import numpy as np from . import Lattice from . import Rotation class Orientation: # ToDo: make subclass of lattice and Rotation? """ Crystallographic orientation. A crystallographic orientation contains a rotation and a lattice. """ __slots__ = ['rotation','lattice'] def __repr__(self): """Report lattice type and orientation.""" return self.lattice.__repr__()+'\n'+self.rotation.__repr__() def __init__(self, rotation, lattice): """ New orientation from rotation and lattice. Parameters ---------- rotation : Rotation Rotation specifying the lattice orientation. lattice : Lattice Lattice type of the crystal. """ if isinstance(lattice, Lattice): self.lattice = lattice else: self.lattice = Lattice(lattice) # assume string if isinstance(rotation, Rotation): self.rotation = rotation else: self.rotation = Rotation.from_quaternion(rotation) # assume quaternion def __getitem__(self,item): """Iterate over leading/leftmost dimension of Orientation array.""" return self.__class__(self.rotation[item],self.lattice) # ToDo: Discuss vectorization/calling signature def disorientation(self, other, SST = True, symmetries = False): """ Disorientation between myself and given other orientation. Rotation axis falls into SST if SST == True. Currently requires same symmetry for both orientations. Look into A. Heinz and P. Neumann 1991 for cases with differing sym. """ if self.lattice.symmetry != other.lattice.symmetry: raise NotImplementedError('disorientation between different symmetry classes not supported yet.') mySymEqs = self.equivalent if SST else self.equivalent[0] #ToDo: This is just me! # take all or only first sym operation otherSymEqs = other.equivalent for i,sA in enumerate(mySymEqs): aInv = sA.rotation.inversed() for j,sB in enumerate(otherSymEqs): b = sB.rotation r = b*aInv for k in range(2): r.inverse() breaker = self.lattice.in_FZ(r.as_Rodrigues(vector=True)) \ and (not SST or other.lattice.in_disorientation_SST(r.as_Rodrigues(vector=True))) if breaker: break if breaker: break if breaker: break return (Orientation(r,self.lattice), i,j, k == 1) if symmetries else r # disorientation ... # ... own sym, other sym, # self-->other: True, self<--other: False @property def in_FZ(self): """Check if orientations fall into Fundamental Zone.""" return self.lattice.in_FZ(self.rotation.as_Rodrigues(vector=True)) @property def equivalent(self): """ Orientations which are symmetrically equivalent. One dimension (length according to number of symmetrically equivalent orientations) is added to the left of the Rotation array. """ o = self.lattice.symmetry.symmetry_operations o = o.reshape(o.shape[:1]+(1,)*len(self.rotation.shape)+(4,)) o = Rotation(np.broadcast_to(o,o.shape[:1]+self.rotation.quaternion.shape)) s = np.broadcast_to(self.rotation.quaternion,o.shape[:1]+self.rotation.quaternion.shape) return self.__class__(o@Rotation(s),self.lattice) def related(self,model): """ Orientations related by the given orientation relationship. One dimension (length according to number of related orientations) is added to the left of the Rotation array. """ o = Rotation.from_matrix(self.lattice.relation_operations(model)['rotations']).as_quaternion() o = o.reshape(o.shape[:1]+(1,)*len(self.rotation.shape)+(4,)) o = Rotation(np.broadcast_to(o,o.shape[:1]+self.rotation.quaternion.shape)) s = np.broadcast_to(self.rotation.quaternion,o.shape[:1]+self.rotation.quaternion.shape) return self.__class__(o@Rotation(s),self.lattice.relation_operations(model)['lattice']) @property def reduced(self): """Transform orientation to fall into fundamental zone according to symmetry.""" eq = self.equivalent in_FZ = eq.in_FZ # remove duplicates (occur for highly symmetric orientations) found = np.zeros_like(in_FZ[0],dtype=bool) q = self.rotation.quaternion[0] for s in range(in_FZ.shape[0]): #something fishy... why does q needs to be initialized? q = np.where(np.expand_dims(np.logical_and(in_FZ[s],~found),-1),eq.rotation.quaternion[s],q) found = np.logical_or(in_FZ[s],found) return self.__class__(q,self.lattice) def inverse_pole(self,axis,proper=False,SST=True): """Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST).""" if SST: eq = self.equivalent pole = eq.rotation @ np.broadcast_to(axis/np.linalg.norm(axis),eq.rotation.shape+(3,)) in_SST = self.lattice.in_SST(pole,proper=proper) # remove duplicates (occur for highly symmetric orientations) found = np.zeros_like(in_SST[0],dtype=bool) p = pole[0] for s in range(in_SST.shape[0]): p = np.where(np.expand_dims(np.logical_and(in_SST[s],~found),-1),pole[s],p) found = np.logical_or(in_SST[s],found) return p else: return self.rotation @ np.broadcast_to(axis/np.linalg.norm(axis),self.rotation.shape+(3,)) def IPF_color(self,axis): #ToDo axis or direction? """TSL color of inverse pole figure for given axis.""" eq = self.equivalent pole = eq.rotation @ np.broadcast_to(axis/np.linalg.norm(axis),eq.rotation.shape+(3,)) in_SST, color = self.lattice.in_SST(pole,color=True) # remove duplicates (occur for highly symmetric orientations) found = np.zeros_like(in_SST[0],dtype=bool) c = color[0] for s in range(in_SST.shape[0]): c = np.where(np.expand_dims(np.logical_and(in_SST[s],~found),-1),color[s],c) found = np.logical_or(in_SST[s],found) return c # ToDo: Discuss vectorization/calling signature @staticmethod def from_average(orientations, weights = []): """Create orientation from average of list of orientations.""" # further read: Orientation distribution analysis in deformed grains # https://doi.org/10.1107/S0021889801003077 if not all(isinstance(item, Orientation) for item in orientations): raise TypeError("Only instances of Orientation can be averaged.") closest = [] ref = orientations[0] for o in orientations: closest.append(o.equivalent[ ref.disorientation(o, SST = False, # select (o[ther]'s) sym orientation symmetries = True)[2]].rotation) # with lowest misorientation return Orientation(Rotation.from_average(closest,weights),ref.lattice) # ToDo: Discuss vectorization/calling signature def average(self,other): """Calculate the average rotation.""" return Orientation.from_average([self,other])