[i], M[:3, :3].T)
x = facet[:, 0]
y = facet[:, 1]
z = facet[:, 2]
# Get points in 2d for image analysis
pts = np.column_stack((x, y))
# Translate points so min sits at the origin
translation = [pts[:, 0].min(), pts[:, 1].min()]
pts -= translation
order = np.int(math.ceil(-np.log10(np.max(pts))))
# Normalise and scale the points so that largest span equals the resolution
# to save on memory and create clear image"
max_factor = np.max([pts[:, 0].max(), pts[:, 1].max()])
f = res/max_factor
#"Temporarily try using the vox_len as a scale factor"
#f = 1/geometry._vox_len
# Scale the offset and define a circular structuring element with radius
r = f*offset
# Only proceed if r is less than half the span of the image"
if r <= res/2:
pts *= f
minp1 = pts[:, 0].min()
minp2 = pts[:, 1].min()
maxp1 = pts[:, 0].max()
maxp2 = pts[:, 1].max()
img = np.zeros([np.int(math.ceil(maxp1-minp1)+1),
np.int(math.ceil(maxp2-minp2)+1)])
int_pts = np.around(pts, 0).astype(int)
for pt in int_pts:
img[pt[0]][pt[1]] = 1
# Pad with zeros all the way around the edges
img_pad = np.zeros([np.shape(img)[0] + 2, np.shape(img)[1] + 2])
img_pad[1:np.shape(img)[0]+1, 1:np.shape(img)[1]+1] = img
# All points should lie on this plane but could be some rounding errors
# so use the order parameter
z_plane = sp.unique(np.around(z, order+2))
if len(z_plane) > 1:
logger.error('Rotation for image analysis failed')
temp_arr = np.ones(1)
temp_arr.fill(np.mean(z_plane))
z_plane = temp_arr
"Fill in the convex hull polygon"
convhullimg = convex_hull_image(img_pad)
# Perform a Distance Transform and black out points less than r to create
# binary erosion. This is faster than performing an erosion and dt can
# also be used later to find incircle"
eroded = ndimage.distance_transform_edt(convhullimg)
eroded[eroded <= r] = 0
eroded[eroded > r] = 1
# If we are left with less than 3 non-zero points then the throat is
# fully occluded
if np.sum(eroded) >= 3:
# Do some image analysis to extract the key properties
regions = regionprops(eroded[1:np.shape(img)[0]+1,
1:np.shape(img)[1]+1].astype(int))
# Change this to cope with genuine multi-region throats
if len(regions) == 1:
for props in regions:
x0, y0 = props.centroid
equiv_diameter[i] = props.equivalent_diameter
area[i] = props.area
perimeter[i] = props.perimeter
coords = props.coords
# Undo the translation, scaling and truncation on the centroid
centroid2d = np.array([x0, y0])/f
centroid2d += (translation)
centroid3d = np.concatenate((centroid2d, z_plane))
# Distance transform the eroded facet to find the incentre and
# inradius
dt = ndimage.distance_transform_edt(eroded)
inx0, iny0 = \
np.asarray(np.unravel_index(dt.argmax(), dt.shape)) \
.astype(float)
incentre2d = np.array([inx0, iny0])
# Undo the translation, scaling and truncation on the incentre
incentre2d /= f
incentre2d += (translation)
incentre3d = np.concatenate((incentre2d, z_plane))
# The offset vertices will be those in the coords that are
# closest to the originals"
offset_verts = []
for pt in int_pts:
vert = np.argmin(np.sum(np.square(coords-pt), axis=1))
if vert not in offset_verts:
offset_verts.append(vert)
# If we are left with less than 3 different vertices then the
# throat is fully occluded as we can't make a shape with
# non-zero area
if len(offset_verts) >= 3:
offset_coords = coords[offset_verts].astype(float)
# Undo the translation, scaling and truncation on the
# offset_verts
offset_coords /= f
offset_coords_3d = \
np.vstack((offset_coords[:, 0]+translation[0],
offset_coords[:, 1]+translation[1],
np.ones(len(offset_verts))*z_plane)).T
# Get matrix to un-rotate the co-ordinates back to the
# original orientation if we rotated in the first place
if rotate_facet:
MI = tr.inverse_matrix(M)
# Unrotate the offset coordinates
incentre[i] = np.dot(incentre3d, MI[:3, :3].T)
centroid[i] = np.dot(centroid3d, MI[:3, :3].T)
eroded_verts[i] = np.dot(offset_coords_3d, MI[:3, :3].T)
else:
incentre[i] = incentre3d
centroid[i] = centroid3d
eroded_verts[i] = offset_coords_3d
inradius[i] = dt.max()
# Undo scaling on other parameters
area[i] /= f*f
perimeter[i] /= f
equiv_diameter[i] /= f
inradius[i] /= f
else:
area[i] = 0
perimeter[i] = 0
equiv_diameter[i] = 0
if kwargs['set_dependent'] is True:
geometry['throat.area'] = area
geometry['throat.perimeter'] = perimeter
geometry['throat.centroid'] = centroid
geometry['throat.diameter'] = equiv_diameter
geometry['throat.indiameter'] = inradius*2
geometry['throat.incentre'] = incentre
return eroded_verts
def _throat_props(self):
r"""
Use the Voronoi vertices and perform image analysis to obtain throat
properties
"""
offset = self.network.fiber_rad
Nt = self.num_throats()
centroid = sp.zeros([Nt, 3])
incenter = sp.zeros([Nt, 3])
area = sp.zeros(Nt)
perimeter = sp.zeros(Nt)
inradius = sp.zeros(Nt)
equiv_diameter = sp.zeros(Nt)
eroded_verts = sp.ndarray(Nt, dtype=object)
res = 200
vertices = self['throat.vertices']
normals = self['throat.normal']
z_axis = [0, 0, 1]
for i in self.throats('delaunay'):
logger.info("Processing throat " + str(i + 1) + " of " + str(Nt))
# For boundaries some facets will already be aligned with the axis
# if this is the case a rotation is unnecessary
angle = tr.angle_between_vectors(normals[i], z_axis)
if angle == 0.0 or angle == np.pi:
# We are already aligned
rotate_facet = False
facet = vertices[i]
else:
rotate_facet = True
M = tr.rotation_matrix(
tr.angle_between_vectors(normals[i], z_axis),
tr.vector_product(normals[i], z_axis))
facet = np.dot(vertices[i], M[:3, :3].T)
x = facet[:, 0]
y = facet[:, 1]
z = facet[:, 2]
# Get points in 2d for image analysis
pts = np.column_stack((x, y))
# Translate points so min sits at the origin
translation = [pts[:, 0].min(), pts[:, 1].min()]
pts -= translation
order = np.int(math.ceil(-np.log10(np.max(pts))))
# Normalise and scale the points so that largest span equals the
# resolution to save on memory and create clear image
max_factor = np.max([pts[:, 0].max(), pts[:, 1].max()])
f = res / max_factor
# Scale the offset and define a structuring element with radius
r = f * offset
# Only proceed if r is less than half the span of the image"
if r <= res / 2:
pts *= f
minp1 = pts[:, 0].min()
minp2 = pts[:, 1].min()
maxp1 = pts[:, 0].max()
maxp2 = pts[:, 1].max()
img = np.zeros([
np.int(math.ceil(maxp1 - minp1) + 1),
np.int(math.ceil(maxp2 - minp2) + 1)
])
int_pts = np.around(pts.astype(float), 0).astype(int)
for pt in int_pts:
img[pt[0]][pt[1]] = 1
# Pad with zeros all the way around the edges
img_pad = np.zeros(
[np.shape(img)[0] + 2,
np.shape(img)[1] + 2])
img_pad[1:np.shape(img)[0] + 1, 1:np.shape(img)[1] + 1] = img
# All points should lie on this plane but could be some
# rounding errors so use the order parameter
z_plane = sp.unique(np.around(z.astype(float), order + 1))
if len(z_plane) > 1:
logger.error('Throat ' + str(i) + ' Rotation Failure')
temp_arr = np.ones(1)
temp_arr.fill(np.mean(z_plane))
z_plane = temp_arr
"Fill in the convex hull polygon"
convhullimg = convex_hull_image(img_pad)
# Perform a Distance Transform and black out points less than r
# to create binary erosion. This is faster than performing an
# erosion and dt can also be used later to find incircle
eroded = ndimage.distance_transform_edt(convhullimg)
eroded[eroded <= r] = 0
eroded[eroded > r] = 1
# If we are left with less than 3 non-zero points then the
# throat is fully occluded
if np.sum(eroded) >= 3:
# Do some image analysis to extract the key properties
cropped = eroded[1:np.shape(img)[0] + 1,
1:np.shape(img)[1] + 1].astype(int)
regions = regionprops(cropped)
# Change this to cope with genuine multi-region throats
if len(regions) == 1:
for props in regions:
x0, y0 = props.centroid
equiv_diameter[i] = props.equivalent_diameter
area[i] = props.area
perimeter[i] = props.perimeter
coords = props.coords
# Undo the translation, scaling and truncation on the
# centroid
centroid2d = [x0, y0] / f
centroid2d += (translation)
centroid3d = np.concatenate((centroid2d, z_plane))
# Distance transform the eroded facet to find the
# incenter and inradius
dt = ndimage.distance_transform_edt(eroded)
temp = np.unravel_index(dt.argmax(), dt.shape)
inx0, iny0 = np.asarray(temp).astype(float)
incenter2d = [inx0, iny0]
# Undo the translation, scaling and truncation on the
# incenter
incenter2d /= f
incenter2d += (translation)
incenter3d = np.concatenate((incenter2d, z_plane))
# The offset vertices will be those in the coords that
# are closest to the originals
offset_verts = []
for pt in int_pts:
vert = np.argmin(
np.sum(np.square(coords - pt), axis=1))
if vert not in offset_verts:
offset_verts.append(vert)
# If we are left with less than 3 different vertices
# then the throat is fully occluded as we can't make a
# shape with non-zero area
if len(offset_verts) >= 3:
offset_coords = coords[offset_verts].astype(float)
# Undo the translation, scaling and truncation on
# the offset_verts
offset_coords /= f
offset_coords_3d = \
np.vstack((offset_coords[:, 0]+translation[0],
offset_coords[:, 1]+translation[1],
np.ones(len(offset_verts))*z_plane))
oc_3d = offset_coords_3d.T
# Get matrix to un-rotate the co-ordinates back to
# the original orientation if we rotated in the
# first place
if rotate_facet:
MI = tr.inverse_matrix(M)
# Unrotate the offset coordinates
incenter[i] = np.dot(incenter3d, MI[:3, :3].T)
centroid[i] = np.dot(centroid3d, MI[:3, :3].T)
eroded_verts[i] = np.dot(oc_3d, MI[:3, :3].T)
else:
incenter[i] = incenter3d
centroid[i] = centroid3d
eroded_verts[i] = oc_3d
inradius[i] = dt.max()
# Undo scaling on other parameters
area[i] /= f * f
perimeter[i] /= f
equiv_diameter[i] /= f
inradius[i] /= f
else:
area[i] = 0
perimeter[i] = 0
equiv_diameter[i] = 0
self['throat.area'] = area
self['throat.perimeter'] = perimeter
self['throat.centroid'] = centroid
self['throat.diameter'] = equiv_diameter
self['throat.indiameter'] = inradius * 2
self['throat.incenter'] = incenter
self['throat.offset_vertices'] = eroded_verts