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DAMASK_EICMD
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added optional keyword `degrees´ to q.asEulers(). 

added methods inFZ, equivalentQuaternions, and equivalentOrientations to Orientation class.
general polishing…
This commit is contained in:
Philip Eisenlohr 2015-06-21 12:05:17 +00:00
parent e310763c52
commit 2d8af638b0
1 changed files with 49 additions and 41 deletions
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72
lib/damask/orientation.py
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@ -58,36 +58,36 @@ class Quaternion:
omega = math.acos(self.w)
vRescale = math.sin(exponent*omega)/math.sin(omega)
Q = Quaternion()
Q.w = math.cos(exponent*omega)
Q.x = self.x * vRescale
Q.y = self.y * vRescale
Q.z = self.z * vRescale
Q.w = math.cos(exponent*omega)
return Q
def __ipow__(self, exponent):
omega = math.acos(self.w)
vRescale = math.sin(exponent*omega)/math.sin(omega)
self.w = np.cos(exponent*omega)
self.x *= vRescale
self.y *= vRescale
self.z *= vRescale
self.w = np.cos(exponent*omega)
return self
def __mul__(self, other):
try: # quaternion
Aw = self.w
Ax = self.x
Ay = self.y
Az = self.z
Aw = self.w
Bw = other.w
Bx = other.x
By = other.y
Bz = other.z
Bw = other.w
Q = Quaternion()
Q.w = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw
Q.x = + Ax * Bw + Ay * Bz - Az * By + Aw * Bx
Q.y = - Ax * Bz + Ay * Bw + Az * Bx + Aw * By
Q.z = + Ax * By - Ay * Bx + Az * Bw + Aw * Bz
Q.w = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw
return Q
except: pass
try: # vector (perform active rotation, i.e. q*v*q.conjugated)
@ -309,10 +309,7 @@ class Quaternion:
angle = math.atan2(y,x)
if angle < 1e-3:
return angle, np.array([1.0, 0.0, 0.0])
else:
return angle, np.array([self.x / s, self.y / s, self.z / s])
return angle, np.array([1.0, 0.0, 0.0] if angle < 1e-3 else [self.x / s, self.y / s, self.z / s])
def asRodrigues(self):
if self.w != 0.0:
@ -320,7 +317,7 @@ class Quaternion:
else:
return np.array([float('inf')]*3)
def asEulers(self,type='bunge'):
def asEulers(self,type='bunge',degrees=False):
'''
conversion taken from:
Melcher, A.; Unser, A.; Reichhardt, M.; Nestler, B.; Pötschke, M.; Selzer, M.
@ -362,7 +359,7 @@ class Quaternion:
# if angles[2] < 0.0:
# angles[2] += 2*math.pi
return angles
return np.degrees(angles) if degrees else angles
# # Static constructors
@ -407,12 +404,15 @@ class Quaternion:
@classmethod
def fromEulers(cls, eulers, type = 'Bunge'):
c1 = math.cos(eulers[0] / 2.0)
s1 = math.sin(eulers[0] / 2.0)
c2 = math.cos(eulers[1] / 2.0)
s2 = math.sin(eulers[1] / 2.0)
c3 = math.cos(eulers[2] / 2.0)
s3 = math.sin(eulers[2] / 2.0)
eulers *= 0.5 # reduce to half angles
c1 = math.cos(eulers[0])
s1 = math.sin(eulers[0])
c2 = math.cos(eulers[1])
s2 = math.sin(eulers[1])
c3 = math.cos(eulers[2])
s3 = math.sin(eulers[2])
if type.lower() == 'bunge' or type.lower() == 'zxz':
w = c1 * c2 * c3 - s1 * c2 * s3
@ -797,10 +797,19 @@ class Orientation:
def asMatrix(self):
return self.quaternion.asMatrix()
def inFZ(self):
return self.symmetry.inFZ(self.quaternion.asRodrigues())
def equivalentQuaternions(self):
return self.symmetry.equivalentQuaternions(self.quaternion)
def equivalentOrientations(self):
return map(lambda q: Orientation(quaternion=q,symmetry=self.symmetry.lattice),
self.equivalentQuaternions())
def reduced(self):
'''
Transform orientation to fall into fundamental zone according to own (or given) symmetry
Transform orientation to fall into fundamental zone according to symmetry
'''
for me in self.symmetry.equivalentQuaternions(self.quaternion):
@ -821,9 +830,7 @@ class Orientation:
for me in self.symmetry.equivalentQuaternions(self.quaternion):
me.conjugate()
for they in other.symmetry.equivalentQuaternions(other.quaternion):
# theQ = me * they
theQ = they * me
# if theQ.x < 0.0 or theQ.y < 0.0 or theQ.z < 0.0: theQ.conjugate() # speed up scanning since minimum angle is usually found for positive x,y,z
breaker = lowerSymmetry.inDisorientationSST(theQ.asRodrigues()) #\
# or lowerSymmetry.inDisorientationSST(theQ.conjugated().asRodrigues())
if breaker: break
@ -838,9 +845,9 @@ class Orientation:
'''
if SST: # pole requested to be within SST
for i,q in enumerate(self.symmetry.equivalentQuaternions(self.quaternion)): # test all symmetric equivalent orientations
for i,q in enumerate(self.symmetry.equivalentQuaternions(self.quaternion)): # test all symmetric equivalent quaternions
pole = q.conjugated()*axis # align crystal direction to axis
if self.symmetry.inSST(pole): print i;break # found SST version
if self.symmetry.inSST(pole): break # found SST version
else:
pole = self.quaternion.conjugated()*axis # align crystal direction to axis
@ -876,11 +883,11 @@ class Orientation:
if not all(isinstance(item, Orientation) for item in orientationList):
raise TypeError("Only instances of Orientation can be averaged.")
n = len(orientationList)
tmp_m = orientationList.pop(0).quaternion.asM()
for tmp_o in orientationList:
tmp_m += tmp_o.quaternion.asM()
eig, vec = np.linalg.eig(tmp_m/n)
N = len(orientationList)
M = orientationList.pop(0).quaternion.asM()
for o in orientationList:
M += o.quaternion.asM()
eig, vec = np.linalg.eig(M/N)
return Orientation(quaternion = Quaternion(quatArray = vec.T[eig.argmax()]))
@ -1082,15 +1089,16 @@ class Orientation:
[[ 1, 0, 0],[ 1, 1, 0]]]),
}
myPlane = planes [relationModel][variant,me]
myPlane /= np.linalg.norm(myPlane)
myNormal = normals[relationModel][variant,me]
myPlane = myPlane/np.linalg.norm(myPlane)
myNormal = myNormal/np.linalg.norm(myNormal)
myNormal /= np.linalg.norm(myNormal)
myMatrix = np.array([myPlane,myNormal,np.cross(myNormal,myPlane)])
otherPlane = planes [relationModel][variant,other]
otherPlane /= np.linalg.norm(otherPlane)
otherNormal = normals[relationModel][variant,other]
otherPlane = otherPlane/np.linalg.norm(otherPlane)
otherNormal = otherNormal/np.linalg.norm(otherNormal)
otherNormal /= np.linalg.norm(otherNormal)
otherMatrix = np.array([otherPlane,otherNormal,np.cross(otherNormal,otherPlane)])
myMatrix = np.dot(self.asMatrix(),myMatrix)
return Orientation(matrix=np.dot(otherMatrix.T,myMatrix))
return Orientation(matrix=np.dot(otherMatrix.T,myMatrix)) # no symmetry information ??