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 sfepy.discrete.common.extmods.cmesh import (create_mesh_graph,
graph_components)
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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)
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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
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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
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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
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def merge_lines(mesh, eps=1e-18):
"""
Merge edges of an edge-only mesh that are in the same direction w.r.t. the
tolerance `eps`.
"""
coors, ngroups, conns, mat_ids, ctype = mesh
conns = conns[0]
# vertices to edges map
n_v = coors.shape[0]
n_e = conns.shape[0]
row = nm.repeat(nm.arange(n_e), 2)
aux = sps.coo_matrix((nm.ones((n_e * 2,), dtype=bool),
(row, conns.flatten())), shape=(n_e, n_v))
v2e = aux.tocsc()
n_epv = nm.diff(v2e.indptr)
# directional vectors of edges
de = coors[conns[:, 1], :] - coors[conns[:, 0], :]
de = de / nm.linalg.norm(de, axis=1)[:, nm.newaxis]
eflag = nm.ones((n_e, ), dtype=bool)
valid_e = nm.where(eflag)[0]
e_remove = []
while len(valid_e) > 0:
ie = valid_e[0]
d = de[ie]
buff = [(ie, conns[ie, 0]), (ie, conns[ie, 1])]
eflag[ie] = False # invalidate edge
while len(buff) > 0:
e, v = buff.pop(-1)
if n_epv[v] == 2:
idx = v2e.indptr[v]
aux = v2e.indices[idx]
next_e = v2e.indices[idx + 1] if aux == e else aux
if not eflag[next_e]: # valid edge?
continue
if nm.linalg.norm(de[next_e] - d) < eps\
or nm.linalg.norm(de[next_e] + d) < eps:
next_ec = conns[next_e, :]
new_v = next_ec[0] if next_ec[1] == v else next_ec[1]
idx = 0 if conns[e, 0] == v else 1
conns[e, idx] = new_v # reconnect edge
idx = v2e.indptr[new_v]
aux = v2e.indices[idx]
idx += 0 if aux == next_e else 1
v2e.indices[idx] = e # update v2e map
buff.append((e, new_v)) # continue in searching
eflag[next_e] = False # invalidate edge
e_remove.append(next_e)
valid_e = nm.where(eflag)[0]
if len(e_remove) > 0:
# remove unused edges and vertices
eflag.fill(True)
eflag[nm.asarray(e_remove)] = False
remap = -nm.ones((n_v, ), dtype=nm.int64)
remap[conns[eflag, :]] = 1
vidx = nm.where(remap > 0)[0]
remap[vidx] = nm.arange(len(vidx))
conns_new = remap[conns[eflag, :]]
return coors[vidx, :], ngroups[vidx],\
[conns_new], [mat_ids[0][eflag]], ctype
else:
return mesh
def _get_facets(vertices, offsets, ii, n_fp):
facets = []
for ic in range(n_fp):
facets.append(vertices[offsets[ii] + ic][:, None])
facets = nm.concatenate(facets, axis=1)
return nm.ascontiguousarray(facets.astype(nm.int32))
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def get_surface_faces(domain):
cmesh = domain.cmesh
faces = cmesh.get_surface_facets()
vertices_f, offs_f = cmesh.get_incident(0, faces,
cmesh.dim - 1, ret_offsets=True)
n_fp = nm.diff(offs_f)
surf_faces = []
itri = nm.where(n_fp == 3)[0]
if itri.size:
surf_faces.append(_get_facets(vertices_f, offs_f, itri, 3))
itet = nm.where(n_fp == 4)[0]
if itet.size:
surf_faces.append(_get_facets(vertices_f, offs_f, itet, 4))
cells_c, offs_c = cmesh.get_incident(cmesh.dim, faces, cmesh.dim - 1,
ret_offsets=True)
ids = cmesh.get_local_ids(faces, cmesh.dim - 1, cells_c, offs_c,
cmesh.dim)
lst = nm.c_[cells_c, ids]
return lst, surf_faces
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def surface_graph(surf_faces, n_nod):
nnz, prow, icol = create_mesh_graph(n_nod, n_nod, len(surf_faces),
surf_faces, surf_faces)
data = nm.empty((nnz,), dtype=nm.int32)
data.fill(2)
return sps.csr_matrix((data, icol, prow), (n_nod, n_nod))
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def surface_components(gr_s, surf_faces):
"""
Determine surface components given surface mesh connectivity graph.
"""
n_nod = gr_s.shape[0]
n_comp, flag = graph_components(n_nod, gr_s.indptr, gr_s.indices)
comps = []
for ii, face in enumerate(surf_faces):
comp = flag[face[:,0]]
comps.append(comp)
return n_comp, comps