def __init__(self, shape=[1, 1, 1], num_points=None, **kwargs):
points = kwargs.pop('points', None)
points = self._parse_points(shape=shape,
num_points=num_points,
points=points)
# Deal with points that are only 2D...they break tessellations
if points.shape[1] == 3 and len(sp.unique(points[:, 2])) == 1:
points = points[:, :2]
# Perform tessellation
vor = sptl.Voronoi(points=points)
self._vor = vor
# Combine points
pts_all = sp.vstack((vor.points, vor.vertices))
Nall = sp.shape(pts_all)[0]
# Create adjacency matrix in lil format for quick construction
am = sprs.lil_matrix((Nall, Nall))
for ridge in vor.ridge_dict.keys():
# Make Delaunay-to-Delauny connections
[am.rows[i].extend([ridge[0], ridge[1]]) for i in ridge]
# Get voronoi vertices for current ridge
row = vor.ridge_dict[ridge].copy()
# Index Voronoi vertex numbers by number of delaunay points
row = [i + vor.npoints for i in row if i > -1]
# Make Voronoi-to-Delaunay connections
[am.rows[i].extend(row) for i in ridge]
# Make Voronoi-to-Voronoi connections
row.append(row[0])
[am.rows[row[i]].append(row[i+1]) for i in range(len(row)-1)]
# Finalize adjacency matrix by assigning data values
am.data = am.rows # Values don't matter, only shape, so use 'rows'
# Convert to COO format for direct acces to row and col
am = am.tocoo()
# Extract rows and cols
conns = sp.vstack((am.row, am.col)).T
# Convert to sanitized adjacency matrix
am = topotools.conns_to_am(conns)
# Finally, retrieve conns back from am
conns = sp.vstack((am.row, am.col)).T
# Translate adjacency matrix and points to OpenPNM format
coords = sp.around(pts_all, decimals=10)
if coords.shape[1] == 2: # Make points back into 3D if necessary
coords = sp.vstack((coords.T, sp.zeros((coords.shape[0], )))).T
super().__init__(conns=conns, coords=coords, **kwargs)
# Label all pores and throats by type
self['pore.delaunay'] = False
self['pore.delaunay'][0:vor.npoints] = True
self['pore.voronoi'] = False
self['pore.voronoi'][vor.npoints:] = True
# Label throats between Delaunay pores
self['throat.delaunay'] = False
Ts = sp.all(self['throat.conns'] < vor.npoints, axis=1)
self['throat.delaunay'][Ts] = True
# Label throats between Voronoi pores
self['throat.voronoi'] = False
Ts = sp.all(self['throat.conns'] >= vor.npoints, axis=1)
self['throat.voronoi'][Ts] = True
# Label throats connecting a Delaunay and a Voronoi pore
self['throat.interconnect'] = False
Ts = self.throats(labels=['delaunay', 'voronoi'], mode='not')
self['throat.interconnect'][Ts] = True
# Trim all pores that lie outside of the specified domain
self._trim_external_pores(shape=shape)
self._label_faces()
def voronoi_delaunay_dual(points, shape, crop=False):
r"""
Generate a dual Voronoi-Delaunay network from given base points
Parameters
----------
points : array_like or scalar
The points to be tessellated. If a scalar is given a set of points
of that size is generated.
shape : array_like
The size of the domain in which the points lie
crop : bool, optional (default is ``False``)
If ``True`` then all points lying beyond the given domain shape will
be removed
Returns
-------
network : dict
A dictionary containing 'vert.coords' and 'edge.conns'
vor : Voronoi object
The Voronoi tessellation object produced by ``scipy.spatial.Voronoi``
tri : Delaunay object
The Delaunay triangulation object produced ``scipy.spatial.Delaunay``
"""
# Generate a set of base points if number was given
points = tools.parse_points(points=points, shape=shape)
mask = ~np.all(points == 0, axis=0)
# Perform tessellations
vor = sptl.Voronoi(points=points[:, mask])
tri = sptl.Delaunay(points=points[:, mask])
# Combine points
pts_all = np.vstack((vor.points, vor.vertices))
Nall = np.shape(pts_all)[0]
# Create adjacency matrix in lil format for quick construction
am = sprs.lil_matrix((Nall, Nall))
for ridge in vor.ridge_dict.keys():
# Make Delaunay-to-Delaunay connections
for i in ridge:
am.rows[i].extend([ridge[0], ridge[1]])
# Get Voronoi vertices for current ridge
row = vor.ridge_dict[ridge].copy()
# Index Voronoi vertex numbers by number of Delaunay points
row = [i + vor.npoints for i in row if i > -1]
# Make Voronoi-to-Delaunay connections
for i in ridge:
am.rows[i].extend(row)
# Make Voronoi-to-Voronoi connections
row.append(row[0])
for i in range(len(row)-1):
am.rows[row[i]].append(row[i+1])
# Finalize adjacency matrix by assigning data values
am.data = am.rows # Values don't matter, only shape, so use 'rows'
# Convert to COO format for direct acces to row and col
am = am.tocoo()
# Extract rows and cols
conns = np.vstack((am.row, am.col)).T
# Convert to sanitized adjacency matrix
am = conns_to_am(conns)
# Finally, retrieve conns back from am
conns = np.vstack((am.row, am.col)).T
# Convert coords to 3D by adding col of 0's if necessary
coords = np.around(pts_all, decimals=10)
if np.any(mask == False):
verts = np.zeros([np.shape(coords)[0], 3])
for i, col in enumerate(np.where(mask)[0]):
verts[:, col] = coords[:, i]
else:
verts = np.copy(coords)
# Assign coords and conns to network dict
network = {}
network['vert.coords'] = verts
network['edge.conns'] = conns
# Identify and trim pores outside the domain if requested
if crop:
Ps = isoutside(verts, shape=shape)
network = tools.trim(network=network, vert_ids=np.where(Ps)[0])
return network, vor, tri