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