import copy import multiprocessing as mp from functools import partial import os import warnings import numpy as np import pandas as pd import h5py from scipy import ndimage, spatial from vtk.util.numpy_support import vtk_to_numpy as vtk_to_np from . import environment from . import VTK from . import util from . import grid_filters from . import Rotation class Grid: """Geometry definition for grid solvers.""" def __init__(self,material,size,origin=[0.0,0.0,0.0],comments=[]): """ New grid definition from array of materials, size, and origin. Parameters ---------- material : numpy.ndarray Material index array (3D). size : list or numpy.ndarray Physical size of the grid in meter. origin : list or numpy.ndarray, optional Physical origin of the grid in meter. comments : list of str, optional Comment lines. """ 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 diff(self,other): """ Report property differences of self relative to other. Parameters ---------- other : damask.Grid Grid to compare self against. """ message = [] if np.any(other.cells != self.cells): message.append(util.deemph(f'cells a b c: {util.srepr(other.cells," x ")}')) message.append(util.emph( f'cells a b c: {util.srepr( self.cells," x ")}')) if not np.allclose(other.size,self.size): message.append(util.deemph(f'size x y z: {util.srepr(other.size," x ")}')) message.append(util.emph( f'size x y z: {util.srepr( self.size," x ")}')) if not np.allclose(other.origin,self.origin): message.append(util.deemph(f'origin x y z: {util.srepr(other.origin," ")}')) message.append(util.emph( f'origin x y z: {util.srepr( self.origin," ")}')) if other.N_materials != self.N_materials: message.append(util.deemph(f'# materials: {other.N_materials}')) message.append(util.emph( f'# materials: { self.N_materials}')) if np.nanmax(other.material) != np.nanmax(self.material): message.append(util.deemph(f'max material: {np.nanmax(other.material)}')) message.append(util.emph( f'max material: {np.nanmax( self.material)}')) return util.return_message(message) @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 rectilinear grid file. Parameters ---------- fname : str or or pathlib.Path Grid file to read. Valid extension is .vtr, which will be appended if not given. """ v = VTK.load(fname if str(fname).endswith('.vtr') else str(fname)+'.vtr') comments = v.get_comments() cells = np.array(v.vtk_data.GetDimensions())-1 bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T for i,c in enumerate([v.vtk_data.GetXCoordinates(),v.vtk_data.GetYCoordinates(),v.vtk_data.GetZCoordinates()]): if not np.allclose(vtk_to_np(c),np.linspace(bbox[0][i],bbox[1][i],cells[i]+1)): raise ValueError('regular grid spacing violated') 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. """ warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.1.0', DeprecationWarning) 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_DREAM3D(fname,base_group,point_data=None,material='FeatureIds'): """ Load from DREAM.3D file. Parameters ---------- fname : str Filename of the DREAM.3D file base_group : str Name of the group (folder) below 'DataContainers', for example 'SyntheticVolumeDataContainer'. point_data : str, optional Name of the group (folder) containing the pointwise material data, for example 'CellData'. Defaults to None, in which case points are consecutively numbered. material : str, optional Name of the dataset containing the material ID. Defaults to 'FeatureIds'. """ root_dir ='DataContainers' f = h5py.File(fname, 'r') g = os.path.join(root_dir,base_group,'_SIMPL_GEOMETRY') cells = f[os.path.join(g,'DIMENSIONS')][()] size = f[os.path.join(g,'SPACING')][()] * cells origin = f[os.path.join(g,'ORIGIN')][()] ma = np.arange(cells.prod(),dtype=int) \ if point_data is None else \ np.reshape(f[os.path.join(root_dir,base_group,point_data,material)],cells.prod()) return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','load_DREAM3D')) @staticmethod def from_table(table,coordinates,labels): """ Generate 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 combintation of values results in one material ID. """ 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): """ Generate 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. """ 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]]))) coords = grid_filters.coordinates0_point(cells*3,size*3,-size).reshape(-1,3) 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',1))) result = pool.map_async(partial(Grid._find_closest_seed,seeds_p,weights_p), [coord for coord in coords]) pool.close() pool.join() material_ = np.array(result.get()) if periodic: material_ = material_.reshape(cells*3) material_ = material_[cells[0]:cells[0]*2,cells[1]:cells[1]*2,cells[2]:cells[2]*2]%seeds.shape[0] else: material_ = material_.reshape(cells) 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): """ Generate 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. """ coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3) KDTree = spatial.cKDTree(seeds,boxsize=size) if periodic else spatial.cKDTree(seeds) devNull,material_ = KDTree.query(coords) 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)): """ Generate 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 (1,2). 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 ---------- Sébastien B G Blanquer, Maike Werner, Markus Hannula, Shahriar Sharifi, Guillaume P R Lajoinie, David Eglin, Jari Hyttinen, André A Poot, and Dirk W Grijpma Surface curvature in triply-periodic minimal surface architectures as a distinct design parameter in preparing advanced tissue engineering scaffolds https://doi.org/10.1088/1758-5090/aa6553 Meinhard Wohlgemuth, Nataliya Yufa, James Hoffman, and Edwin L. Thomas Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries https://doi.org/10.1021/ma0019499 Meng-Ting Hsieh, Lorenzo Valdevit Minisurf – A minimal surface generator for finite element modeling and additive manufacturing https://doi.org/10.1016/j.simpa.2020.100026 """ 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 rectilinear grid file. Parameters ---------- fname : str or pathlib.Path Filename to write. Valid extension is .vtr, it will be appended if not given. compress : bool, optional Compress with zlib algorithm. Defaults to True. """ v = VTK.from_rectilinear_grid(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('.vtr') else str(fname)+'.vtr',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) 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. """ # 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. """ 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'. """ 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. """ 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. """ 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.""" _,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. """ if fill is None: fill = np.nanmax(self.material) + 1 dtype = float if np.isnan(fill) or int(fill) != fill or self.material.dtype==np.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. """ 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. """ 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).""" 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. """ 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'. """ 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')