Source code for sfepy.mesh.mesh_tools

```from __future__ import absolute_import
from sfepy.discrete.fem import Mesh, FEDomain
import scipy.sparse as sps
import numpy as nm
from sfepy.base.compat import factorial
from sfepy.base.base import output
from six.moves import range

[docs]def elems_q2t(el):

nel, nnd = el.shape
if nnd > 4:
q2t = nm.array([[0, 2, 3, 6],
[0, 3, 7, 6],
[0, 7, 4, 6],
[0, 5, 6, 4],
[1, 5, 6, 0],
[1, 6, 2, 0]])

else:
q2t = nm.array([[0, 1, 2],
[0, 2, 3]])

ns, nn = q2t.shape
nel *= ns

out = nm.zeros((nel, nn), dtype=nm.int32);

for ii in range(ns):
idxs = nm.arange(ii, nel, ns)

out[idxs,:] = el[:, q2t[ii,:]]

return nm.ascontiguousarray(out)

[docs]def triangulate(mesh, verbose=False):
"""
Triangulate a 2D or 3D tensor product mesh: quadrilaterals->triangles,
hexahedrons->tetrahedrons.

Parameters
----------
mesh : Mesh
The input mesh.

Returns
-------
mesh : Mesh
The triangulated mesh.
"""
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break

if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo, verbose=verbose)

new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)

output('new mesh: %d elements' % new_conns.shape[0], verbose=verbose)
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])

return mesh

[docs]def smooth_mesh(mesh, n_iter=4, lam=0.6307, mu=-0.6347,
weights=None, bconstr=True,
volume_corr=False):
"""
FE mesh smoothing.

Based on:

[1] Steven K. Boyd, Ralph Muller, Smooth surface meshing for automated
finite element model generation from 3D image data, Journal of
Biomechanics, Volume 39, Issue 7, 2006, Pages 1287-1295,
ISSN 0021-9290, 10.1016/j.jbiomech.2005.03.006.
(http://www.sciencedirect.com/science/article/pii/S0021929005001442)

Parameters
----------
mesh : mesh
FE mesh.
n_iter : integer, optional
Number of iteration steps.
lam : float, optional
Smoothing factor, see [1].
mu : float, optional
Unshrinking factor, see [1].
weights : array, optional
Edge weights, see [1].
bconstr: logical, optional
Boundary constraints, if True only surface smoothing performed.
volume_corr: logical, optional
Correct volume after smoothing process.

Returns
-------
coors : array
Coordinates of mesh nodes.
"""

def laplacian(coors, weights):

n_nod = coors.shape[0]
displ = (weights - sps.identity(n_nod)) * coors

return displ

def taubin(coors0, weights, lam, mu, n_iter):

coors = coors0.copy()

for ii in range(n_iter):
displ = laplacian(coors, weights)
if nm.mod(ii, 2) == 0:
coors += lam * displ
else:
coors += mu * displ

return coors

def get_volume(el, nd):
from sfepy.linalg.utils import dets_fast

dim = nd.shape[1]
nnd = el.shape[1]

etype = '%d_%d' % (dim, nnd)
if etype == '2_4' or etype == '3_8':
el = elems_q2t(el)

nel = el.shape[0]

#bc = nm.zeros((dim, ), dtype=nm.double)
mul = 1.0 / factorial(dim)
if dim == 3:
mul *= -1.0

mtx = nm.ones((nel, dim + 1, dim + 1), dtype=nm.double)
mtx[:,:,:-1] = nd[el,:]
vols = mul * dets_fast(mtx)
vol = vols.sum()
bc = nm.dot(vols, mtx.sum(1)[:,:-1] / nnd)

bc /= vol

return vol, bc

from sfepy.base.timing import Timer

output('smoothing...')
timer = Timer(start=True)

if weights is None:
n_nod = mesh.n_nod
domain = FEDomain('mesh', mesh)
cmesh = domain.cmesh

# initiate all vertices as inner - hierarchy = 2
node_group = nm.ones((n_nod,), dtype=nm.int16) * 2
# boundary vertices - set hierarchy = 4
if bconstr:
# get "vertices of surface"
facets = cmesh.get_surface_facets()
f_verts = cmesh.get_incident(0, facets, cmesh.dim - 1)
node_group[f_verts] = 4

# generate costs matrix
e_verts = cmesh.get_conn(1, 0).indices
fc1, fc2 = e_verts[0::2], e_verts[1::2]
idxs = nm.where(node_group[fc2] >= node_group[fc1])
rows1 = fc1[idxs]
cols1 = fc2[idxs]
idxs = nm.where(node_group[fc1] >= node_group[fc2])
rows2 = fc2[idxs]
cols2 = fc1[idxs]
crows = nm.concatenate((rows1, rows2))
ccols = nm.concatenate((cols1, cols2))
costs = sps.coo_matrix((nm.ones_like(crows), (crows, ccols)),
shape=(n_nod, n_nod),
dtype=nm.double)

# generate weights matrix
idxs = list(range(n_nod))
aux = sps.coo_matrix((1.0 / nm.asarray(costs.sum(1)).squeeze(),
(idxs, idxs)),
shape=(n_nod, n_nod),
dtype=nm.double)

#aux.setdiag(1.0 / costs.sum(1))
weights = (aux.tocsc() * costs.tocsc()).tocsr()

coors = taubin(mesh.coors, weights, lam, mu, n_iter)

output('...done in %.2f s' % timer.stop())

if volume_corr:
output('rescaling...')
timer.start()
volume0, bc = get_volume(mesh.conns[0], mesh.coors)
volume, _ = get_volume(mesh.conns[0], coors)

scale = volume0 / volume
output('scale factor: %.2f' % scale)

coors = (coors - bc) * scale + bc

output('...done in %.2f s' % timer.stop())

return coors

[docs]def expand2d(mesh2d, dist, rep):
"""
Expand 2D planar mesh into 3D volume,
convert triangular/quad mesh to tetrahedrons/hexahedrons.

Parameters
----------
mesh2d : Mesh
The 2D mesh.
dist : float
The elements size in the 3rd direction.
rep : int
The number of elements in the 3rd direction.

Returns
-------
mesh3d : Mesh
The 3D mesh.
"""
if len(mesh2d.descs) > 1:
raise ValueError('More than one cell type (%s). Not supported!'
% ', '.join(mesh2d.descs))

nel = mesh2d.n_el
nnd = mesh2d.n_nod
et = mesh2d.descs[0]
coors = mesh2d.coors
conn = mesh2d.get_conn(et)

zcoor = nm.arange(rep + 1) * dist
coors3d = nm.hstack([nm.tile(coors, (rep + 1, 1)),
nm.tile(zcoor, (nnd,1)).T.flatten()[:,nm.newaxis]])
ngroups = nm.tile(mesh2d.cmesh.vertex_groups, (rep + 1,))

if et == '2_4':
descs3d = '3_8'
conn3d = nm.zeros((nel * rep, 8), dtype=nm.int32)
mats3d = nm.tile(mesh2d.cmesh.cell_groups, (1, rep)).squeeze()

elif et == '2_3':
descs3d = '3_4'
conn3d = nm.zeros((3 * nel * rep, 4), dtype=nm.int32)
mats3d = nm.tile(mesh2d.cmesh.cell_groups, (1, 3 * rep)).squeeze()

for ii in range(rep):
bgn0 = nnd * ii
bgn1 = bgn0 + nnd
if et == '2_4':
bge0 = nel * ii
bge1 = bge0 + nel
conn3d[bge0:bge1,:4] = conn + bgn0
conn3d[bge0:bge1,4:] = conn + bgn1

elif et == '2_3':
# 0 1 2 5
bge0 = 3 * nel * ii
bge1 = bge0 + nel
conn3d[bge0:bge1,:] = nm.array([conn[:,0] + bgn0,
conn[:,1] + bgn0,
conn[:,2] + bgn0,
conn[:,2] + bgn1]).T
# 0 1 5 4
bge0 += nel
bge1 += nel
conn3d[bge0:bge1,:] = nm.array([conn[:,0] + bgn0,
conn[:,1] + bgn0,
conn[:,2] + bgn1,
conn[:,1] + bgn1]).T
# 0 4 5 3
bge0 += nel
bge1 += nel
conn3d[bge0:bge1,:] = nm.array([conn[:,0] + bgn0,
conn[:,1] + bgn1,
conn[:,2] + bgn1,
conn[:,0] + bgn1]).T

mesh3d = Mesh.from_data('mesh', coors3d, ngroups, [conn3d],
[mats3d], [descs3d])

return mesh3d
```