Source code for damask.seeds

"""Functionality for generation of seed points for Voronoi or Laguerre tessellation."""

from scipy import spatial as _spatial
import numpy as _np

from . import util as _util
from . import grid_filters as _grid_filters


[docs]def from_random(size,N_seeds,cells=None,rng_seed=None): """ Place seeds randomly in space. Parameters ---------- size : numpy.ndarray of shape (3) Physical size of the seeding domain. N_seeds : int Number of seeds. cells : numpy.ndarray of shape (3), optional. If given, ensures that each seed results in a grain when a standard Voronoi tessellation is performed using the given grid resolution (i.e. size/cells). rng_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. Returns ------- coords : numpy.ndarray of shape (N_seeds,3) Seed coordinates in 3D space. """ rng = _np.random.default_rng(rng_seed) if cells is None: coords = rng.random((N_seeds,3)) * size else: grid_coords = _grid_filters.coordinates0_point(cells,size).reshape(-1,3,order='F') coords = grid_coords[rng.choice(_np.prod(cells),N_seeds, replace=False)] \ + _np.broadcast_to(size/cells,(N_seeds,3))*(rng.random((N_seeds,3))*.5-.25) # wobble without leaving cells return coords
[docs]def from_Poisson_disc(size,N_seeds,N_candidates,distance,periodic=True,rng_seed=None): """ Place seeds 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. rng_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. Returns ------- coords : numpy.ndarray of shape (N_seeds,3) Seed coordinates in 3D space. """ rng = _np.random.default_rng(rng_seed) coords = _np.empty((N_seeds,3)) coords[0] = rng.random(3) * size s = 1 i = 0 progress = _util._ProgressBar(N_seeds+1,'',50) while s < N_seeds: candidates = rng.random((N_candidates,3))*_np.broadcast_to(size,(N_candidates,3)) tree = _spatial.cKDTree(coords[:s],boxsize=size) if periodic else \ _spatial.cKDTree(coords[:s]) distances = tree.query(candidates)[0] best = distances.argmax() if distances[best] > distance: # require minimum separation coords[s] = candidates[best] # maximum separation to existing point cloud s += 1 progress.update(s) i = 0 else: i += 1 if i == 100: raise ValueError('Seeding not possible') return coords
[docs]def from_grid(grid,selection=None,invert=False,average=False,periodic=True): """ Create seeds from grid description. Parameters ---------- grid : damask.Grid Grid, 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. Returns ------- coords, materials : numpy.ndarray of shape (:,3), numpy.ndarray of shape (:) Seed coordinates in 3D space, material IDs. """ material = grid.material.reshape((-1,1),order='F') mask = _np.full(grid.cells.prod(),True,dtype=bool) if selection is None else \ _np.isin(material,selection,invert=invert).flatten() coords = _grid_filters.coordinates0_point(grid.cells,grid.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,:]-grid.origin)/grid.size coords_[i] = grid.origin + grid.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)