203 lines
7.8 KiB
Python
203 lines
7.8 KiB
Python
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])
|