DAMASK_EICMD/python/damask/_orientation.py

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import numpy as np
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from . import Lattice
from . import Rotation
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class Orientation:
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"""
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:
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self.rotation = Rotation.from_quaternion(rotation) # assume quaternion
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if self.rotation.quaternion.shape != (4,):
raise NotImplementedError('Support for multiple rotations missing')
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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.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation
otherSymEqs = other.equivalentOrientations()
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.symmetry.inFZ(r.asRodrigues(vector=True)) \
and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues(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
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def inFZ(self):
return self.lattice.symmetry.inFZ(self.rotation.asRodrigues(vector=True))
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def equivalentOrientations(self,members=[]):
"""List of orientations which are symmetrically equivalent."""
try:
iter(members) # asking for (even empty) list of members?
except TypeError:
return self.__class__(self.lattice.symmetry.symmetryOperations(members)*self.rotation,self.lattice) # no, return rotation object
else:
return [self.__class__(q*self.rotation,self.lattice) \
for q in self.lattice.symmetry.symmetryOperations(members)] # yes, return list of rotations
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def relatedOrientations(self,model):
"""List of orientations related by the given orientation relationship."""
r = self.lattice.relationOperations(model)
return [self.__class__(o*self.rotation,r['lattice']) for o in r['rotations']]
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def reduced(self):
"""Transform orientation to fall into fundamental zone according to symmetry."""
for me in self.equivalentOrientations():
if self.lattice.symmetry.inFZ(me.rotation.asRodrigues(vector=True)): break
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return self.__class__(me.rotation,self.lattice)
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def inversePole(self,
axis,
proper = False,
SST = True):
"""Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)."""
if SST: # pole requested to be within SST
for i,o in enumerate(self.equivalentOrientations()): # test all symmetric equivalent quaternions
pole = o.rotation*axis # align crystal direction to axis
if self.lattice.symmetry.inSST(pole,proper): break # found SST version
else:
pole = self.rotation*axis # align crystal direction to axis
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return (pole,i if SST else 0)
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def IPFcolor(self,axis):
"""TSL color of inverse pole figure for given axis."""
color = np.zeros(3,'d')
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for o in self.equivalentOrientations():
pole = o.rotation*axis # align crystal direction to axis
inSST,color = self.lattice.symmetry.inSST(pole,color=True)
if inSST: break
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return color
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@staticmethod
def fromAverage(orientations,
weights = []):
"""Create orientation from average of list of orientations."""
if not all(isinstance(item, Orientation) for item in orientations):
raise TypeError("Only instances of Orientation can be averaged.")
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closest = []
ref = orientations[0]
for o in orientations:
closest.append(o.equivalentOrientations(
ref.disorientation(o,
SST = False, # select (o[ther]'s) sym orientation
symmetries = True)[2]).rotation) # with lowest misorientation
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return Orientation(Rotation.fromAverage(closest,weights),ref.lattice)
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def average(self,other):
"""Calculate the average rotation."""
return Orientation.fromAverage([self,other])