154 lines
5.7 KiB
Python
154 lines
5.7 KiB
Python
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"""Functionality for generation of seed points for Voronoi or Laguerre tessellation."""
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from typing import Tuple as _Tuple
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from scipy import spatial as _spatial
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import numpy as _np
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from ._typehints import FloatSequence as _FloatSequence, IntSequence as _IntSequence, \
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NumpyRngSeed as _NumpyRngSeed, IntCollection as _IntCollection
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from . import util as _util
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from . import grid_filters as _grid_filters
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def from_random(size: _FloatSequence,
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N_seeds: int,
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cells: _IntSequence = None,
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rng_seed: _NumpyRngSeed = None) -> _np.ndarray:
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"""
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Place seeds randomly in space.
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Parameters
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----------
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size : sequence of float, len (3)
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Physical size of the seeding domain.
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N_seeds : int
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Number of seeds.
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cells : sequence of int, len (3), optional.
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If given, ensures that each seed results in a grain when a standard Voronoi
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tessellation is performed using the given grid resolution (i.e. size/cells).
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rng_seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional
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A seed to initialize the BitGenerator. Defaults to None.
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If None, then fresh, unpredictable entropy will be pulled from the OS.
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Returns
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-------
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coords : numpy.ndarray, shape (N_seeds,3)
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Seed coordinates in 3D space.
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"""
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size_ = _np.array(size,float)
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rng = _np.random.default_rng(rng_seed)
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if cells is None:
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coords = rng.random((N_seeds,3)) * size_
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else:
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grid_coords = _grid_filters.coordinates0_point(cells,size).reshape(-1,3,order='F')
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coords = grid_coords[rng.choice(_np.prod(cells),N_seeds, replace=False)] \
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+ _np.broadcast_to(size_/_np.array(cells,_np.int64),(N_seeds,3))*(rng.random((N_seeds,3))*.5-.25) # wobble w/o leaving grid
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return coords
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def from_Poisson_disc(size: _FloatSequence,
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N_seeds: int,
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N_candidates: int,
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distance: float,
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periodic: bool = True,
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rng_seed: _NumpyRngSeed = None) -> _np.ndarray:
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"""
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Place seeds according to a Poisson disc distribution.
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Parameters
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----------
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size : sequence of float, len (3)
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Physical size of the seeding domain.
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N_seeds : int
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Number of seeds.
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N_candidates : int
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Number of candidates to consider for finding best candidate.
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distance : float
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Minimum acceptable distance to other seeds.
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periodic : bool, optional
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Calculate minimum distance for periodically repeated grid.
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rng_seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional
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A seed to initialize the BitGenerator. Defaults to None.
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If None, then fresh, unpredictable entropy will be pulled from the OS.
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Returns
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-------
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coords : numpy.ndarray, shape (N_seeds,3)
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Seed coordinates in 3D space.
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"""
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rng = _np.random.default_rng(rng_seed)
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coords = _np.empty((N_seeds,3))
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coords[0] = rng.random(3) * _np.array(size,float)
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s = 1
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i = 0
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progress = _util.ProgressBar(N_seeds+1,'',50)
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while s < N_seeds:
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i += 1
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candidates = rng.random((N_candidates,3))*_np.broadcast_to(size,(N_candidates,3))
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tree = _spatial.cKDTree(coords[:s],boxsize=size) if periodic else \
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_spatial.cKDTree(coords[:s])
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distances = tree.query(candidates)[0]
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if distances.max() > distance: # require minimum separation
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i = 0
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coords[s] = candidates[distances.argmax()] # maximum separation to existing point cloud
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s += 1
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progress.update(s)
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if i >= 100:
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raise ValueError('seeding not possible')
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return coords
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def from_grid(grid,
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selection: _IntCollection = None,
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invert_selection: bool = False,
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average: bool = False,
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periodic: bool = True) -> _Tuple[_np.ndarray, _np.ndarray]:
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"""
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Create seeds from grid description.
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Parameters
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----------
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grid : damask.Grid
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Grid from which the material IDs are used as seeds.
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selection : int or collection of int, optional
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Material IDs to consider.
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invert_selection : bool, optional
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Consider all material IDs except those in selection. Defaults to False.
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average : bool, optional
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Seed corresponds to center of gravity of material ID cloud.
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periodic : bool, optional
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Center of gravity accounts for periodic boundaries.
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Returns
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-------
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coords, materials : numpy.ndarray, shape (:,3); numpy.ndarray, shape (:)
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Seed coordinates in 3D space, material IDs.
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"""
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material = grid.material.reshape((-1,1),order='F')
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mask = _np.full(grid.cells.prod(),True,dtype=bool) if selection is None else \
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_np.isin(material,_util.aslist(selection),invert=invert_selection).flatten()
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coords = _grid_filters.coordinates0_point(grid.cells,grid.size).reshape(-1,3,order='F')
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if not average:
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return (coords[mask],material[mask])
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else:
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materials = _np.unique(material[mask])
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coords_ = _np.zeros((materials.size,3),dtype=float)
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for i,mat in enumerate(materials):
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pc = (2*_np.pi*coords[material[:,0]==mat,:]-grid.origin)/grid.size
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coords_[i] = grid.origin + grid.size / 2 / _np.pi * (_np.pi +
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_np.arctan2(-_np.average(_np.sin(pc),axis=0),
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-_np.average(_np.cos(pc),axis=0))) \
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if periodic else \
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_np.average(coords[material[:,0]==mat,:],axis=0)
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return (coords_,materials)
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