reflect recent changes in orientation class
This commit is contained in:
Chen Zhang
parent
be4068661b
commit
ba418a5c97
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@ -316,18 +316,6 @@ cdef class Quaternion:
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self.z = 0.0
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return self
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def rotateBy_angleaxis(self, angle, axis):
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self *= Quaternion.fromAngleAxis(angle, axis)
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return self
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def rotateBy_Eulers(self, eulers):
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self *= Quaternion.fromEulers(eulers, type)
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return self
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def rotateBy_matrix(self, m):
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self *= Quaternion.fromMatrix(m)
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return self
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def normalize(self):
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cdef double d
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@ -386,6 +374,7 @@ cdef class Quaternion:
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[ 2.0*(self.x*self.z-self.y*self.w), 2.0*(self.x*self.w+self.y*self.z), 1.0-2.0*(self.x*self.x+self.y*self.y)]])
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def asAngleAxis(self):
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# keep the return as radians for simplicity
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cdef double s,x,y
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if self.w > 1:
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@ -396,8 +385,12 @@ cdef class Quaternion:
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y = 2*self.w * s
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angle = math.atan2(y,x)
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if angle < 0.0:
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angle *= -1.0
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s *= -1.0
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return angle, np.array([1.0, 0.0, 0.0] if angle < 1e-3 else [self.x/s, self.y/s, self.z/s])
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return (angle,
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np.array([1.0, 0.0, 0.0] if np.abs(angle) < 1e-3 else [self.x/s, self.y/s, self.z/s]) )
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def asRodrigues(self):
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if self.w != 0.0:
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@ -405,8 +398,12 @@ cdef class Quaternion:
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else:
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return np.array([float('inf')]*3)
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def asEulers(self,type='bunge',degrees=False):
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"""conversion taken from:
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def asEulers(self,
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type='bunge',
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degrees=False,
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standardRange=False):
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"""
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CONVERSION TAKEN FROM:
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Melcher, A.; Unser, A.; Reichhardt, M.; Nestler, B.; Pötschke, M.; Selzer, M.
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Conversion of EBSD data by a quaternion based algorithm to be used for grain structure simulations
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Technische Mechanik 30 (2010) pp 401--413
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@ -416,11 +413,11 @@ cdef class Quaternion:
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angles = [0.0,0.0,0.0]
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if type.lower() == 'bunge' or type.lower() == 'zxz':
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if abs(self.x - self.y) < 1e-8:
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if abs(self.x) < 1e-4 and abs(self.y) < 1e-4:
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x = self.w**2 - self.z**2
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y = 2.*self.w*self.z
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angles[0] = math.atan2(y,x)
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elif abs(self.w - self.z) < 1e-8:
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elif abs(self.w) < 1e-4 and abs(self.z) < 1e-4:
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x = self.x**2 - self.y**2
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y = 2.*self.x*self.y
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angles[0] = math.atan2(y,x)
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@ -439,6 +436,12 @@ cdef class Quaternion:
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x = (self.w * self.x + self.y * self.z)/2./chi
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y = (self.z * self.x - self.y * self.w)/2./chi
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angles[2] = math.atan2(y,x)
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if standardRange:
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angles[0] %= 2*math.pi
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if angles[1] < 0.0:
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angles[1] += math.pi
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angles[2] *= -1.0
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angles[2] %= 2*math.pi
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return np.degrees(angles) if degrees else angles
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@ -524,7 +527,7 @@ cdef class Quaternion:
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if m.shape != (3,3) and np.prod(m.shape) == 9:
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m = m.reshape(3,3)
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tr=m[0,0]+m[1,1]+m[2,2]
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tr=np.trace(m)
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if tr > 0.00000001:
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s = math.sqrt(tr + 1.0)*2.0
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@ -663,77 +666,82 @@ cdef class Symmetry:
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def __cmp__(self,other):
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return cmp(self.lattice,other.lattice)
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def symmetryQuats(self):
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'''
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List of symmetry operations as quaternions.
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'''
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if self.lattice == 'cubic':
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symQuats = [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ],
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[ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2), 0.0, -0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
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[ 0.0, -0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
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[ 0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, -0.5 ],
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[-0.5, 0.5, -0.5, 0.5 ],
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[-0.5, -0.5, 0.5, 0.5 ],
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[-0.5, -0.5, 0.5, -0.5 ],
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[-0.5, -0.5, -0.5, 0.5 ],
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[-0.5, 0.5, -0.5, -0.5 ],
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[-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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[ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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[-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ],
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[-0.5*math.sqrt(2), 0.0, -0.5*math.sqrt(2), 0.0 ],
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[-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ],
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[-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ],
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]
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elif self.lattice == 'hexagonal':
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ],
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[ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
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[ 0.0,0.0,0.0,1.0 ],
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[-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
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[-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ],
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[ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ],
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[ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ],
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]
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elif self.lattice == 'tetragonal':
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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[ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
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[ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
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[ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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[-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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]
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elif self.lattice == 'orthorhombic':
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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]
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else:
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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]
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return map(Quaternion,symQuats)
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def equivalentQuaternions(self,quaternion):
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'''
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List of symmetrically equivalent quaternions based on own symmetry.
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'''
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if self.lattice == CUBIC:
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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[ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ],
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[ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
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[ 0.0,-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
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[ 0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5,-0.5 ],
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[-0.5, 0.5,-0.5, 0.5 ],
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[-0.5,-0.5, 0.5, 0.5 ],
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[-0.5,-0.5, 0.5,-0.5 ],
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[-0.5,-0.5,-0.5, 0.5 ],
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[-0.5, 0.5,-0.5,-0.5 ],
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[-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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[ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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[-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ],
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[-0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2), 0.0 ],
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[-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ],
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[-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ],
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]
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elif self.lattice == HEXAGONAL:
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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[-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ],
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[-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ],
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[ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ],
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[ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ],
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[ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ],
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[ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ],
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[ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
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[-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
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]
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elif self.lattice == TETRAGONAL:
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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[ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
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[ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
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[ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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[-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
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]
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elif self.lattice == ORTHORHOMBIC:
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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]
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else:
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symQuats = [
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[ 1.0,0.0,0.0,0.0 ],
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]
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# due to the use of list comprehension, the speed grain is quite
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# limited
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return [quaternion*Quaternion(q) for q in symQuats]
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return [quaternion*Quaternion(q) for q in self.symmetryQuats()]
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def inFZ(self,R):
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'''
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@ -772,21 +780,23 @@ cdef class Symmetry:
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cdef double epsilon = 0.0
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if self.lattice == CUBIC:
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return R[0] >= R[1]+epsilon and R[1] >= R[2]+epsilon and R[2] >= epsilon and self.inFZ(R)
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return R[0] >= R[1]+epsilon and R[1] >= R[2]+epsilon and R[2] >= epsilon
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elif self.lattice == HEXAGONAL:
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return R[0] >= math.sqrt(3)*(R[1]+epsilon) and R[1] >= epsilon and R[2] >= epsilon and self.inFZ(R)
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return R[0] >= math.sqrt(3)*(R[1]+epsilon) and R[1] >= epsilon and R[2] >= epsilon
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elif self.lattice == TETRAGONAL:
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return R[0] >= R[1]+epsilon and R[1] >= epsilon and R[2] >= epsilon and self.inFZ(R)
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return R[0] >= R[1]+epsilon and R[1] >= epsilon and R[2] >= epsilon
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elif self.lattice == ORTHORHOMBIC:
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return R[0] >= epsilon and R[1] >= epsilon and R[2] >= epsilon and self.inFZ(R)
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return R[0] >= epsilon and R[1] >= epsilon and R[2] >= epsilon
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else:
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return True
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def inSST(self,vector,color = False):
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def inSST(self,
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vector,
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color = False):
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'''
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Check whether given vector falls into standard stereographic triangle of own symmetry.
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Return inverse pole figure color if requested.
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@ -826,7 +836,9 @@ cdef class Symmetry:
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if np.all(basis == 0.0):
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theComponents = -np.ones(3,'d')
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else:
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theComponents = np.dot(basis,np.array([vector[0],vector[1],abs(vector[2])]))
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v = np.array(vector,dtype = float)
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v[2] = abs(v[2]) # z component projects identical for positive and negative values
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theComponents = np.dot(basis,v)
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inSST = np.all(theComponents >= 0.0)
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@ -924,7 +936,7 @@ cdef class Orientation:
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return Orientation(quaternion=me,symmetry=self.symmetry.lattice)
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def disorientation(self,other):
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def disorientation_old(self,other):
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'''
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Disorientation between myself and given other orientation
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(either reduced according to my own symmetry or given one)
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@ -944,6 +956,30 @@ cdef class Orientation:
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return Orientation(quaternion=theQ,symmetry=self.symmetry.lattice) #, me.conjugated(), they
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def disorientation(self,other):
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'''
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Disorientation between myself and given other orientation
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(currently needs to be of same symmetry.
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look into A. Heinz and P. Neumann 1991 for cases with differing sym.)
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'''
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if self.symmetry != other.symmetry:
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raise TypeError('disorientation between different symmetry classes not supported yet.')
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misQ = self.quaternion.conjugated()*other.quaternion
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for i,sA in enumerate(self.symmetry.symmetryQuats()):
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for j,sB in enumerate(other.symmetry.symmetryQuats()):
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theQ = sA.conjugated()*misQ*sB
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for k in xrange(2):
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theQ.conjugate()
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hitSST = other.symmetry.inDisorientationSST(theQ)
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hitFZ = self.symmetry.inFZ(theQ)
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breaker = hitSST and hitFZ
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if breaker: break
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if breaker: break
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if breaker: break
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return Orientation(quaternion=theQ,symmetry=self.symmetry.lattice) # disorientation, own sym, other sym, self-->other: True, self<--other: False
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def inversePole(self,axis,SST = True):
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'''
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axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)
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