def marching_cubes(mtx, vsize=nm.array([1.0, 1.0, 1.0]), isoval=0.5):
dd = mtx.shape
vidxs = nm.where(mtx)
edims = nm.array(mtx.shape) + 2
emtx = nm.zeros(edims, dtype=nm.int8)
emtx[(vidxs[0] + 1, vidxs[1] + 1, vidxs[2] + 1)] = 1
nmtx = nm.zeros(edims, dtype=nm.int8)
set_nodemtx(nmtx, vidxs, 'q')
nidxs = nm.where(nmtx)
del(nmtx)
tri = []
vsize = vsize.squeeze()
for ii in nm.array(nidxs).T:
val = []
coors = []
for l in gen_grid_tab:
val.append(emtx[tuple(ii + l)])
coors.append(nm.array(ii + l - 0.5) * vsize)
val = nm.array(val)
if nm.all(val < 1) or nm.all(val > isoval):
continue
aux = iso_element(val, coors, isoval)
if aux is not None:
tri += aux
return nm.array(tri)
def gen_mesh_from_voxels(voxels, dims, etype='q', mtype='v'):
"""
Generate FE mesh from voxels (volumetric data).
Parameters:
voxels : array
Voxel matrix, 1=material.
dims : array
Size of one voxel.
etype : integer, optional
'q' - quadrilateral or hexahedral elements
't' - triangular or tetrahedral elements
mtype : integer, optional
'v' - volumetric mesh
's' - surface mesh
Returns:
mesh : Mesh instance
Finite element mesh.
"""
dims = dims.squeeze()
dim = len(dims)
nddims = nm.array(voxels.shape) + 2
nodemtx = nm.zeros(nddims, dtype=nm.int8)
vxidxs = nm.where(voxels)
set_nodemtx(nodemtx, vxidxs, etype)
ndidx = nm.where(nodemtx)
del(nodemtx)
coors = nm.array(ndidx).transpose() * dims
nnod = coors.shape[0]
nodeid = -nm.ones(nddims, dtype=nm.int32)
nodeid[ndidx] = nm.arange(nnod)
if mtype == 's':
felems = []
nn = nm.zeros(nddims, dtype=nm.int8)
# generate elements
if dim == 2:
ix, iy = vxidxs
if mtype == 'v':
elems = nm.array([nodeid[ix,iy],
nodeid[ix + 1,iy],
nodeid[ix + 1,iy + 1],
nodeid[ix,iy + 1]]).transpose()
edim = 2
else:
fc = nm.zeros(nddims + (2,), dtype=nm.int32)
# x
fc[ix,iy,:] = nm.array([nodeid[ix,iy + 1],
nodeid[ix,iy]]).transpose()
fc[ix + 1,iy,:] = nm.array([nodeid[ix + 1,iy],
nodeid[ix + 1,iy + 1]]).transpose()
nn[ix,iy] = 1
nn[ix + 1,iy] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
# y
fc.fill(0)
nn.fill(0)
fc[ix,iy,:] = nm.array([nodeid[ix,iy],
nodeid[ix + 1,iy]]).transpose()
fc[ix,iy + 1,:] = nm.array([nodeid[ix + 1,iy + 1],
nodeid[ix,iy + 1]]).transpose()
nn[ix,iy] = 1
nn[ix,iy + 1] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
elems = nm.concatenate(felems)
edim = 1
elif dim == 3:
ix, iy, iz = vxidxs
if mtype == 'v':
elems = nm.array([nodeid[ix,iy,iz],
nodeid[ix + 1,iy,iz],
nodeid[ix + 1,iy + 1,iz],
nodeid[ix,iy + 1,iz],
nodeid[ix,iy,iz + 1],
nodeid[ix + 1,iy,iz + 1],
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix,iy + 1,iz + 1]]).transpose()
edim = 3
else:
fc = nm.zeros(tuple(nddims) + (4,), dtype=nm.int32)
# x
fc[ix,iy,iz,:] = nm.array([nodeid[ix,iy,iz],
nodeid[ix,iy,iz + 1],
nodeid[ix,iy + 1,iz + 1],
nodeid[ix,iy + 1,iz]]).transpose()
fc[ix + 1,iy,iz,:] = nm.array([nodeid[ix + 1,iy,iz],
nodeid[ix + 1,iy + 1,iz],
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix + 1,iy,iz + 1]]).transpose()
nn[ix,iy,iz] = 1
nn[ix + 1,iy,iz] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
# y
fc.fill(0)
nn.fill(0)
fc[ix,iy,iz,:] = nm.array([nodeid[ix,iy,iz],
nodeid[ix + 1,iy,iz],
nodeid[ix + 1,iy,iz + 1],
nodeid[ix,iy,iz + 1]]).transpose()
fc[ix,iy + 1,iz,:] = nm.array([nodeid[ix,iy + 1,iz],
nodeid[ix,iy + 1,iz + 1],
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix + 1,iy + 1,iz]]).transpose()
nn[ix,iy,iz] = 1
nn[ix,iy + 1,iz] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
# z
fc.fill(0)
nn.fill(0)
fc[ix,iy,iz,:] = nm.array([nodeid[ix,iy,iz],
nodeid[ix,iy + 1,iz],
nodeid[ix + 1,iy + 1,iz],
nodeid[ix + 1,iy,iz]]).transpose()
fc[ix,iy,iz + 1,:] = nm.array([nodeid[ix,iy,iz + 1],
nodeid[ix + 1,iy,iz + 1],\
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix,iy + 1,iz + 1]]).transpose()
nn[ix,iy,iz] = 1
nn[ix,iy,iz + 1] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
elems = nm.concatenate(felems)
edim = 2
# reduce inner nodes
if mtype == 's':
aux = nm.zeros((nnod,), dtype=nm.int32)
for ii in elems.T:
aux[ii] = 1
idx = nm.where(aux)
aux.fill(0)
nnod = idx[0].shape[0]
aux[idx] = range(nnod)
coors = coors[idx]
for ii in range(elems.shape[1]):
elems[:,ii] = aux[elems[:,ii]]
if etype == 't':
elems = elems_q2t(elems)
nel = elems.shape[0]
nelnd = elems.shape[1]
etype = '%d_%d' % (edim, nelnd)
return coors, nm.ascontiguousarray(elems), etype
def gen_mesh_from_voxels(voxels, dims, etype='q', mtype='v'):
"""
Generate FE mesh from voxels (volumetric data).
Parameters
----------
voxels : array
Voxel matrix, 1=material.
dims : array
Size of one voxel.
etype : integer, optional
'q' - quadrilateral or hexahedral elements
't' - triangular or tetrahedral elements
Returns
-------
mesh : Mesh instance
Finite element mesh.
"""
dims = dims.squeeze()
dim = len(dims)
nddims = nm.array(voxels.shape) + 2
nodemtx = nm.zeros(nddims, dtype=nm.int8)
vxidxs = nm.where(voxels)
set_nodemtx(nodemtx, vxidxs, etype)
ndidx = nm.where(nodemtx)
del (nodemtx)
coors = nm.array(ndidx).transpose() * dims
nnod = coors.shape[0]
nodeid = -nm.ones(nddims, dtype=nm.int32)
nodeid[ndidx] = nm.arange(nnod)
if mtype == 's':
felems = []
nn = nm.zeros(nddims, dtype=nm.int8)
# generate elements
if dim == 2:
ix, iy = vxidxs
if mtype == 'v':
elems = nm.array([
nodeid[ix, iy], nodeid[ix + 1, iy], nodeid[ix + 1, iy + 1],
nodeid[ix, iy + 1]
]).transpose()
edim = 2
else:
fc = nm.zeros(nddims + (2, ), dtype=nm.int32)
# x
fc[ix, iy, :] = nm.array([nodeid[ix, iy + 1],
nodeid[ix, iy]]).transpose()
fc[ix + 1,
iy, :] = nm.array([nodeid[ix + 1, iy],
nodeid[ix + 1, iy + 1]]).transpose()
nn[ix, iy] = 1
nn[ix + 1, iy] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
# y
fc.fill(0)
nn.fill(0)
fc[ix, iy, :] = nm.array([nodeid[ix, iy], nodeid[ix + 1,
iy]]).transpose()
fc[ix, iy + 1, :] = nm.array(
[nodeid[ix + 1, iy + 1], nodeid[ix, iy + 1]]).transpose()
nn[ix, iy] = 1
nn[ix, iy + 1] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
elems = nm.concatenate(felems)
edim = 1
elif dim == 3:
ix, iy, iz = vxidxs
if mtype == 'v':
elems = nm.array([
nodeid[ix, iy, iz], nodeid[ix + 1, iy, iz], nodeid[ix + 1,
iy + 1, iz],
nodeid[ix, iy + 1,
iz], nodeid[ix, iy, iz + 1], nodeid[ix + 1, iy, iz + 1],
nodeid[ix + 1, iy + 1, iz + 1], nodeid[ix, iy + 1, iz + 1]
]).transpose()
edim = 3
else:
fc = nm.zeros(tuple(nddims) + (4, ), dtype=nm.int32)
# x
fc[ix,iy,iz,:] = nm.array([nodeid[ix,iy,iz], nodeid[ix,iy,iz + 1],\
nodeid[ix,iy + 1,iz + 1], nodeid[ix,iy + 1,iz]]).transpose()
fc[ix + 1,iy,iz,:] = nm.array([nodeid[ix + 1,iy,iz], nodeid[ix + 1,iy + 1,iz],\
nodeid[ix + 1,iy + 1,iz + 1], nodeid[ix + 1,iy,iz + 1]]).transpose()
nn[ix, iy, iz] = 1
nn[ix + 1, iy, iz] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
# y
fc.fill(0)
nn.fill(0)
fc[ix,iy,iz,:] = nm.array([nodeid[ix,iy,iz], nodeid[ix + 1,iy,iz],\
nodeid[ix + 1,iy,iz + 1], nodeid[ix,iy,iz + 1]]).transpose()
fc[ix,iy + 1,iz,:] = nm.array([nodeid[ix,iy + 1,iz], nodeid[ix,iy + 1,iz + 1],\
nodeid[ix + 1,iy + 1,iz + 1], nodeid[ix + 1,iy + 1,iz]]).transpose()
nn[ix, iy, iz] = 1
nn[ix, iy + 1, iz] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
# z
fc.fill(0)
nn.fill(0)
fc[ix,iy,iz,:] = nm.array([nodeid[ix,iy,iz], nodeid[ix,iy + 1,iz],\
nodeid[ix + 1,iy + 1,iz], nodeid[ix + 1,iy,iz]]).transpose()
fc[ix,iy,iz + 1,:] = nm.array([nodeid[ix,iy,iz + 1], nodeid[ix + 1,iy,iz + 1],\
nodeid[ix + 1,iy + 1,iz + 1], nodeid[ix,iy + 1,iz + 1]]).transpose()
nn[ix, iy, iz] = 1
nn[ix, iy, iz + 1] += 1
idx = nm.where(nn == 1)
felems.append(fc[idx])
elems = nm.concatenate(felems)
edim = 2
# reduce inner nodes
if mtype == 's':
aux = nm.zeros((nnod, ), dtype=nm.int32)
for ii in elems.T:
aux[ii] = 1
idx = nm.where(aux)
aux.fill(0)
nnod = idx[0].shape[0]
aux[idx] = range(nnod)
coors = coors[idx]
for ii in range(elems.shape[1]):
elems[:, ii] = aux[elems[:, ii]]
if etype == 't':
elems = elems_q2t(elems)
nel = elems.shape[0]
nelnd = elems.shape[1]
mesh = Mesh.from_data('voxel_data', coors, nm.ones(
(nnod, ), dtype=nm.int32), {0: nm.ascontiguousarray(elems)},
{0: nm.ones((nel, ), dtype=nm.int32)},
{0: '%d_%d' % (edim, nelnd)})
return mesh