import os import copy import warnings import multiprocessing as mp from functools import partial import typing from typing import Union, Optional, TextIO, List, Sequence 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 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), comments: Union[str, Sequence[str]] = None, initial_conditions = 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]. comments : (list of) str, optional Comments, e.g. history of operations. """ self.material = material self.size = size # type: ignore self.origin = origin # type: ignore self.comments = [] if comments is None else comments # type: ignore self.ic = initial_conditions if initial_conditions is not None else {} def __repr__(self) -> str: """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.ic.keys()] if self.ic else [])) def __copy__(self) -> 'Grid': """Create deep copy.""" return copy.deepcopy(self) copy = __copy__ def __eq__(self, other: object) -> bool: """ 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(int).astype(float)): self._material = self.material.astype(int) @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 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], comments = comments, initial_conditions = ic) @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(int(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('int') - (1 if material.min() > 0 else 0) return Grid(material.reshape(cells,order='F'),size,origin,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. """ 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(v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe') - 1, bbox[1] - bbox[0], bbox[0], 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(ma.reshape(cells,order='F'),size,origin,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(ma.reshape(cells,order='F'),size,origin,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. 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)\ .add(self.material.flatten(order='F'),'material') for label,data in self.ic.items(): v = v.add(data.flatten(order='F'),label) 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) \ .add(self.material.flatten('F'),'material') \ .show('material',colormap) 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(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(int),(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, comments = self.comments+[util.execution_stamp('Grid','add_primitive')], ) 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 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 clean(self, stencil: int = 3, selection: IntSequence = None, periodic: bool = True) -> 'Grid': """ Smooth grid by selecting most frequent material index within given stencil at each location. Parameters ---------- stencil : int, optional Size of smoothing stencil. selection : sequence of int, optional Field values that can be altered. Defaults to all. periodic : bool, optional Assume grid to be periodic. Defaults to True. Returns ------- updated : damask.Grid Updated grid-based geometry. """ def mostFrequent(arr: np.ndarray, selection = None): me = arr[arr.size//2] if selection is None or me in selection: unique, inverse = np.unique(arr, return_inverse=True) return unique[np.argmax(np.bincount(inverse))] else: return me return Grid(material = ndimage.filters.generic_filter( self.material, mostFrequent, size=(stencil if selection is None else stencil//2*2+1,)*3, mode=('wrap' if periodic else 'nearest'), extra_keywords=dict(selection=selection), ).astype(self.material.dtype), size = self.size, origin = self.origin, comments = self.comments+[util.execution_stamp('Grid','clean')], ) 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, comments = self.comments+[util.execution_stamp('Grid','renumber')], ) def rotate(self, R: Rotation, fill: int = None) -> 'Grid': """ Rotate grid (pad if required). Parameters ---------- R : damask.Rotation Rotation to apply to the grid. fill : int, optional Material index to fill the corners. 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(int),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 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 [0,0,0]. fill : int, optional Material index to fill the background. Defaults to material.max() + 1. Returns ------- updated : damask.Grid Updated grid-based geometry. Examples -------- Remove 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]) cells : 33 x 32 x 16 size : 0.0001 x 0.0001 x 5e-05 m³ origin: 0.0 0.0 0.0 m # materials: 1 """ offset_ = np.array(offset,int) if offset is not None else np.zeros(3,int) cells_ = np.array(cells,int) 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 substitute(self, from_material: IntSequence, to_material: IntSequence) -> 'Grid': """ Substitute material indices. Parameters ---------- from_material : sequence of int Material indices to be substituted. to_material : 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,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, 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, comments = self.comments+[util.execution_stamp('Grid','sort')], ) def vicinity_offset(self, vicinity: int = 1, offset: int = None, trigger: IntSequence = [], periodic: bool = True) -> 'Grid': """ Offset material index of points in the vicinity of xxx. Different from themselves (or listed as triggers) within a given (cubic) vicinity, i.e. within the region close to a grain/phase boundary. ToDo: use include/exclude as in seeds.from_grid Parameters ---------- vicinity : int, optional Voxel distance checked for presence of other materials. Defaults to 1. offset : int, optional Offset (positive or negative) to tag material indices, defaults to material.max()+1. trigger : sequence of int, optional List of material indices that trigger a change. Defaults to [], meaning that any different neighbor triggers a change. 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, trigger): me = stencil[stencil.shape[0]//2] return np.any(stencil != me if len(trigger) == 0 else np.in1d(stencil,np.array(list(set(trigger) - {me})))) offset_ = np.nanmax(self.material)+1 if offset is None else offset mask = ndimage.filters.generic_filter(self.material, tainted_neighborhood, size=1+2*vicinity, mode='wrap' if periodic else 'nearest', extra_keywords={'trigger':trigger}) return Grid(material = np.where(mask, self.material + offset_,self.material), size = self.size, origin = self.origin, 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')