from scipy import spatial as _spatial import numpy as _np from . import util from . import grid_filters def from_random(size,N_seeds,grid=None,seed=None): """ Random seeding in space. Parameters ---------- size : numpy.ndarray of shape (3) Physical size of the seeding domain. N_seeds : int Number of seeds. grid : numpy.ndarray of shape (3), optional. If given, ensures that all seeds initiate one grain if using a standard Voronoi tessellation. seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional A seed to initialize the BitGenerator. Defaults to None. If None, then fresh, unpredictable entropy will be pulled from the OS. """ rng = _np.random.default_rng(seed) if grid is None: coords = rng.random((N_seeds,3)) * size else: grid_coords = grid_filters.cell_coord0(grid,size).reshape(-1,3,order='F') coords = grid_coords[rng.choice(_np.prod(grid),N_seeds, replace=False)] \ + _np.broadcast_to(size/grid,(N_seeds,3))*(rng.random((N_seeds,3))*.5-.25) # wobble without leaving grid return coords def from_Poisson_disc(size,N_seeds,N_candidates,distance,periodic=True,seed=None): """ Seeding in space according to a Poisson disc distribution. Parameters ---------- size : numpy.ndarray of shape (3) Physical size of the seeding domain. N_seeds : int Number of seeds. N_candidates : int Number of candidates to consider for finding best candidate. distance : float Minimum acceptable distance to other seeds. periodic : boolean, optional Calculate minimum distance for periodically repeated grid. seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional A seed to initialize the BitGenerator. Defaults to None. If None, then fresh, unpredictable entropy will be pulled from the OS. """ rng = _np.random.default_rng(seed) coords = _np.empty((N_seeds,3)) coords[0] = rng.random(3) * size i = 1 progress = util._ProgressBar(N_seeds+1,'',50) while i < N_seeds: candidates = rng.random((N_candidates,3))*_np.broadcast_to(size,(N_candidates,3)) tree = _spatial.cKDTree(coords[:i],boxsize=size) if periodic else \ _spatial.cKDTree(coords[:i]) distances, dev_null = tree.query(candidates) best = distances.argmax() if distances[best] > distance: # require minimum separation coords[i] = candidates[best] # maximum separation to existing point cloud i += 1 progress.update(i) return coords def from_geom(geom,selection=None,invert=False,average=False,periodic=True): """ Create seed from existing geometry description. Parameters ---------- geom : damask.Geom Geometry, from which the material IDs are used as seeds. selection : iterable of integers, optional Material IDs to consider. invert : boolean, false Do not consider the material IDs given in selection. Defaults to False. average : boolean, optional Seed corresponds to center of gravity of material ID cloud. periodic : boolean, optional Center of gravity with periodic boundaries. """ material = geom.material.reshape((-1,1),order='F') mask = _np.full(geom.grid.prod(),True,dtype=bool) if selection is None else \ _np.isin(material,selection,invert=invert).flatten() coords = grid_filters.cell_coord0(geom.grid,geom.size).reshape(-1,3,order='F') if not average: return (coords[mask],material[mask]) else: materials = _np.unique(material[mask]) coords_ = _np.zeros((materials.size,3),dtype=float) for i,mat in enumerate(materials): pc = (2*_np.pi*coords[material[:,0]==mat,:]-geom.origin)/geom.size coords_[i] = geom.origin + geom.size / 2 / _np.pi * (_np.pi + _np.arctan2(-_np.average(_np.sin(pc),axis=0), -_np.average(_np.cos(pc),axis=0))) \ if periodic else \ _np.average(coords[material[:,0]==mat,:],axis=0) return (coords_,materials)