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])