1329 lines
52 KiB
Python
1329 lines
52 KiB
Python
import os
|
||
import copy
|
||
import warnings
|
||
import multiprocessing as mp
|
||
from functools import partial
|
||
import typing
|
||
from typing import Union, Optional, TextIO, List, Sequence, Dict
|
||
from pathlib import Path
|
||
|
||
import numpy as np
|
||
import pandas as pd
|
||
import h5py
|
||
from scipy import ndimage, spatial
|
||
|
||
from . import VTK
|
||
from . import util
|
||
from . import grid_filters
|
||
from . import Rotation
|
||
from . import Table
|
||
from . import Colormap
|
||
from ._typehints import FloatSequence, IntSequence, IntCollection, NumpyRngSeed
|
||
|
||
class Grid:
|
||
"""
|
||
Geometry definition for grid solvers.
|
||
|
||
Create and manipulate geometry definitions for storage as VTK
|
||
image data files ('.vti' extension). A grid contains the
|
||
material ID (referring to the entry in 'material.yaml') and
|
||
the physical size.
|
||
"""
|
||
|
||
def __init__(self,
|
||
material: np.ndarray,
|
||
size: FloatSequence,
|
||
origin: FloatSequence = np.zeros(3),
|
||
initial_conditions: Dict[str,np.ndarray] = None,
|
||
comments: Union[str, Sequence[str]] = None):
|
||
"""
|
||
New geometry definition for grid solvers.
|
||
|
||
Parameters
|
||
----------
|
||
material : numpy.ndarray, shape (:,:,:)
|
||
Material indices. The shape of the material array defines
|
||
the number of cells.
|
||
size : sequence of float, len (3)
|
||
Physical size of grid in meter.
|
||
origin : sequence of float, len (3), optional
|
||
Coordinates of grid origin in meter. Defaults to [0.0,0.0,0.0].
|
||
initial_conditions : dictionary, optional
|
||
Labels and values of the inital conditions at each material point.
|
||
comments : str or iterable of str, optional
|
||
Additional, human-readable information, e.g. history of operations.
|
||
|
||
"""
|
||
self.material = material
|
||
self.size = size # type: ignore
|
||
self.origin = origin # type: ignore
|
||
self.initial_conditions = {} if initial_conditions is None else initial_conditions
|
||
comments_ = [comments] if isinstance(comments,str) else comments
|
||
self.comments = [] if comments_ is None else [str(c) for c in comments_]
|
||
|
||
def __repr__(self) -> str:
|
||
"""
|
||
Return repr(self).
|
||
|
||
Give short human-readable summary.
|
||
|
||
"""
|
||
mat_min = np.nanmin(self.material)
|
||
mat_max = np.nanmax(self.material)
|
||
mat_N = self.N_materials
|
||
return util.srepr([
|
||
f'cells: {util.srepr(self.cells, " × ")}',
|
||
f'size: {util.srepr(self.size, " × ")} m³',
|
||
f'origin: {util.srepr(self.origin," ")} m',
|
||
f'# materials: {mat_N}' + ('' if mat_min == 0 and mat_max+1 == mat_N else
|
||
f' (min: {mat_min}, max: {mat_max})')
|
||
]+(['initial_conditions:']+[f' - {f}' for f in self.initial_conditions] if self.initial_conditions else []))
|
||
|
||
|
||
def __copy__(self) -> 'Grid':
|
||
"""
|
||
Return deepcopy(self).
|
||
|
||
Create deep copy.
|
||
|
||
"""
|
||
return copy.deepcopy(self)
|
||
|
||
copy = __copy__
|
||
|
||
|
||
def __eq__(self,
|
||
other: object) -> bool:
|
||
"""
|
||
Return self==other.
|
||
|
||
Test equality of other.
|
||
|
||
Parameters
|
||
----------
|
||
other : damask.Grid
|
||
Grid to compare self against.
|
||
|
||
"""
|
||
if not isinstance(other, Grid):
|
||
return NotImplemented
|
||
return bool( np.allclose(other.size,self.size)
|
||
and np.allclose(other.origin,self.origin)
|
||
and np.all(other.cells == self.cells)
|
||
and np.all(other.material == self.material))
|
||
|
||
|
||
@property
|
||
def material(self) -> np.ndarray:
|
||
"""Material indices."""
|
||
return self._material
|
||
|
||
@material.setter
|
||
def material(self,
|
||
material: np.ndarray):
|
||
if len(material.shape) != 3:
|
||
raise ValueError(f'invalid material shape {material.shape}')
|
||
if material.dtype not in np.sctypes['float'] and material.dtype not in np.sctypes['int']:
|
||
raise TypeError(f'invalid material data type "{material.dtype}"')
|
||
|
||
self._material = np.copy(material)
|
||
|
||
if self.material.dtype in np.sctypes['float'] and \
|
||
np.all(self.material == self.material.astype(np.int64).astype(float)):
|
||
self._material = self.material.astype(np.int64)
|
||
|
||
|
||
@property
|
||
def size(self) -> np.ndarray:
|
||
"""Physical size of grid in meter."""
|
||
return self._size
|
||
|
||
@size.setter
|
||
def size(self,
|
||
size: FloatSequence):
|
||
if len(size) != 3 or any(np.array(size) < 0):
|
||
raise ValueError(f'invalid size {size}')
|
||
|
||
self._size = np.array(size)
|
||
|
||
@property
|
||
def origin(self) -> np.ndarray:
|
||
"""Coordinates of grid origin in meter."""
|
||
return self._origin
|
||
|
||
@origin.setter
|
||
def origin(self,
|
||
origin: FloatSequence):
|
||
if len(origin) != 3:
|
||
raise ValueError(f'invalid origin {origin}')
|
||
|
||
self._origin = np.array(origin)
|
||
|
||
@property
|
||
def initial_conditions(self) -> Dict[str,np.ndarray]:
|
||
"""Fields of initial conditions."""
|
||
self._ic = dict(zip(self._ic.keys(), # type: ignore
|
||
[v if isinstance(v,np.ndarray) else
|
||
np.broadcast_to(v,self.cells) for v in self._ic.values()])) # type: ignore
|
||
return self._ic
|
||
|
||
@initial_conditions.setter
|
||
def initial_conditions(self,
|
||
ic: Dict[str,np.ndarray]):
|
||
if not isinstance(ic,dict):
|
||
raise TypeError('initial conditions is not a dictionary')
|
||
|
||
self._ic = ic
|
||
|
||
@property
|
||
def comments(self) -> List[str]:
|
||
"""Comments, e.g. history of operations."""
|
||
return self._comments
|
||
|
||
@comments.setter
|
||
def comments(self,
|
||
comments: Union[str, Sequence[str]]):
|
||
self._comments = [str(c) for c in comments] if isinstance(comments,list) else [str(comments)]
|
||
|
||
|
||
@property
|
||
def cells(self) -> np.ndarray:
|
||
"""Number of cells in x,y,z direction."""
|
||
return np.asarray(self.material.shape)
|
||
|
||
|
||
@property
|
||
def N_materials(self) -> int:
|
||
"""Number of (unique) material indices within grid."""
|
||
return np.unique(self.material).size
|
||
|
||
|
||
@staticmethod
|
||
def load(fname: Union[str, Path]) -> 'Grid':
|
||
"""
|
||
Load from VTK image data file.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or pathlib.Path
|
||
Grid file to read.
|
||
Valid extension is .vti, which will be appended if not given.
|
||
|
||
Returns
|
||
-------
|
||
loaded : damask.Grid
|
||
Grid-based geometry from file.
|
||
|
||
"""
|
||
v = VTK.load(fname if str(fname).endswith('.vti') else str(fname)+'.vti')
|
||
cells = np.array(v.vtk_data.GetDimensions())-1
|
||
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
|
||
comments = v.comments
|
||
ic = {label:v.get(label).reshape(cells,order='F') for label in set(v.labels['Cell Data']) - {'material'}}
|
||
|
||
return Grid(material = v.get('material').reshape(cells,order='F'),
|
||
size = bbox[1] - bbox[0],
|
||
origin = bbox[0],
|
||
initial_conditions = ic,
|
||
comments = comments,
|
||
)
|
||
|
||
|
||
@typing.no_type_check
|
||
@staticmethod
|
||
def load_ASCII(fname)-> 'Grid':
|
||
"""
|
||
Load from geom file.
|
||
|
||
Storing geometry files in ASCII format is deprecated.
|
||
This function will be removed in a future version of DAMASK.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str, pathlib.Path, or file handle
|
||
Geometry file to read.
|
||
|
||
Returns
|
||
-------
|
||
loaded : damask.Grid
|
||
Grid-based geometry from file.
|
||
|
||
"""
|
||
warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
|
||
if isinstance(fname, (str, Path)):
|
||
f = open(fname)
|
||
elif isinstance(fname, TextIO):
|
||
f = fname
|
||
else:
|
||
raise TypeError
|
||
|
||
f.seek(0)
|
||
try:
|
||
header_length_,keyword = f.readline().split()[:2]
|
||
header_length = int(header_length_)
|
||
except ValueError:
|
||
header_length,keyword = (-1, 'invalid')
|
||
if not keyword.startswith('head') or header_length < 3:
|
||
raise TypeError('invalid or missing header length information')
|
||
|
||
comments = []
|
||
content = f.readlines()
|
||
for i,line in enumerate(content[:header_length]):
|
||
items = line.split('#')[0].lower().strip().split()
|
||
if (key := items[0] if items else '') == 'grid':
|
||
cells = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']])
|
||
elif key == 'size':
|
||
size = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']])
|
||
elif key == 'origin':
|
||
origin = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']])
|
||
else:
|
||
comments.append(line.strip())
|
||
|
||
material = np.empty(cells.prod()) # initialize as flat array
|
||
i = 0
|
||
for line in content[header_length:]:
|
||
if len(items := line.split('#')[0].split()) == 3:
|
||
if items[1].lower() == 'of':
|
||
material_entry = np.ones(int(items[0]))*float(items[2])
|
||
elif items[1].lower() == 'to':
|
||
material_entry = np.linspace(int(items[0]),int(items[2]),
|
||
abs(int(items[2])-int(items[0]))+1,dtype=float)
|
||
else: material_entry = list(map(float, items))
|
||
else: material_entry = list(map(float, items))
|
||
material[i:i+len(material_entry)] = material_entry
|
||
i += len(items)
|
||
|
||
if i != cells.prod():
|
||
raise TypeError(f'mismatch between {cells.prod()} expected entries and {i} found')
|
||
|
||
if not np.any(np.mod(material,1) != 0.0): # no float present
|
||
material = material.astype(np.int64) - (1 if material.min() > 0 else 0)
|
||
|
||
return Grid(material = material.reshape(cells,order='F'),
|
||
size = size,
|
||
origin = origin,
|
||
comments = comments)
|
||
|
||
|
||
@staticmethod
|
||
def load_Neper(fname: Union[str, Path]) -> 'Grid':
|
||
"""
|
||
Load from Neper VTK file.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or pathlib.Path
|
||
Geometry file to read.
|
||
|
||
Returns
|
||
-------
|
||
loaded : damask.Grid
|
||
Grid-based geometry from file.
|
||
|
||
Examples
|
||
--------
|
||
Read a periodic polycrystal generated with Neper.
|
||
|
||
>>> import damask
|
||
>>> N_grains = 20
|
||
>>> cells = (32,32,32)
|
||
>>> damask.util.run(f'neper -T -n {N_grains} -tesrsize {cells[0]}:{cells[1]}:{cells[2]} -periodicity all -format vtk')
|
||
>>> damask.Grid.load_Neper(f'n{N_grains}-id1.vtk')
|
||
cells: 32 × 32 × 32
|
||
size: 1.0 × 1.0 × 1.0 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 20
|
||
|
||
"""
|
||
v = VTK.load(fname,'ImageData')
|
||
cells = np.array(v.vtk_data.GetDimensions())-1
|
||
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
|
||
|
||
return Grid(material = v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe') - 1,
|
||
size = bbox[1] - bbox[0],
|
||
origin = bbox[0],
|
||
comments = util.execution_stamp('Grid','load_Neper'),
|
||
)
|
||
|
||
|
||
@staticmethod
|
||
def load_DREAM3D(fname: Union[str, Path],
|
||
feature_IDs: str = None, cell_data: str = None,
|
||
phases: str = 'Phases', Euler_angles: str = 'EulerAngles',
|
||
base_group: str = None) -> 'Grid':
|
||
"""
|
||
Load DREAM.3D (HDF5) file.
|
||
|
||
Data in DREAM.3D files can be stored per cell ('CellData') and/or
|
||
per grain ('Grain Data'). Per default, cell-wise data is assumed.
|
||
|
||
damask.ConfigMaterial.load_DREAM3D gives the corresponding material definition.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or or pathlib.Path
|
||
Filename of the DREAM.3D (HDF5) file.
|
||
feature_IDs : str, optional
|
||
Name of the dataset containing the mapping between cells and
|
||
grain-wise data. Defaults to 'None', in which case cell-wise
|
||
data is used.
|
||
cell_data : str, optional
|
||
Name of the group (folder) containing cell-wise data. Defaults to
|
||
None in wich case it is automatically detected.
|
||
phases : str, optional
|
||
Name of the dataset containing the phase ID. It is not used for
|
||
grain-wise data, i.e. when feature_IDs is not None.
|
||
Defaults to 'Phases'.
|
||
Euler_angles : str, optional
|
||
Name of the dataset containing the crystallographic orientation as
|
||
Euler angles in radians It is not used for grain-wise data, i.e.
|
||
when feature_IDs is not None. Defaults to 'EulerAngles'.
|
||
base_group : str, optional
|
||
Path to the group (folder) that contains geometry (_SIMPL_GEOMETRY),
|
||
and grain- or cell-wise data. Defaults to None, in which case
|
||
it is set as the path that contains _SIMPL_GEOMETRY/SPACING.
|
||
|
||
Returns
|
||
-------
|
||
loaded : damask.Grid
|
||
Grid-based geometry from file.
|
||
|
||
"""
|
||
b = util.DREAM3D_base_group(fname) if base_group is None else base_group
|
||
c = util.DREAM3D_cell_data_group(fname) if cell_data is None else cell_data
|
||
f = h5py.File(fname, 'r')
|
||
|
||
cells = f['/'.join([b,'_SIMPL_GEOMETRY','DIMENSIONS'])][()]
|
||
size = f['/'.join([b,'_SIMPL_GEOMETRY','SPACING'])] * cells
|
||
origin = f['/'.join([b,'_SIMPL_GEOMETRY','ORIGIN'])][()]
|
||
|
||
if feature_IDs is None:
|
||
phase = f['/'.join([b,c,phases])][()].reshape(-1,1)
|
||
O = Rotation.from_Euler_angles(f['/'.join([b,c,Euler_angles])]).as_quaternion().reshape(-1,4) # noqa
|
||
unique,unique_inverse = np.unique(np.hstack([O,phase]),return_inverse=True,axis=0)
|
||
ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \
|
||
np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse]
|
||
else:
|
||
ma = f['/'.join([b,c,feature_IDs])][()].flatten()
|
||
|
||
return Grid(material = ma.reshape(cells,order='F'),
|
||
size = size,
|
||
origin = origin,
|
||
comments = util.execution_stamp('Grid','load_DREAM3D'),
|
||
)
|
||
|
||
|
||
@staticmethod
|
||
def from_table(table: Table,
|
||
coordinates: str,
|
||
labels: Union[str, Sequence[str]]) -> 'Grid':
|
||
"""
|
||
Create grid from ASCII table.
|
||
|
||
Parameters
|
||
----------
|
||
table : damask.Table
|
||
Table that contains material information.
|
||
coordinates : str
|
||
Label of the vector column containing the spatial coordinates.
|
||
Need to be ordered (1./x fast, 3./z slow).
|
||
labels : (list of) str
|
||
Label(s) of the columns containing the material definition.
|
||
Each unique combination of values results in one material ID.
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from values in table.
|
||
|
||
"""
|
||
cells,size,origin = grid_filters.cellsSizeOrigin_coordinates0_point(table.get(coordinates))
|
||
|
||
labels_ = [labels] if isinstance(labels,str) else labels
|
||
unique,unique_inverse = np.unique(np.hstack([table.get(l) for l in labels_]),return_inverse=True,axis=0)
|
||
|
||
ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \
|
||
np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse]
|
||
|
||
return Grid(material = ma.reshape(cells,order='F'),
|
||
size = size,
|
||
origin = origin,
|
||
comments = util.execution_stamp('Grid','from_table'),
|
||
)
|
||
|
||
|
||
@staticmethod
|
||
def _find_closest_seed(seeds: np.ndarray,
|
||
weights: np.ndarray,
|
||
point: np.ndarray) -> np.integer:
|
||
return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
|
||
|
||
@staticmethod
|
||
def from_Laguerre_tessellation(cells: IntSequence,
|
||
size: FloatSequence,
|
||
seeds: np.ndarray,
|
||
weights: FloatSequence,
|
||
material: IntSequence = None,
|
||
periodic: bool = True):
|
||
"""
|
||
Create grid from Laguerre tessellation.
|
||
|
||
Parameters
|
||
----------
|
||
cells : sequence of int, len (3)
|
||
Number of cells in x,y,z direction.
|
||
size : sequence of float, len (3)
|
||
Physical size of the grid in meter.
|
||
seeds : numpy.ndarray, shape (:,3)
|
||
Position of the seed points in meter. All points need to lay within the box.
|
||
weights : sequence of float, len (seeds.shape[0])
|
||
Weights of the seeds. Setting all weights to 1.0 gives a standard Voronoi tessellation.
|
||
material : sequence of int, len (seeds.shape[0]), optional
|
||
Material ID of the seeds.
|
||
Defaults to None, in which case materials are consecutively numbered.
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from tessellation.
|
||
|
||
"""
|
||
weights_p: FloatSequence
|
||
if periodic:
|
||
weights_p = np.tile(weights,27) # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
|
||
seeds_p = np.vstack((seeds -np.array([size[0],0.,0.]),seeds, seeds +np.array([size[0],0.,0.])))
|
||
seeds_p = np.vstack((seeds_p-np.array([0.,size[1],0.]),seeds_p,seeds_p+np.array([0.,size[1],0.])))
|
||
seeds_p = np.vstack((seeds_p-np.array([0.,0.,size[2]]),seeds_p,seeds_p+np.array([0.,0.,size[2]])))
|
||
else:
|
||
weights_p = np.array(weights,float)
|
||
seeds_p = seeds
|
||
|
||
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
|
||
|
||
pool = mp.Pool(int(os.environ.get('OMP_NUM_THREADS',4)))
|
||
result = pool.map_async(partial(Grid._find_closest_seed,seeds_p,weights_p), coords)
|
||
pool.close()
|
||
pool.join()
|
||
material_ = np.array(result.get()).reshape(cells)
|
||
|
||
if periodic: material_ %= len(weights)
|
||
|
||
return Grid(material = material_ if material is None else np.array(material)[material_],
|
||
size = size,
|
||
comments = util.execution_stamp('Grid','from_Laguerre_tessellation'),
|
||
)
|
||
|
||
|
||
@staticmethod
|
||
def from_Voronoi_tessellation(cells: IntSequence,
|
||
size: FloatSequence,
|
||
seeds: np.ndarray,
|
||
material: IntSequence = None,
|
||
periodic: bool = True) -> 'Grid':
|
||
"""
|
||
Create grid from Voronoi tessellation.
|
||
|
||
Parameters
|
||
----------
|
||
cells : sequence of int, len (3)
|
||
Number of cells in x,y,z direction.
|
||
size : sequence of float, len (3)
|
||
Physical size of the grid in meter.
|
||
seeds : numpy.ndarray, shape (:,3)
|
||
Position of the seed points in meter. All points need to lay within the box.
|
||
material : sequence of int, len (seeds.shape[0]), optional
|
||
Material ID of the seeds.
|
||
Defaults to None, in which case materials are consecutively numbered.
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from tessellation.
|
||
|
||
"""
|
||
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
|
||
tree = spatial.cKDTree(seeds,boxsize=size) if periodic else \
|
||
spatial.cKDTree(seeds)
|
||
try:
|
||
material_ = tree.query(coords, workers = int(os.environ.get('OMP_NUM_THREADS',4)))[1]
|
||
except TypeError:
|
||
material_ = tree.query(coords, n_jobs = int(os.environ.get('OMP_NUM_THREADS',4)))[1] # scipy <1.6
|
||
|
||
return Grid(material = (material_ if material is None else np.array(material)[material_]).reshape(cells),
|
||
size = size,
|
||
comments = util.execution_stamp('Grid','from_Voronoi_tessellation'),
|
||
)
|
||
|
||
|
||
_minimal_surface = \
|
||
{'Schwarz P': lambda x,y,z: np.cos(x) + np.cos(y) + np.cos(z),
|
||
'Double Primitive': lambda x,y,z: ( 0.5 * (np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x))
|
||
+ 0.2 * (np.cos(2*x) + np.cos(2*y) + np.cos(2*z)) ),
|
||
'Schwarz D': lambda x,y,z: ( np.sin(x)*np.sin(y)*np.sin(z)
|
||
+ np.sin(x)*np.cos(y)*np.cos(z)
|
||
+ np.cos(x)*np.cos(y)*np.sin(z)
|
||
+ np.cos(x)*np.sin(y)*np.cos(z) ),
|
||
'Complementary D': lambda x,y,z: ( np.cos(3*x+y)*np.cos(z) - np.sin(3*x-y)*np.sin(z) + np.cos(x+3*y)*np.cos(z)
|
||
+ np.sin(x-3*y)*np.sin(z) + np.cos(x-y)*np.cos(3*z) - np.sin(x+y)*np.sin(3*z) ),
|
||
'Double Diamond': lambda x,y,z: 0.5 * (np.sin(x)*np.sin(y)
|
||
+ np.sin(y)*np.sin(z)
|
||
+ np.sin(z)*np.sin(x)
|
||
+ np.cos(x) * np.cos(y) * np.cos(z) ),
|
||
'Dprime': lambda x,y,z: 0.5 * ( np.cos(x)*np.cos(y)*np.cos(z)
|
||
+ np.cos(x)*np.sin(y)*np.sin(z)
|
||
+ np.sin(x)*np.cos(y)*np.sin(z)
|
||
+ np.sin(x)*np.sin(y)*np.cos(z)
|
||
- np.sin(2*x)*np.sin(2*y)
|
||
- np.sin(2*y)*np.sin(2*z)
|
||
- np.sin(2*z)*np.sin(2*x) ) - 0.2,
|
||
'Gyroid': lambda x,y,z: np.cos(x)*np.sin(y) + np.cos(y)*np.sin(z) + np.cos(z)*np.sin(x),
|
||
'Gprime': lambda x,y,z : ( np.sin(2*x)*np.cos(y)*np.sin(z)
|
||
+ np.sin(2*y)*np.cos(z)*np.sin(x)
|
||
+ np.sin(2*z)*np.cos(x)*np.sin(y) ) + 0.32,
|
||
'Karcher K': lambda x,y,z: ( 0.3 * ( np.cos(x) + np.cos(y) + np.cos(z)
|
||
+ np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x) )
|
||
- 0.4 * ( np.cos(2*x) + np.cos(2*y) + np.cos(2*z) ) ) + 0.2,
|
||
'Lidinoid': lambda x,y,z: 0.5 * ( np.sin(2*x)*np.cos(y)*np.sin(z)
|
||
+ np.sin(2*y)*np.cos(z)*np.sin(x)
|
||
+ np.sin(2*z)*np.cos(x)*np.sin(y)
|
||
- np.cos(2*x)*np.cos(2*y)
|
||
- np.cos(2*y)*np.cos(2*z)
|
||
- np.cos(2*z)*np.cos(2*x) ) + 0.15,
|
||
'Neovius': lambda x,y,z: ( 3 * (np.cos(x)+np.cos(y)+np.cos(z))
|
||
+ 4 * np.cos(x)*np.cos(y)*np.cos(z) ),
|
||
'Fisher-Koch S': lambda x,y,z: ( np.cos(2*x)*np.sin( y)*np.cos( z)
|
||
+ np.cos( x)*np.cos(2*y)*np.sin( z)
|
||
+ np.sin( x)*np.cos( y)*np.cos(2*z) ),
|
||
}
|
||
|
||
|
||
@staticmethod
|
||
def from_minimal_surface(cells: IntSequence,
|
||
size: FloatSequence,
|
||
surface: str,
|
||
threshold: float = 0.0,
|
||
periods: int = 1,
|
||
materials: IntSequence = (0,1)) -> 'Grid':
|
||
"""
|
||
Create grid from definition of triply periodic minimal surface.
|
||
|
||
Parameters
|
||
----------
|
||
cells : sequence of int, len (3)
|
||
Number of cells in x,y,z direction.
|
||
size : sequence of float, len (3)
|
||
Physical size of the grid in meter.
|
||
surface : str
|
||
Type of the minimal surface. See notes for details.
|
||
threshold : float, optional.
|
||
Threshold of the minimal surface. Defaults to 0.0.
|
||
periods : integer, optional.
|
||
Number of periods per unit cell. Defaults to 1.
|
||
materials : sequence of int, len (2)
|
||
Material IDs. Defaults to (0,1).
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from definition of minimal surface.
|
||
|
||
Notes
|
||
-----
|
||
The following triply-periodic minimal surfaces are implemented:
|
||
- Schwarz P
|
||
- Double Primitive
|
||
- Schwarz D
|
||
- Complementary D
|
||
- Double Diamond
|
||
- Dprime
|
||
- Gyroid
|
||
- Gprime
|
||
- Karcher K
|
||
- Lidinoid
|
||
- Neovius
|
||
- Fisher-Koch S
|
||
|
||
References
|
||
----------
|
||
S.B.G. Blanquer et al., Biofabrication 9(2):025001, 2017
|
||
https://doi.org/10.1088/1758-5090/aa6553
|
||
|
||
M. Wohlgemuth et al., Macromolecules 34(17):6083-6089, 2001
|
||
https://doi.org/10.1021/ma0019499
|
||
|
||
M.-T. Hsieh and L. Valdevit, Software Impacts 6:100026, 2020
|
||
https://doi.org/10.1016/j.simpa.2020.100026
|
||
|
||
Examples
|
||
--------
|
||
Minimal surface of 'Gyroid' type.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> damask.Grid.from_minimal_surface([64]*3,np.ones(3)*1.e-4,'Gyroid')
|
||
cells : 64 x 64 x 64
|
||
size : 0.0001 x 0.0001 x 0.0001 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 2
|
||
|
||
Minimal surface of 'Neovius' type with non-default material IDs.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> damask.Grid.from_minimal_surface([80]*3,np.ones(3)*5.e-4,
|
||
... 'Neovius',materials=(1,5))
|
||
cells : 80 x 80 x 80
|
||
size : 0.0005 x 0.0005 x 0.0005 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 2 (min: 1, max: 5)
|
||
|
||
"""
|
||
x,y,z = np.meshgrid(periods*2.0*np.pi*(np.arange(cells[0])+0.5)/cells[0],
|
||
periods*2.0*np.pi*(np.arange(cells[1])+0.5)/cells[1],
|
||
periods*2.0*np.pi*(np.arange(cells[2])+0.5)/cells[2],
|
||
indexing='ij',sparse=True)
|
||
return Grid(material = np.where(threshold < Grid._minimal_surface[surface](x,y,z),materials[1],materials[0]),
|
||
size = size,
|
||
comments = util.execution_stamp('Grid','from_minimal_surface'),
|
||
)
|
||
|
||
|
||
def save(self,
|
||
fname: Union[str, Path],
|
||
compress: bool = True):
|
||
"""
|
||
Save as VTK image data file.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or pathlib.Path
|
||
Filename to write. Valid extension is .vti, it will be appended if not given.
|
||
compress : bool, optional
|
||
Compress with zlib algorithm. Defaults to True.
|
||
|
||
"""
|
||
v = VTK.from_image_data(self.cells,self.size,self.origin)\
|
||
.set('material',self.material.flatten(order='F'))
|
||
for label,data in self.initial_conditions.items():
|
||
v = v.set(label,data.flatten(order='F'))
|
||
v.comments = self.comments
|
||
|
||
v.save(fname,parallel=False,compress=compress)
|
||
|
||
|
||
def save_ASCII(self,
|
||
fname: Union[str, TextIO]):
|
||
"""
|
||
Save as geom file.
|
||
|
||
Storing geometry files in ASCII format is deprecated.
|
||
This function will be removed in a future version of DAMASK.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or file handle
|
||
Geometry file to write with extension '.geom'.
|
||
compress : bool, optional
|
||
Compress geometry with 'x of y' and 'a to b'.
|
||
|
||
"""
|
||
warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
|
||
header = [f'{len(self.comments)+4} header'] + self.comments \
|
||
+ ['grid a {} b {} c {}'.format(*self.cells),
|
||
'size x {} y {} z {}'.format(*self.size),
|
||
'origin x {} y {} z {}'.format(*self.origin),
|
||
'homogenization 1',
|
||
]
|
||
|
||
format_string = '%g' if self.material.dtype in np.sctypes['float'] else \
|
||
'%{}i'.format(1+int(np.floor(np.log10(np.nanmax(self.material)))))
|
||
np.savetxt(fname,
|
||
self.material.reshape([self.cells[0],np.prod(self.cells[1:])],order='F').T,
|
||
header='\n'.join(header), fmt=format_string, comments='')
|
||
|
||
|
||
def show(self,
|
||
colormap: Union[Colormap, str] = 'cividis') -> None:
|
||
"""
|
||
Show on screen.
|
||
|
||
Parameters
|
||
----------
|
||
colormap : damask.Colormap or str, optional
|
||
Colormap for visualization of material IDs. Defaults to 'cividis'.
|
||
|
||
"""
|
||
VTK.from_image_data(self.cells,self.size,self.origin) \
|
||
.set('material',self.material.flatten('F'),) \
|
||
.show('material',colormap)
|
||
|
||
|
||
def canvas(self,
|
||
cells: IntSequence = None,
|
||
offset: IntSequence = None,
|
||
fill: int = None) -> 'Grid':
|
||
"""
|
||
Crop or enlarge/pad grid.
|
||
|
||
Parameters
|
||
----------
|
||
cells : sequence of int, len (3), optional
|
||
Number of cells x,y,z direction.
|
||
offset : sequence of int, len (3), optional
|
||
Offset (measured in cells) from old to new grid.
|
||
Defaults to [0,0,0].
|
||
fill : int, optional
|
||
Material ID to fill the background.
|
||
Defaults to material.max() + 1.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Remove lower 1/2 of the microstructure in z-direction.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
|
||
>>> g.canvas([32,32,16],[0,0,16])
|
||
cells : 33 x 32 x 16
|
||
size : 0.0001 x 0.0001 x 5e-05 m³
|
||
origin: 0.0 0.0 5e-05 m
|
||
# materials: 1
|
||
|
||
"""
|
||
offset_ = np.array(offset,np.int64) if offset is not None else np.zeros(3,np.int64)
|
||
cells_ = np.array(cells,np.int64) if cells is not None else self.cells
|
||
|
||
canvas = np.full(cells_,np.nanmax(self.material) + 1 if fill is None else fill,self.material.dtype)
|
||
|
||
LL = np.clip( offset_, 0,np.minimum(self.cells, cells_+offset_))
|
||
UR = np.clip( offset_+cells_, 0,np.minimum(self.cells, cells_+offset_))
|
||
ll = np.clip(-offset_, 0,np.minimum( cells_,self.cells-offset_))
|
||
ur = np.clip(-offset_+self.cells,0,np.minimum( cells_,self.cells-offset_))
|
||
|
||
canvas[ll[0]:ur[0],ll[1]:ur[1],ll[2]:ur[2]] = self.material[LL[0]:UR[0],LL[1]:UR[1],LL[2]:UR[2]]
|
||
|
||
return Grid(material = canvas,
|
||
size = self.size/self.cells*np.asarray(canvas.shape),
|
||
origin = self.origin+offset_*self.size/self.cells,
|
||
comments = self.comments+[util.execution_stamp('Grid','canvas')],
|
||
)
|
||
|
||
|
||
def mirror(self,
|
||
directions: Sequence[str],
|
||
reflect: bool = False) -> 'Grid':
|
||
"""
|
||
Mirror grid along given directions.
|
||
|
||
Parameters
|
||
----------
|
||
directions : (sequence of) {'x', 'y', 'z'}
|
||
Direction(s) along which the grid is mirrored.
|
||
reflect : bool, optional
|
||
Reflect (include) outermost layers. Defaults to False.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Mirror along x- and y-direction.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
|
||
>>> g.mirror('xy',True)
|
||
cells : 64 x 64 x 32
|
||
size : 0.0002 x 0.0002 x 0.0001 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 1
|
||
|
||
"""
|
||
if not set(directions).issubset(valid := ['x', 'y', 'z']):
|
||
raise ValueError(f'invalid direction "{set(directions).difference(valid)}" specified')
|
||
|
||
limits: Sequence[Optional[int]] = [None,None] if reflect else [-2,0]
|
||
mat = self.material.copy()
|
||
|
||
if 'x' in directions:
|
||
mat = np.concatenate([mat,mat[limits[0]:limits[1]:-1,:,:]],0)
|
||
if 'y' in directions:
|
||
mat = np.concatenate([mat,mat[:,limits[0]:limits[1]:-1,:]],1)
|
||
if 'z' in directions:
|
||
mat = np.concatenate([mat,mat[:,:,limits[0]:limits[1]:-1]],2)
|
||
|
||
return Grid(material = mat,
|
||
size = self.size/self.cells*np.asarray(mat.shape),
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','mirror')],
|
||
)
|
||
|
||
|
||
def flip(self,
|
||
directions: Sequence[str]) -> 'Grid':
|
||
"""
|
||
Flip grid along given directions.
|
||
|
||
Parameters
|
||
----------
|
||
directions : (sequence of) {'x', 'y', 'z'}
|
||
Direction(s) along which the grid is flipped.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
if not set(directions).issubset(valid := ['x', 'y', 'z']):
|
||
raise ValueError(f'invalid direction "{set(directions).difference(valid)}" specified')
|
||
|
||
|
||
mat = np.flip(self.material, [valid.index(d) for d in directions if d in valid])
|
||
|
||
return Grid(material = mat,
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','flip')],
|
||
)
|
||
|
||
|
||
def rotate(self,
|
||
R: Rotation,
|
||
fill: int = None) -> 'Grid':
|
||
"""
|
||
Rotate grid (and pad if required).
|
||
|
||
Parameters
|
||
----------
|
||
R : damask.Rotation
|
||
Rotation to apply to the grid.
|
||
fill : int, optional
|
||
Material ID to fill enlarged bounding box.
|
||
Defaults to material.max() + 1.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
material = self.material
|
||
# These rotations are always applied in the reference coordinate system, i.e. (z,x,z) not (z,x',z'')
|
||
# see https://www.cs.utexas.edu/~theshark/courses/cs354/lectures/cs354-14.pdf
|
||
for angle,axes in zip(R.as_Euler_angles(degrees=True)[::-1], [(0,1),(1,2),(0,1)]):
|
||
material_temp = ndimage.rotate(material,angle,axes,order=0,prefilter=False,
|
||
output=self.material.dtype,
|
||
cval=np.nanmax(self.material) + 1 if fill is None else fill)
|
||
# avoid scipy interpolation errors for rotations close to multiples of 90°
|
||
material = material_temp if np.prod(material_temp.shape) != np.prod(material.shape) else \
|
||
np.rot90(material,k=np.rint(angle/90.).astype(np.int64),axes=axes)
|
||
|
||
origin = self.origin-(np.asarray(material.shape)-self.cells)*.5 * self.size/self.cells
|
||
|
||
return Grid(material = material,
|
||
size = self.size/self.cells*np.asarray(material.shape),
|
||
origin = origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','rotate')],
|
||
)
|
||
|
||
|
||
def scale(self,
|
||
cells: IntSequence,
|
||
periodic: bool = True) -> 'Grid':
|
||
"""
|
||
Scale grid to new cells.
|
||
|
||
Parameters
|
||
----------
|
||
cells : sequence of int, len (3)
|
||
Number of cells in x,y,z direction.
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Double resolution.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
|
||
>>> g.scale(g.cells*2)
|
||
cells : 64 x 64 x 64
|
||
size : 0.0001 x 0.0001 x 0.0001 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 1
|
||
|
||
"""
|
||
return Grid(material = ndimage.interpolation.zoom(
|
||
self.material,
|
||
cells/self.cells,
|
||
output=self.material.dtype,
|
||
order=0,
|
||
mode='wrap' if periodic else 'nearest',
|
||
prefilter=False
|
||
),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','scale')],
|
||
)
|
||
|
||
|
||
def renumber(self) -> 'Grid':
|
||
"""
|
||
Renumber sorted material indices as 0,...,N-1.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
_,renumbered = np.unique(self.material,return_inverse=True)
|
||
|
||
return Grid(material = renumbered.reshape(self.cells),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
initial_conditions = self.initial_conditions,
|
||
comments = self.comments+[util.execution_stamp('Grid','renumber')],
|
||
)
|
||
|
||
|
||
def substitute(self,
|
||
from_material: Union[int,IntSequence],
|
||
to_material: Union[int,IntSequence]) -> 'Grid':
|
||
"""
|
||
Substitute material indices.
|
||
|
||
Parameters
|
||
----------
|
||
from_material : int or sequence of int
|
||
Material indices to be substituted.
|
||
to_material : int or sequence of int
|
||
New material indices.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
material = self.material.copy()
|
||
for f,t in zip(from_material if isinstance(from_material,(Sequence,np.ndarray)) else [from_material],
|
||
to_material if isinstance(to_material,(Sequence,np.ndarray)) else [to_material]): # ToDo Python 3.10 has strict mode for zip
|
||
material[self.material==f] = t
|
||
|
||
return Grid(material = material,
|
||
size = self.size,
|
||
origin = self.origin,
|
||
initial_conditions = self.initial_conditions,
|
||
comments = self.comments+[util.execution_stamp('Grid','substitute')],
|
||
)
|
||
|
||
|
||
def sort(self) -> 'Grid':
|
||
"""
|
||
Sort material indices such that min(material) is located at (0,0,0).
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
a = self.material.flatten(order='F')
|
||
from_ma = pd.unique(a)
|
||
sort_idx = np.argsort(from_ma)
|
||
ma = np.unique(a)[sort_idx][np.searchsorted(from_ma,a,sorter = sort_idx)]
|
||
|
||
return Grid(material = ma.reshape(self.cells,order='F'),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
initial_conditions = self.initial_conditions,
|
||
comments = self.comments+[util.execution_stamp('Grid','sort')],
|
||
)
|
||
|
||
|
||
def clean(self,
|
||
distance: float = np.sqrt(3),
|
||
selection: IntCollection = None,
|
||
invert_selection: bool = False,
|
||
periodic: bool = True,
|
||
rng_seed: NumpyRngSeed = None) -> 'Grid':
|
||
"""
|
||
Smooth grid by selecting most frequent material ID within given stencil at each location.
|
||
|
||
Parameters
|
||
----------
|
||
distance : float, optional
|
||
Voxel distance checked for presence of other materials.
|
||
Defaults to sqrt(3).
|
||
selection : int or collection of int, optional
|
||
Material IDs to consider. Defaults to all.
|
||
invert_selection : bool, optional
|
||
Consider all material IDs except those in selection. Defaults to False.
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. 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
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Notes
|
||
-----
|
||
If multiple material IDs are most frequent within a stencil, a random choice is taken.
|
||
|
||
"""
|
||
def most_frequent(stencil: np.ndarray,
|
||
selection: Union[None,set],
|
||
rng):
|
||
me = stencil[stencil.size//2]
|
||
if selection is None or me in selection:
|
||
unique, counts = np.unique(stencil,return_counts=True)
|
||
return rng.choice(unique[counts==np.max(counts)])
|
||
else:
|
||
return me
|
||
|
||
rng = np.random.default_rng(rng_seed)
|
||
|
||
d = np.floor(distance).astype(np.int64)
|
||
ext = np.linspace(-d,d,1+2*d,dtype=float),
|
||
xx,yy,zz = np.meshgrid(ext,ext,ext)
|
||
footprint = xx**2+yy**2+zz**2 <= distance**2+distance*1e-8
|
||
selection_ = None if selection is None else \
|
||
set(self.material.flatten()) - set(util.aslist(selection)) if invert_selection else \
|
||
set(self.material.flatten()) & set(util.aslist(selection))
|
||
material = ndimage.filters.generic_filter(
|
||
self.material,
|
||
most_frequent,
|
||
footprint=footprint,
|
||
mode='wrap' if periodic else 'nearest',
|
||
extra_keywords=dict(selection=selection_,rng=rng),
|
||
).astype(self.material.dtype)
|
||
return Grid(material = material,
|
||
size = self.size,
|
||
origin = self.origin,
|
||
initial_conditions = self.initial_conditions,
|
||
comments = self.comments+[util.execution_stamp('Grid','clean')],
|
||
)
|
||
|
||
|
||
def add_primitive(self,
|
||
dimension: Union[FloatSequence, IntSequence],
|
||
center: Union[FloatSequence, IntSequence],
|
||
exponent: Union[FloatSequence, float],
|
||
fill: int = None,
|
||
R: Rotation = Rotation(),
|
||
inverse: bool = False,
|
||
periodic: bool = True) -> 'Grid':
|
||
"""
|
||
Insert a primitive geometric object at a given position.
|
||
|
||
Parameters
|
||
----------
|
||
dimension : sequence of int or float, len (3)
|
||
Dimension (diameter/side length) of the primitive.
|
||
If given as integers, cell centers are addressed.
|
||
If given as floats, physical coordinates are addressed.
|
||
center : sequence of int or float, len (3)
|
||
Center of the primitive.
|
||
If given as integers, cell centers are addressed.
|
||
If given as floats, physical coordinates are addressed.
|
||
exponent : float or sequence of float, len (3)
|
||
Exponents for the three axes.
|
||
0 gives octahedron (ǀxǀ^(2^0) + ǀyǀ^(2^0) + ǀzǀ^(2^0) < 1)
|
||
1 gives sphere (ǀxǀ^(2^1) + ǀyǀ^(2^1) + ǀzǀ^(2^1) < 1)
|
||
fill : int, optional
|
||
Fill value for primitive. Defaults to material.max()+1.
|
||
R : damask.Rotation, optional
|
||
Rotation of primitive. Defaults to no rotation.
|
||
inverse : bool, optional
|
||
Retain original materials within primitive and fill outside.
|
||
Defaults to False.
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Add a sphere at the center.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([64]*3,int), np.ones(3)*1e-4)
|
||
>>> g.add_primitive(np.ones(3)*5e-5,np.ones(3)*5e-5,1)
|
||
cells : 64 x 64 x 64
|
||
size : 0.0001 x 0.0001 x 0.0001 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 2
|
||
|
||
Add a cube at the origin.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([64]*3,int), np.ones(3)*1e-4)
|
||
>>> g.add_primitive(np.ones(3,int)*32,np.zeros(3),np.inf)
|
||
cells : 64 x 64 x 64
|
||
size : 0.0001 x 0.0001 x 0.0001 m³
|
||
origin: 0.0 0.0 0.0 m
|
||
# materials: 2
|
||
|
||
"""
|
||
# radius and center
|
||
r = np.array(dimension)/2.0*self.size/self.cells if np.array(dimension).dtype in np.sctypes['int'] else \
|
||
np.array(dimension)/2.0
|
||
c = (np.array(center) + .5)*self.size/self.cells if np.array(center).dtype in np.sctypes['int'] else \
|
||
(np.array(center) - self.origin)
|
||
|
||
coords = grid_filters.coordinates0_point(self.cells,self.size,
|
||
-(0.5*(self.size + (self.size/self.cells
|
||
if np.array(center).dtype in np.sctypes['int'] else
|
||
0)) if periodic else c))
|
||
coords_rot = R.broadcast_to(tuple(self.cells))@coords
|
||
|
||
with np.errstate(all='ignore'):
|
||
mask = np.sum(np.power(np.abs(coords_rot)/r,2.0**np.array(exponent)),axis=-1) > 1.0
|
||
|
||
if periodic: # translate back to center
|
||
mask = np.roll(mask,((c/self.size-0.5)*self.cells).round().astype(np.int64),(0,1,2))
|
||
|
||
return Grid(material = np.where(np.logical_not(mask) if inverse else mask,
|
||
self.material,
|
||
np.nanmax(self.material)+1 if fill is None else fill),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
initial_conditions = self.initial_conditions,
|
||
comments = self.comments+[util.execution_stamp('Grid','add_primitive')],
|
||
)
|
||
|
||
|
||
def vicinity_offset(self,
|
||
distance: float = np.sqrt(3),
|
||
offset: int = None,
|
||
selection: IntCollection = None,
|
||
invert_selection: bool = False,
|
||
periodic: bool = True) -> 'Grid':
|
||
"""
|
||
Offset material ID of points in the vicinity of selected (or just other) material IDs.
|
||
|
||
Trigger points are variations in material ID, i.e. grain/phase
|
||
boundaries or explicitly given material IDs.
|
||
|
||
Parameters
|
||
----------
|
||
distance : float, optional
|
||
Voxel distance checked for presence of other materials.
|
||
Defaults to sqrt(3).
|
||
offset : int, optional
|
||
Offset (positive or negative) to tag material IDs.
|
||
Defaults to material.max()+1.
|
||
selection : int or collection of int, optional
|
||
Material IDs that trigger an offset.
|
||
Defaults to any other than own material ID.
|
||
invert_selection : bool, optional
|
||
Consider all material IDs except those in selection.
|
||
Defaults to False.
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
def tainted_neighborhood(stencil: np.ndarray, selection: Union[None,set]):
|
||
me = stencil[stencil.size//2]
|
||
return np.any(stencil != me if selection is None else
|
||
np.in1d(stencil,np.array(list(selection - {me}))))
|
||
|
||
d = np.floor(distance).astype(np.int64)
|
||
ext = np.linspace(-d,d,1+2*d,dtype=float),
|
||
xx,yy,zz = np.meshgrid(ext,ext,ext)
|
||
footprint = xx**2+yy**2+zz**2 <= distance**2+distance*1e-8
|
||
offset_ = np.nanmax(self.material)+1 if offset is None else offset
|
||
selection_ = None if selection is None else \
|
||
set(self.material.flatten()) - set(util.aslist(selection)) if invert_selection else \
|
||
set(self.material.flatten()) & set(util.aslist(selection))
|
||
mask = ndimage.filters.generic_filter(self.material,
|
||
tainted_neighborhood,
|
||
footprint=footprint,
|
||
mode='wrap' if periodic else 'nearest',
|
||
extra_keywords=dict(selection=selection_),
|
||
)
|
||
|
||
return Grid(material = np.where(mask, self.material + offset_,self.material),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
initial_conditions = self.initial_conditions,
|
||
comments = self.comments+[util.execution_stamp('Grid','vicinity_offset')],
|
||
)
|
||
|
||
|
||
def get_grain_boundaries(self,
|
||
periodic: bool = True,
|
||
directions: Sequence[str] = 'xyz') -> VTK:
|
||
"""
|
||
Create VTK unstructured grid containing grain boundaries.
|
||
|
||
Parameters
|
||
----------
|
||
periodic : bool, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
directions : (sequence of) {'x', 'y', 'z'}, optional
|
||
Direction(s) along which the boundaries are determined.
|
||
Defaults to 'xyz'.
|
||
|
||
Returns
|
||
-------
|
||
grain_boundaries : damask.VTK
|
||
VTK-based geometry of grain boundary network.
|
||
|
||
"""
|
||
if not set(directions).issubset(valid := ['x', 'y', 'z']):
|
||
raise ValueError(f'invalid direction "{set(directions).difference(valid)}" specified')
|
||
|
||
o = [[0, self.cells[0]+1, np.prod(self.cells[:2]+1)+self.cells[0]+1, np.prod(self.cells[:2]+1)],
|
||
[0, np.prod(self.cells[:2]+1), np.prod(self.cells[:2]+1)+1, 1],
|
||
[0, 1, self.cells[0]+1+1, self.cells[0]+1]] # offset for connectivity
|
||
|
||
connectivity = []
|
||
for i,d in enumerate(['x','y','z']):
|
||
if d not in directions: continue
|
||
mask = self.material != np.roll(self.material,1,i)
|
||
for j in [0,1,2]:
|
||
mask = np.concatenate((mask,np.take(mask,[0],j)*(i==j)),j)
|
||
if i == 0 and not periodic: mask[0,:,:] = mask[-1,:,:] = False
|
||
if i == 1 and not periodic: mask[:,0,:] = mask[:,-1,:] = False
|
||
if i == 2 and not periodic: mask[:,:,0] = mask[:,:,-1] = False
|
||
|
||
base_nodes = np.argwhere(mask.flatten(order='F')).reshape(-1,1)
|
||
connectivity.append(np.block([base_nodes + o[i][k] for k in range(4)]))
|
||
|
||
coords = grid_filters.coordinates0_node(self.cells,self.size,self.origin).reshape(-1,3,order='F')
|
||
return VTK.from_unstructured_grid(coords,np.vstack(connectivity),'QUAD')
|