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using new Orientation class

This commit is contained in:
Martin Diehl 2019-02-24 08:08:14 +01:00
parent 9dc8dff4b1
commit d3ac3cc0f5
8 changed files with 244 additions and 727 deletions
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4
.gitlab-ci.yml
View File

@ -207,7 +207,9 @@ Post_ParaviewRelated:
Post_OrientationConversion:
stage: postprocessing
script: OrientationConversion/test.py
script:
- OrientationConversion/test.py
- OrientationConversion/test2.py
except:
- master
- release

2
PRIVATE

@ -1 +1 @@
Subproject commit f0090997df817f0a0b5a480a60e81929875b1010
Subproject commit 8deb37dd4526fb5e1425fe1d2360508d01b6ac3e

8
processing/post/addIPFcolor.py
View File

@ -41,6 +41,10 @@ parser.set_defaults(pole = (0.0,0.0,1.0),
(options, filenames) = parser.parse_args()
# damask.Orientation requires Bravais lattice, but we are only interested in symmetry
symmetry2lattice={'cubic':'bcc','hexagonal':'hex','tetragonal':'bct'}
lattice = symmetry2lattice[options.symmetry]
pole = np.array(options.pole)
pole /= np.linalg.norm(pole)
@ -78,8 +82,8 @@ for name in filenames:
outputAlive = True
while outputAlive and table.data_read(): # read next data line of ASCII table
o = damask.Orientation(quaternion = np.array(list(map(float,table.data[column:column+4]))),
symmetry = options.symmetry).reduced()
o = damask.Orientation(np.array(list(map(float,table.data[column:column+4]))),
lattice = lattice).reduced()
table.data_append(o.IPFcolor(pole))
outputAlive = table.data_write() # output processed line

4
processing/post/addPole.py
View File

@ -75,9 +75,9 @@ for name in filenames:
# ------------------------------------------ process data ------------------------------------------
outputAlive = True
while outputAlive and table.data_read(): # read next data line of ASCII table
o = damask.Orientation(quaternion = np.array(list(map(float,table.data[column:column+4]))))
o = damask.Rotation(np.array(list(map(float,table.data[column:column+4]))))
rotatedPole = o.quaternion*pole # rotate pole according to crystal orientation
rotatedPole = o*pole # rotate pole according to crystal orientation
(x,y) = rotatedPole[0:2]/(1.+abs(pole[2])) # stereographic projection
table.data_append([np.sqrt(x*x+y*y),np.arctan2(y,x)] if options.polar else [x,y]) # cartesian coordinates

2
processing/post/rotateData.py
View File

@ -31,7 +31,7 @@ parser.add_option('--degrees',
action = 'store_true',
help = 'angles are given in degrees')
parser.set_defaults(rotation = (0.,1.,0.,0.), # no rotation about 1,0,0
parser.set_defaults(rotation = (0.,1.,1.,1.), # no rotation about 1,1,1
degrees = False,
)

3
processing/pre/geom_fromTable.py
View File

@ -52,11 +52,8 @@ parser.add_option('--crystallite',
parser.set_defaults(symmetry = [damask.Symmetry.lattices[-1]],
tolerance = 0.0,
degrees = False,
homogenization = 1,
crystallite = 1,
verbose = False,
pos = 'pos',
)

2
python/damask/__init__.py
View File

@ -13,7 +13,7 @@ from .asciitable import ASCIItable # noqa
from .config import Material # noqa
from .colormaps import Colormap, Color # noqa
from .orientation import Quaternion, Symmetry, Rotation, Orientation # noqa
from .orientation import Symmetry, Lattice, Rotation, Orientation # noqa
#from .block import Block # only one class
from .result import Result # noqa

624
python/damask/orientation.py
View File

@ -1,13 +1,13 @@
# -*- coding: UTF-8 no BOM -*-
import math,os
import math
import numpy as np
from . import Lambert
P = -1
####################################################################################################
class Quaternion2:
class Quaternion:
u"""
Quaternion with basic operations
@ -50,7 +50,7 @@ class Quaternion2:
def __add__(self, other):
"""Addition"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
return self.__class__(q=self.q + other.q,
p=self.p + other.p)
else:
@ -58,7 +58,7 @@ class Quaternion2:
def __iadd__(self, other):
"""In-place addition"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
self.q += other.q
self.p += other.p
return self
@ -72,7 +72,7 @@ class Quaternion2:
def __sub__(self, other):
"""Subtraction"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
return self.__class__(q=self.q - other.q,
p=self.p - other.p)
else:
@ -80,7 +80,7 @@ class Quaternion2:
def __isub__(self, other):
"""In-place subtraction"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
self.q -= other.q
self.p -= other.p
return self
@ -96,7 +96,7 @@ class Quaternion2:
def __mul__(self, other):
"""Multiplication with quaternion or scalar"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
return self.__class__(q=self.q*other.q - np.dot(self.p,other.p),
p=self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p))
elif isinstance(other, (int, float)):
@ -107,7 +107,7 @@ class Quaternion2:
def __imul__(self, other):
"""In-place multiplication with quaternion or scalar"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
self.q = self.q*other.q - np.dot(self.p,other.p)
self.p = self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p)
return self
@ -120,7 +120,7 @@ class Quaternion2:
def __truediv__(self, other):
"""Divsion with quaternion or scalar"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
s = other.conjugate()/abs(other)**2.
return self.__class__(q=self.q * s,
p=self.p * s)
@ -133,7 +133,7 @@ class Quaternion2:
def __itruediv__(self, other):
"""In-place divsion with quaternion or scalar"""
if isinstance(other, Quaternion2):
if isinstance(other, Quaternion):
s = other.conjugate()/abs(other)**2.
self *= s
return self
@ -215,7 +215,8 @@ class Rotation:
u"""
Orientation stored as unit quaternion.
All methods and naming conventions based on Rowenhorst_etal2015
Following: D Rowenhorst et al. Consistent representations of and conversions between 3D rotations
10.1088/0965-0393/23/8/083501
Convention 1: coordinate frames are right-handed
Convention 2: a rotation angle ω is taken to be positive for a counterclockwise rotation
when viewing from the end point of the rotation axis towards the origin
@ -242,10 +243,10 @@ class Rotation:
If a quaternion is given, it needs to comply with the convection. Use .fromQuaternion
to check the input.
"""
if isinstance(quaternion,Quaternion2):
if isinstance(quaternion,Quaternion):
self.quaternion = quaternion.copy()
else:
self.quaternion = Quaternion2(q=quaternion[0],p=quaternion[1:4])
self.quaternion = Quaternion(q=quaternion[0],p=quaternion[1:4])
self.quaternion.homomorph() # ToDo: Needed?
def __repr__(self):
@ -455,373 +456,6 @@ class Rotation:
return self.__class__(other.quaternion*self.quaternion.conjugated())
# ******************************************************************************************
class Quaternion:
u"""
Orientation represented as unit quaternion.
All methods and naming conventions based on Rowenhorst_etal2015
Convention 1: coordinate frames are right-handed
Convention 2: a rotation angle ω is taken to be positive for a counterclockwise rotation
when viewing from the end point of the rotation axis towards the origin
Convention 3: rotations will be interpreted in the passive sense
Convention 4: Euler angle triplets are implemented using the Bunge convention,
with the angular ranges as [0, 2π],[0, π],[0, 2π]
Convention 5: the rotation angle ω is limited to the interval [0, π]
Convention 6: P = -1 (as default)
w is the real part, (x, y, z) are the imaginary parts.
Vector "a" (defined in coordinate system "A") is passively rotated
resulting in new coordinates "b" when expressed in system "B".
b = Q * a
b = np.dot(Q.asMatrix(),a)
"""
def __init__(self,
quat = None,
q = 1.0,
p = np.zeros(3,dtype=float)):
"""Initializes to identity unless specified"""
self.q = quat[0] if quat is not None else q
self.p = np.array(quat[1:4]) if quat is not None else p
self.homomorph()
def __iter__(self):
"""Components"""
return iter(self.asList())
def __copy__(self):
"""Copy"""
return self.__class__(q=self.q,p=self.p.copy())
copy = __copy__
def __repr__(self):
"""Readable string"""
return 'Quaternion(real={q:+.6f}, imag=<{p[0]:+.6f}, {p[1]:+.6f}, {p[2]:+.6f}>)'.format(q=self.q,p=self.p)
def __pow__(self, exponent):
"""Power"""
omega = math.acos(self.q)
return self.__class__(q= math.cos(exponent*omega),
p=self.p * math.sin(exponent*omega)/math.sin(omega))
def __ipow__(self, exponent):
"""In-place power"""
omega = math.acos(self.q)
self.q = math.cos(exponent*omega)
self.p *= math.sin(exponent*omega)/math.sin(omega)
return self
def __mul__(self, other):
"""Multiplication"""
# Rowenhorst_etal2015 MSMSE: value of P is selected as -1
P = -1.0
try: # quaternion
return self.__class__(q=self.q*other.q - np.dot(self.p,other.p),
p=self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p))
except: pass
try: # vector (perform passive rotation)
( x, y, z) = self.p
(Vx,Vy,Vz) = other[0:3]
A = self.q*self.q - np.dot(self.p,self.p)
B = 2.0 * (x*Vx + y*Vy + z*Vz)
C = 2.0 * P*self.q
return np.array([
A*Vx + B*x + C*(y*Vz - z*Vy),
A*Vy + B*y + C*(z*Vx - x*Vz),
A*Vz + B*z + C*(x*Vy - y*Vx),
])
except: pass
try: # scalar
return self.__class__(q=self.q*other,
p=self.p*other)
except:
return self.copy()
def __imul__(self, other):
"""In-place multiplication"""
# Rowenhorst_etal2015 MSMSE: value of P is selected as -1
P = -1.0
try: # Quaternion
self.q = self.q*other.q - np.dot(self.p,other.p)
self.p = self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p)
except: pass
return self
def __div__(self, other):
"""Division"""
if isinstance(other, (int,float)):
return self.__class__(q=self.q / other,
p=self.p / other)
else:
return NotImplemented
def __idiv__(self, other):
"""In-place division"""
if isinstance(other, (int,float)):
self.q /= other
self.p /= other
return self
def __add__(self, other):
"""Addition"""
if isinstance(other, Quaternion):
return self.__class__(q=self.q + other.q,
p=self.p + other.p)
else:
return NotImplemented
def __iadd__(self, other):
"""In-place addition"""
if isinstance(other, Quaternion):
self.q += other.q
self.p += other.p
return self
def __sub__(self, other):
"""Subtraction"""
if isinstance(other, Quaternion):
return self.__class__(q=self.q - other.q,
p=self.p - other.p)
else:
return NotImplemented
def __isub__(self, other):
"""In-place subtraction"""
if isinstance(other, Quaternion):
self.q -= other.q
self.p -= other.p
return self
def __neg__(self):
"""Additive inverse"""
self.q = -self.q
self.p = -self.p
return self
def __abs__(self):
"""Norm"""
return math.sqrt(self.q ** 2 + np.dot(self.p,self.p))
magnitude = __abs__
def __eq__(self,other):
"""Equal (sufficiently close) to each other"""
return np.isclose(( self-other).magnitude(),0.0) \
or np.isclose((-self-other).magnitude(),0.0)
def __ne__(self,other):
"""Not equal (sufficiently close) to each other"""
return not self.__eq__(other)
def __cmp__(self,other):
"""Linear ordering"""
return (1 if np.linalg.norm(self.asRodrigues()) > np.linalg.norm(other.asRodrigues()) else 0) \
- (1 if np.linalg.norm(self.asRodrigues()) < np.linalg.norm(other.asRodrigues()) else 0)
def magnitude_squared(self):
return self.q ** 2 + np.dot(self.p,self.p)
def normalize(self):
d = self.magnitude()
if d > 0.0:
self.q /= d
self.p /= d
return self
def conjugate(self):
self.p = -self.p
return self
def homomorph(self):
if self.q < 0.0:
self.q = -self.q
self.p = -self.p
return self
def normalized(self):
return self.copy().normalize()
def conjugated(self):
return self.copy().conjugate()
def homomorphed(self):
return self.copy().homomorph()
def asList(self):
return [self.q]+list(self.p)
def asM(self): # to find Averaging Quaternions (see F. Landis Markley et al.)
return np.outer(self.asList(),self.asList())
def asMatrix(self):
# Rowenhorst_etal2015 MSMSE: value of P is selected as -1
P = -1.0
qbarhalf = 0.5*(self.q**2 - np.dot(self.p,self.p))
return 2.0*np.array(
[[ qbarhalf + self.p[0]**2 ,
self.p[0]*self.p[1] -P* self.q*self.p[2],
self.p[0]*self.p[2] +P* self.q*self.p[1] ],
[ self.p[0]*self.p[1] +P* self.q*self.p[2],
qbarhalf + self.p[1]**2 ,
self.p[1]*self.p[2] -P* self.q*self.p[0] ],
[ self.p[0]*self.p[2] -P* self.q*self.p[1],
self.p[1]*self.p[2] +P* self.q*self.p[0],
qbarhalf + self.p[2]**2 ],
])
def asAngleAxis(self,
degrees = False,
flat = False):
angle = 2.0*math.acos(self.q)
if np.isclose(angle,0.0):
angle = 0.0
axis = np.array([0.0,0.0,1.0])
elif np.isclose(self.q,0.0):
angle = math.pi
axis = self.p
else:
axis = np.sign(self.q)*self.p/np.linalg.norm(self.p)
angle = np.degrees(angle) if degrees else angle
return np.hstack((angle,axis)) if flat else (angle,axis)
def asRodrigues(self):
return np.inf*np.ones(3) if np.isclose(self.q,0.0) else self.p/self.q
# # Static constructors
@classmethod
def fromIdentity(cls):
return cls()
@classmethod
def fromRandom(cls,randomSeed = None):
import binascii
if randomSeed is None:
randomSeed = int(binascii.hexlify(os.urandom(4)),16)
np.random.seed(randomSeed)
r = np.random.random(3)
A = math.sqrt(max(0.0,r[2]))
B = math.sqrt(max(0.0,1.0-r[2]))
w = math.cos(2.0*math.pi*r[0])*A
x = math.sin(2.0*math.pi*r[1])*B
y = math.cos(2.0*math.pi*r[1])*B
z = math.sin(2.0*math.pi*r[0])*A
return cls(quat=[w,x,y,z])
@classmethod
def fromRodrigues(cls, rodrigues):
if not isinstance(rodrigues, np.ndarray): rodrigues = np.array(rodrigues)
norm = np.linalg.norm(rodrigues)
halfangle = math.atan(norm)
s = math.sin(halfangle)
c = math.cos(halfangle)
return cls(q=c,p=s*rodrigues/norm)
@classmethod
def fromAngleAxis(cls,
angle,
axis,
degrees = False):
if not isinstance(axis, np.ndarray): axis = np.array(axis,dtype=float)
axis = axis.astype(float)/np.linalg.norm(axis)
angle = np.radians(angle) if degrees else angle
s = math.sin(0.5 * angle)
c = math.cos(0.5 * angle)
return cls(q=c,p=axis*s)
@classmethod
def fromEulers(cls,
eulers,
degrees = False):
if not isinstance(eulers, np.ndarray): eulers = np.array(eulers,dtype=float)
eulers = np.radians(eulers) if degrees else eulers
sigma = 0.5*(eulers[0]+eulers[2])
delta = 0.5*(eulers[0]-eulers[2])
c = np.cos(0.5*eulers[1])
s = np.sin(0.5*eulers[1])
# Rowenhorst_etal2015 MSMSE: value of P is selected as -1
P = -1.0
w = c * np.cos(sigma)
x = -P * s * np.cos(delta)
y = -P * s * np.sin(delta)
z = -P * c * np.sin(sigma)
return cls(quat=[w,x,y,z])
# Modified Method to calculate Quaternion from Orientation Matrix,
# Source: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
@classmethod
def fromMatrix(cls, m):
if m.shape != (3,3) and np.prod(m.shape) == 9:
m = m.reshape(3,3)
# Rowenhorst_etal2015 MSMSE: value of P is selected as -1
P = -1.0
w = 0.5*math.sqrt(max(0.0,1.0+m[0,0]+m[1,1]+m[2,2]))
x = P*0.5*math.sqrt(max(0.0,1.0+m[0,0]-m[1,1]-m[2,2]))
y = P*0.5*math.sqrt(max(0.0,1.0-m[0,0]+m[1,1]-m[2,2]))
z = P*0.5*math.sqrt(max(0.0,1.0-m[0,0]-m[1,1]+m[2,2]))
x *= -1 if m[2,1] < m[1,2] else 1
y *= -1 if m[0,2] < m[2,0] else 1
z *= -1 if m[1,0] < m[0,1] else 1
return cls(quat=np.array([w,x,y,z])/math.sqrt(w**2 + x**2 + y**2 + z**2))
@classmethod
def new_interpolate(cls, q1, q2, t):
"""
Interpolation
See http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070017872_2007014421.pdf
for (another?) way to interpolate quaternions.
"""
assert isinstance(q1, Quaternion) and isinstance(q2, Quaternion)
Q = cls()
costheta = q1.q*q2.q + np.dot(q1.p,q2.p)
if costheta < 0.:
costheta = -costheta
q1 = q1.conjugated()
elif costheta > 1.:
costheta = 1.
theta = math.acos(costheta)
if abs(theta) < 0.01:
Q.q = q2.q
Q.p = q2.p
return Q
sintheta = math.sqrt(1.0 - costheta * costheta)
if abs(sintheta) < 0.01:
Q.q = (q1.q + q2.q) * 0.5
Q.p = (q1.p + q2.p) * 0.5
return Q
ratio1 = math.sin((1.0 - t) * theta) / sintheta
ratio2 = math.sin( t * theta) / sintheta
Q.q = q1.q * ratio1 + q2.q * ratio2
Q.p = q1.p * ratio1 + q2.p * ratio2
return Q
# ******************************************************************************************
class Symmetry:
"""
@ -932,26 +566,16 @@ class Symmetry:
[ 1.0,0.0,0.0,0.0 ],
]
return list(map(Quaternion,
np.array(symQuats)[np.atleast_1d(np.array(who)) if who != [] else range(len(symQuats))]))
def equivalentQuaternions(self,
quaternion,
who = []):
"""List of symmetrically equivalent quaternions based on own symmetry."""
return [q*quaternion for q in self.symmetryQuats(who)]
return np.array(symQuats)
def inFZ(self,R):
"""Check whether given Rodrigues vector falls into fundamental zone of own symmetry."""
if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentally passed quaternion
# fundamental zone in Rodrigues space is point symmetric around origin
"""
Check whether given Rodrigues vector falls into fundamental zone of own symmetry.
if R.shape[0]==4: # transition old (length not stored separately) to new
Fundamental zone in Rodrigues space is point symmetric around origin.
"""
Rabs = abs(R[0:3]*R[3])
else:
Rabs = abs(R)
if self.lattice == 'cubic':
return math.sqrt(2.0)-1.0 >= Rabs[0] \
@ -1367,27 +991,30 @@ class Lattice:
relationship = models[model]
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()),
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()), # target lattice
'rotations':[] }
myPlane_id = relationship['mapping'][self.lattice]
otherPlane_id = (myPlane_id+1)%2
myDir_id = myPlane_id +2
otherDir_id = otherPlane_id +2
for miller in np.hstack((relationship['planes'],relationship['directions'])):
myPlane = miller[myPlane_id]/ np.linalg.norm(miller[myPlane_id])
myDir = miller[myDir_id]/ np.linalg.norm(miller[myDir_id])
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane]).T
otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id])
otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id])
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane]).T
otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane]).T
r['rotations'].append(Rotation.fromMatrix(np.dot(otherMatrix,myMatrix.T)))
return r
class Orientation2:
class Orientation:
"""
Crystallographic orientation
@ -1431,27 +1058,23 @@ class Orientation2:
for i,sA in enumerate(mySymEqs):
for j,sB in enumerate(otherSymEqs):
theQ = sB.rotation*mis*sA.rotation.inversed()
r = sB.rotation*mis*sA.rotation.inversed()
for k in range(2):
theQ.inversed()
breaker = self.lattice.symmetry.inFZ(theQ.asRodrigues()) \
and (not SST or other.lattice.symmetry.inDisorientationSST(theQ.asRodrigues()))
r.inversed()
breaker = self.lattice.symmetry.inFZ(r.asRodrigues()) \
and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues()))
if breaker: break
if breaker: break
if breaker: break
# disorientation, own sym, other sym, self-->other: True, self<--other: False
return theQ
return r
def inFZ(self):
return self.lattice.symmetry.inFZ(self.rotation.asRodrigues())
def equivalentOrientations(self):
"""List of orientations which are symmetrically equivalent"""
q = self.lattice.symmetry.symmetryQuats()
q2 = [Quaternion2(q=a.asList()[0],p=a.asList()[1:4]) for a in q] # convert Quaternion to Quaternion2
x = [self.__class__(q3*self.rotation.quaternion,self.lattice) for q3 in q2]
return x
return [self.__class__(q*self.rotation.quaternion,self.lattice) for q in self.lattice.symmetry.symmetryQuats()]
def relatedOrientations(self,model):
"""List of orientations related by the given orientation relationship"""
@ -1465,176 +1088,68 @@ class Orientation2:
return self.__class__(me.rotation,self.lattice)
# ******************************************************************************************
class Orientation:
__slots__ = ['quaternion','symmetry']
def __init__(self,
quaternion = Quaternion.fromIdentity(),
Rodrigues = None,
Eulers = None,
random = False, # integer to have a fixed seed or True for real random
symmetry = None,
degrees = False,
):
if random: # produce random orientation
if isinstance(random, bool ):
self.quaternion = Quaternion.fromRandom()
else:
self.quaternion = Quaternion.fromRandom(randomSeed=random)
elif isinstance(Eulers, np.ndarray) and Eulers.shape == (3,): # based on given Euler angles
self.quaternion = Quaternion.fromEulers(Eulers,degrees=degrees)
elif isinstance(Rodrigues, np.ndarray) and Rodrigues.shape == (3,): # based on given Rodrigues vector
self.quaternion = Quaternion.fromRodrigues(Rodrigues)
elif isinstance(quaternion, Quaternion): # based on given quaternion
self.quaternion = quaternion.homomorphed()
elif (isinstance(quaternion, np.ndarray) and quaternion.shape == (4,)) or \
(isinstance(quaternion, list) and len(quaternion) == 4 ): # based on given quaternion-like array
self.quaternion = Quaternion(quat=quaternion).homomorphed()
self.symmetry = Symmetry(symmetry)
def __copy__(self):
"""Copy"""
return self.__class__(quaternion=self.quaternion,symmetry=self.symmetry.lattice)
copy = __copy__
def __repr__(self):
"""Value as all implemented representations"""
return '\n'.join([
'Symmetry: {}'.format(self.symmetry),
'Quaternion: {}'.format(self.quaternion),
'Matrix:\n{}'.format( '\n'.join(['\t'.join(list(map(str,self.asMatrix()[i,:]))) for i in range(3)]) ),
])
def asRodrigues(self):
return self.quaternion.asRodrigues()
rodrigues = property(asRodrigues)
def asAngleAxis(self,
degrees = False,
flat = False):
return self.quaternion.asAngleAxis(degrees,flat)
def asMatrix(self):
return self.quaternion.asMatrix()
matrix = property(asMatrix)
def inFZ(self):
return self.symmetry.inFZ(self.quaternion.asRodrigues())
def equivalentQuaternions(self,
who = []):
return self.symmetry.equivalentQuaternions(self.quaternion,who)
def equivalentOrientations(self,
who = []):
return [Orientation(quaternion = q, symmetry = self.symmetry.lattice) for q in self.equivalentQuaternions(who)]
def reduced(self):
"""Transform orientation to fall into fundamental zone according to symmetry"""
for me in self.symmetry.equivalentQuaternions(self.quaternion):
if self.symmetry.inFZ(me.asRodrigues()): break
return Orientation(quaternion=me,symmetry=self.symmetry.lattice)
def disorientation(self,
other,
SST = True):
"""
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.symmetry != other.symmetry:
raise NotImplementedError('disorientation between different symmetry classes not supported yet.')
misQ = other.quaternion*self.quaternion.conjugated()
mySymQs = self.symmetry.symmetryQuats() if SST else self.symmetry.symmetryQuats()[:1] # take all or only first sym operation
otherSymQs = other.symmetry.symmetryQuats()
for i,sA in enumerate(mySymQs):
for j,sB in enumerate(otherSymQs):
theQ = sB*misQ*sA.conjugated()
for k in range(2):
theQ.conjugate()
breaker = self.symmetry.inFZ(theQ) \
and (not SST or other.symmetry.inDisorientationSST(theQ))
if breaker: break
if breaker: break
if breaker: break
# disorientation, own sym, other sym, self-->other: True, self<--other: False
return (Orientation(quaternion = theQ,symmetry = self.symmetry.lattice),
i,j, k == 1)
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,q in enumerate(self.symmetry.equivalentQuaternions(self.quaternion)): # test all symmetric equivalent quaternions
pole = q*axis # align crystal direction to axis
if self.symmetry.inSST(pole,proper): break # found SST version
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.quaternion*axis # align crystal direction to axis
pole = self.rotation*axis # align crystal direction to axis
return (pole,i if SST else 0)
def IPFcolor(self,axis):
"""TSL color of inverse pole figure for given axis"""
color = np.zeros(3,'d')
for q in self.symmetry.equivalentQuaternions(self.quaternion):
pole = q*axis # align crystal direction to axis
inSST,color = self.symmetry.inSST(pole,color=True)
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
return color
@classmethod
def average(cls,
orientations,
multiplicity = []):
"""
Average orientation
ref: F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman.
Averaging Quaternions,
Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197.
doi: 10.2514/1.28949
usage:
a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry='hexagonal')
b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
avg = Orientation.average([a,b])
"""
if not all(isinstance(item, Orientation) for item in orientations):
raise TypeError("Only instances of Orientation can be averaged.")
# @classmethod
# def average(cls,
# orientations,
# multiplicity = []):
# """
# Average orientation
N = len(orientations)
if multiplicity == [] or not multiplicity:
multiplicity = np.ones(N,dtype='i')
# ref: F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman.
# Averaging Quaternions,
# Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197.
# doi: 10.2514/1.28949
# usage:
# a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry='hexagonal')
# b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
# avg = Orientation.average([a,b])
# """
# if not all(isinstance(item, Orientation) for item in orientations):
# raise TypeError("Only instances of Orientation can be averaged.")
reference = orientations[0] # take first as reference
for i,(o,n) in enumerate(zip(orientations,multiplicity)):
closest = o.equivalentOrientations(reference.disorientation(o,SST = False)[2])[0] # select sym orientation with lowest misorientation
M = closest.quaternion.asM() * n if i == 0 else M + closest.quaternion.asM() * n # noqa add (multiples) of this orientation to average noqa
eig, vec = np.linalg.eig(M/N)
# N = len(orientations)
# if multiplicity == [] or not multiplicity:
# multiplicity = np.ones(N,dtype='i')
return Orientation(quaternion = Quaternion(quat = np.real(vec.T[eig.argmax()])),
symmetry = reference.symmetry.lattice)
# reference = orientations[0] # take first as reference
# for i,(o,n) in enumerate(zip(orientations,multiplicity)):
# closest = o.equivalentOrientations(reference.disorientation(o,SST = False)[2])[0] # select sym orientation with lowest misorientation
# M = closest.quaternion.asM() * n if i == 0 else M + closest.quaternion.asM() * n # noqa add (multiples) of this orientation to average noqa
# eig, vec = np.linalg.eig(M/N)
# return Orientation(quaternion = Quaternion(quat = np.real(vec.T[eig.argmax()])),
# symmetry = reference.symmetry.lattice)
####################################################################################################
# Code below available according to the followin conditions on https://github.com/MarDiehl/3Drotations
# Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations
####################################################################################################
# Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
@ -1769,7 +1284,6 @@ def qu2eu(qu):
eu = np.array([np.arctan2(-P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0]) if iszero(q12) else \
np.array([np.arctan2(2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
else:
#chiInv = 1.0/chi ToDo: needed for what?
eu = np.array([np.arctan2((-P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]-qu[2]*qu[3])*chi ),
np.arctan2( 2.0*chi, q03-q12 ),
np.arctan2(( P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]+qu[2]*qu[3])*chi )])