import os import copy import warnings import multiprocessing as mp from functools import partial 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 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,size,origin=[0.0,0.0,0.0],comments=[]): """ New geometry definition for grid solvers. Parameters ---------- material : numpy.ndarray of shape (:,:,:) Material indices. The shape of the material array defines the number of cells. size : list or numpy.ndarray of shape (3) Physical size of grid in meter. origin : list or numpy.ndarray of shape (3), optional Coordinates of grid origin in meter. comments : list of str, optional Comments, e.g. history of operations. """ self.material = material self.size = size self.origin = origin self.comments = comments def __repr__(self): """Basic information on grid definition.""" mat_min = np.nanmin(self.material) mat_max = np.nanmax(self.material) mat_N = self.N_materials return util.srepr([ f'cells a b c: {util.srepr(self.cells, " x ")}', f'size x y z: {util.srepr(self.size, " x ")}', f'origin x y z: {util.srepr(self.origin," ")}', f'# materials: {mat_N}' + ('' if mat_min == 0 and mat_max+1 == mat_N else f' (min: {mat_min}, max: {mat_max})') ]) def __copy__(self): """Create deep copy.""" return copy.deepcopy(self) copy = __copy__ def __eq__(self,other): """ Test equality of other. Parameters ---------- other : damask.Grid Grid to compare self against. """ return (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): """Material indices.""" return self._material @material.setter def material(self,material): if len(material.shape) != 3: raise ValueError(f'invalid material shape {material.shape}') elif material.dtype not in np.sctypes['float'] + np.sctypes['int']: raise TypeError(f'invalid material data type {material.dtype}') else: 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): """Physical size of grid in meter.""" return self._size @size.setter def size(self,size): if len(size) != 3 or any(np.array(size) < 0): raise ValueError(f'invalid size {size}') else: self._size = np.array(size) @property def origin(self): """Coordinates of grid origin in meter.""" return self._origin @origin.setter def origin(self,origin): if len(origin) != 3: raise ValueError(f'invalid origin {origin}') else: self._origin = np.array(origin) @property def comments(self): """Comments, e.g. history of operations.""" return self._comments @comments.setter def comments(self,comments): self._comments = [str(c) for c in comments] if isinstance(comments,list) else [str(comments)] @property def cells(self): """Number of cells in x,y,z direction.""" return np.asarray(self.material.shape) @property def N_materials(self): """Number of (unique) material indices within grid.""" return np.unique(self.material).size @staticmethod def load(fname): """ Load from VTK image data file. Parameters ---------- fname : str or 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','.vtr')) else str(fname)+'.vti') # compatibility hack comments = v.get_comments() cells = np.array(v.vtk_data.GetDimensions())-1 bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T return Grid(material = v.get('material').reshape(cells,order='F'), size = bbox[1] - bbox[0], origin = bbox[0], comments=comments) @staticmethod def load_ASCII(fname): """ 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 3.1.0', DeprecationWarning,2) try: f = open(fname) except TypeError: f = fname 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('header length information missing or invalid') comments = [] content = f.readlines() for i,line in enumerate(content[:header_length]): items = line.split('#')[0].lower().strip().split() key = items[0] if items else '' if key == '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:]: items = line.split('#')[0].split() if len(items) == 3: if items[1].lower() == 'of': items = np.ones(int(items[0]))*float(items[2]) elif items[1].lower() == 'to': items = np.linspace(int(items[0]),int(items[2]), abs(int(items[2])-int(items[0]))+1,dtype=float) else: items = list(map(float,items)) else: items = list(map(float,items)) material[i:i+len(items)] = items i += len(items) if i != cells.prod(): raise TypeError(f'invalid file: expected {cells.prod()} entries, found {i}') 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): """ Load from Neper VTK file. Parameters ---------- fname : str, pathlib.Path, or file handle Geometry file to read. Returns ------- loaded : damask.Grid Grid-based geometry from file. """ v = VTK.load(fname,'vtkImageData') 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') - 1, bbox[1] - bbox[0], bbox[0], util.execution_stamp('Grid','load_Neper')) @staticmethod def load_DREAM3D(fname, feature_IDs=None,cell_data=None, phases='Phases',Euler_angles='EulerAngles', base_group=None): """ 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 Filename of the DREAM.3D (HDF5) file. feature_IDs : str 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 Name of the group (folder) containing cell-wise data. Defaults to None in wich case it is automatically detected. phases : str 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 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 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,coordinates,labels): """ 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 : str or 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, weights, point): return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights) @staticmethod def from_Laguerre_tessellation(cells,size,seeds,weights,material=None,periodic=True): """ Create grid from Laguerre tessellation. Parameters ---------- cells : int numpy.ndarray of shape (3) Number of cells in x,y,z direction. size : list or numpy.ndarray of shape (3) Physical size of the grid in meter. seeds : numpy.ndarray of shape (:,3) Position of the seed points in meter. All points need to lay within the box. weights : numpy.ndarray of shape (seeds.shape[0]) Weights of the seeds. Setting all weights to 1.0 gives a standard Voronoi tessellation. material : numpy.ndarray of shape (seeds.shape[0]), optional Material ID of the seeds. Defaults to None, in which case materials are consecutively numbered. periodic : Boolean, optional Assume grid to be periodic. Defaults to True. Returns ------- new : damask.Grid Grid-based geometry from tessellation. """ 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 = weights 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 material[material_], size = size, comments = util.execution_stamp('Grid','from_Laguerre_tessellation'), ) @staticmethod def from_Voronoi_tessellation(cells,size,seeds,material=None,periodic=True): """ Create grid from Voronoi tessellation. Parameters ---------- cells : int numpy.ndarray of shape (3) Number of cells in x,y,z direction. size : list or numpy.ndarray of shape (3) Physical size of the grid in meter. seeds : numpy.ndarray of shape (:,3) Position of the seed points in meter. All points need to lay within the box. material : numpy.ndarray of shape (seeds.shape[0]), optional Material ID of the seeds. Defaults to None, in which case materials are consecutively numbered. periodic : Boolean, 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 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,size,surface,threshold=0.0,periods=1,materials=(0,1)): """ Create grid from definition of triply periodic minimal surface. Parameters ---------- cells : int numpy.ndarray of shape (3) Number of cells in x,y,z direction. size : list or numpy.ndarray of shape (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 : (int, int), optional 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(np.array([64]*3,int),np.ones(3), ... 'Gyroid') cells a b c: 64 x 64 x 64 size x y z: 1.0 x 1.0 x 1.0 origin x y z: 0.0 0.0 0.0 # materials: 2 Minimal surface of 'Neovius' type. non-default material IDs. >>> import numpy as np >>> import damask >>> damask.Grid.from_minimal_surface(np.array([80]*3,int),np.ones(3), ... 'Neovius',materials=(1,5)) cells a b c: 80 x 80 x 80 size x y z: 1.0 x 1.0 x 1.0 origin x y z: 0.0 0.0 0.0 # 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,compress=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) v.add(self.material.flatten(order='F'),'material') v.add_comments(self.comments) v.save(fname if str(fname).endswith('.vti') else str(fname)+'.vti',parallel=False,compress=compress) def save_ASCII(self,fname): """ 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 3.1.0', 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): """Show on screen.""" VTK.from_rectilinear_grid(self.cells,self.size,self.origin).show() def add_primitive(self,dimension,center,exponent, fill=None,R=Rotation(),inverse=False,periodic=True): """ Insert a primitive geometric object at a given position. Parameters ---------- dimension : int or float numpy.ndarray of shape (3) Dimension (diameter/side length) of the primitive. If given as integers, cell centers are addressed. If given as floats, coordinates are addressed. center : int or float numpy.ndarray of shape (3) Center of the primitive. If given as integers, cell centers are addressed. If given as floats, coordinates in space are addressed. exponent : numpy.ndarray of shape (3) or float 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 : Boolean, optional Retain original materials within primitive and fill outside. Defaults to False. periodic : Boolean, 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 a b c: 64 x 64 x 64 size x y z: 0.0001 x 0.0001 x 0.0001 origin x y z: 0.0 0.0 0.0 # 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 a b c: 64 x 64 x 64 size x y z: 0.0001 x 0.0001 x 0.0001 origin x y z: 0.0 0.0 0.0 # 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,reflect=False): """ Mirror grid along given directions. Parameters ---------- directions : iterable containing str Direction(s) along which the grid is mirrored. Valid entries are 'x', 'y', 'z'. 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 a b c: 64 x 64 x 32 size x y z: 0.0002 x 0.0002 x 0.0001 origin x y z: 0.0 0.0 0.0 # materials: 1 """ valid = ['x','y','z'] if not set(directions).issubset(valid): raise ValueError(f'invalid direction {set(directions).difference(valid)} specified') limits = [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): """ Flip grid along given directions. Parameters ---------- directions : iterable containing str Direction(s) along which the grid is flipped. Valid entries are 'x', 'y', 'z'. Returns ------- updated : damask.Grid Updated grid-based geometry. """ valid = ['x','y','z'] if not set(directions).issubset(valid): 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,periodic=True): """ Scale grid to new cells. Parameters ---------- cells : numpy.ndarray of shape (3) Number of cells in x,y,z direction. periodic : Boolean, 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 a b c: 64 x 64 x 64 size x y z: 0.0001 x 0.0001 x 0.0001 origin x y z: 0.0 0.0 0.0 # 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=3,selection=None,periodic=True): """ Smooth grid by selecting most frequent material index within given stencil at each location. Parameters ---------- stencil : int, optional Size of smoothing stencil. selection : list, optional Field values that can be altered. Defaults to all. periodic : Boolean, optional Assume grid to be periodic. Defaults to True. Returns ------- updated : damask.Grid Updated grid-based geometry. """ def mostFrequent(arr,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): """ 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,fill=None): """ Rotate grid (pad if required). Parameters ---------- R : damask.Rotation Rotation to apply to the grid. fill : int or float, optional Material index to fill the corners. Defaults to material.max() + 1. Returns ------- updated : damask.Grid Updated grid-based geometry. """ if fill is None: fill = np.nanmax(self.material) + 1 dtype = float if isinstance(fill,float) or self.material.dtype in np.sctypes['float'] else int 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=dtype,cval=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=None,offset=None,fill=None): """ Crop or enlarge/pad grid. Parameters ---------- cells : numpy.ndarray of shape (3) Number of cells x,y,z direction. offset : numpy.ndarray of shape (3) Offset (measured in cells) from old to new grid [0,0,0]. fill : int or float, 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(np.array([32,32,16],int)) cells a b c: 33 x 32 x 16 size x y z: 0.0001 x 0.0001 x 5e-05 origin x y z: 0.0 0.0 0.0 # materials: 1 """ if offset is None: offset = 0 if fill is None: fill = np.nanmax(self.material) + 1 dtype = float if int(fill) != fill or self.material.dtype in np.sctypes['float'] else int canvas = np.full(self.cells if cells is None else cells,fill,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,to_material): """ Substitute material indices. Parameters ---------- from_material : iterable of ints Material indices to be substituted. to_material : iterable of ints New material indices. Returns ------- updated : damask.Grid Updated grid-based geometry. """ def mp(entry,mapper): return mapper[entry] if entry in mapper else entry mp = np.vectorize(mp) mapper = dict(zip(from_material,to_material)) return Grid(material = mp(self.material,mapper).reshape(self.cells), size = self.size, origin = self.origin, comments = self.comments+[util.execution_stamp('Grid','substitute')], ) def sort(self): """ 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=1,offset=None,trigger=[],periodic=True): """ 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 : list of ints, optional List of material indices that trigger a change. Defaults to [], meaning that any different neighbor triggers a change. periodic : Boolean, optional Assume grid to be periodic. Defaults to True. Returns ------- updated : damask.Grid Updated grid-based geometry. """ def tainted_neighborhood(stencil,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=True,directions='xyz'): """ Create VTK unstructured grid containing grain boundaries. Parameters ---------- periodic : Boolean, optional Assume grid to be periodic. Defaults to True. directions : iterable containing str, optional Direction(s) along which the boundaries are determined. Valid entries are 'x', 'y', 'z'. Defaults to 'xyz'. Returns ------- grain_boundaries : damask.VTK VTK-based geometry of grain boundary network. """ valid = ['x','y','z'] if not set(directions).issubset(valid): 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')