"""Functionality for generation of seed points for Voronoi or Laguerre tessellation."""
from typing import Optional as _Optional, Tuple as _Tuple
from scipy import spatial as _spatial
import numpy as _np
from ._typehints import FloatSequence as _FloatSequence, IntSequence as _IntSequence, \
NumpyRngSeed as _NumpyRngSeed
from . import util as _util
from . import grid_filters as _grid_filters
[docs]def from_random(size: _FloatSequence,
N_seeds: int,
cells: _Optional[_IntSequence] = None,
rng_seed: _Optional[_NumpyRngSeed] = None) -> _np.ndarray:
"""
Place seeds randomly in space.
Parameters
----------
size : sequence of float, len (3)
Edge lengths of the seeding domain.
N_seeds : int
Number of seeds.
cells : sequence of int, len (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, shape (N_seeds,3)
Seed coordinates in 3D space.
"""
size_ = _np.array(size,float)
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_/_np.array(cells,_np.int64),(N_seeds,3))*(rng.random((N_seeds,3))*.5-.25) # wobble w/o leaving grid
return coords
[docs]def from_Poisson_disc(size: _FloatSequence,
N_seeds: int,
N_candidates: int,
distance: float,
periodic: bool = True,
rng_seed: _Optional[_NumpyRngSeed] = None) -> _np.ndarray:
"""
Place seeds following a Poisson disc distribution.
Parameters
----------
size : sequence of float, len (3)
Edge lengths 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 : bool, optional
Calculate minimum distance for periodically repeated grid.
Defaults to True.
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, 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) * _np.array(size,float)
s = 1
i = 0
progress = _util.ProgressBar(N_seeds+1,'',50)
while s < N_seeds:
i += 1
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]
if distances.max() > distance: # require minimum separation
i = 0
coords[s] = candidates[distances.argmax()] # maximum separation to existing point cloud
s += 1
progress.update(s)
if i >= 100:
raise ValueError('seeding not possible')
return coords
[docs]def from_grid(grid,
selection: _Optional[_IntSequence] = None,
invert_selection: bool = False,
average: bool = False,
periodic: bool = True) -> _Tuple[_np.ndarray, _np.ndarray]:
"""
Create seeds from grid description.
Parameters
----------
grid : damask.GeomGrid
Grid from which the material IDs are used as seeds.
selection : (sequence of) int, optional
Material IDs to consider.
invert_selection : bool, optional
Consider all material IDs except those in selection. Defaults to False.
average : bool, optional
Seed corresponds to center of gravity of material ID cloud.
Defaults to False.
periodic : bool, optional
Center of gravity accounts for periodic boundaries.
Defaults to True.
Returns
-------
coords, materials : numpy.ndarray, shape (:,3); numpy.ndarray, shape (:)
Seed coordinates in 3D space, material IDs.
Notes
-----
The origin is not considered in order to obtain coordinates
in a coordinate system located at the origin. This is expected
by damask.GeomGrid.from_Voronoi_tessellation.
Examples
--------
Recreate seeds from Voronoi tessellation.
>>> import numpy as np
>>> import scipy.spatial
>>> import damask
>>> seeds = damask.seeds.from_random(np.ones(3),29,[128]*3)
>>> (g := damask.GeomGrid.from_Voronoi_tessellation([128]*3,np.ones(3),seeds))
cells: 128 × 128 × 128
size: 1.0 × 1.0 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 29
>>> COG,matID = damask.seeds.from_grid(g,average=True)
>>> distance,ID = scipy.spatial.KDTree(COG,boxsize=g.size).query(seeds)
>>> np.max(distance) / np.linalg.norm(g.size/g.cells)
7.8057356746350415
>>> (ID == matID).all()
True
"""
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_selection).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.size
coords_[i] = 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)