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