corrected the convention added yesterday; “proper” and ‘improper” was the wrong way around. “proper = True ” considers the bigger (2 adjacent) SST. In general, an improper rotation is implicitly assumed when projecting a pole into the (single) SST, hence this is termed “improper” now.
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@ -688,11 +688,11 @@ class Symmetry:
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def inSST(self,
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vector,
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improper = False,
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proper = False,
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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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Improper considers only vectors with z >= 0, hence uses two neighboring SSTs.
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proper considers only vectors with z >= 0, hence uses two neighboring SSTs.
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Return inverse pole figure color if requested.
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'''
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# basis = {'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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@ -710,40 +710,40 @@ class Symmetry:
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# }
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if self.lattice == 'cubic':
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basis = {'proper':np.array([ [-1. , 0. , 1. ],
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basis = {'improper':np.array([ [-1. , 0. , 1. ],
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[ np.sqrt(2.) , -np.sqrt(2.) , 0. ],
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[ 0. , np.sqrt(3.) , 0. ] ]),
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'improper':np.array([ [ 0. , -1. , 1. ],
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'proper':np.array([ [ 0. , -1. , 1. ],
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[-np.sqrt(2.) , np.sqrt(2.) , 0. ],
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[ np.sqrt(3.) , 0. , 0. ] ]),
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}
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elif self.lattice == 'hexagonal':
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basis = {'proper':np.array([ [ 0. , 0. , 1. ],
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basis = {'improper':np.array([ [ 0. , 0. , 1. ],
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[ 1. , -np.sqrt(3.), 0. ],
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[ 0. , 2. , 0. ] ]),
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'improper':np.array([ [ 0. , 0. , 1. ],
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'proper':np.array([ [ 0. , 0. , 1. ],
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[-1. , np.sqrt(3.) , 0. ],
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[ np.sqrt(3) , -1. , 0. ] ]),
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}
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elif self.lattice == 'tetragonal':
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basis = {'proper':np.array([ [ 0. , 0. , 1. ],
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basis = {'improper':np.array([ [ 0. , 0. , 1. ],
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[ 1. , -1. , 0. ],
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[ 0. , np.sqrt(2.), 0. ] ]),
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'improper':np.array([ [ 0. , 0. , 1. ],
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'proper':np.array([ [ 0. , 0. , 1. ],
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[-1. , 1. , 0. ],
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[ np.sqrt(2.) , 0. , 0. ] ]),
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}
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elif self.lattice == 'orthorhombic':
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basis = {'proper':np.array([ [ 0., 0., 1.],
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basis = {'improper':np.array([ [ 0., 0., 1.],
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[ 1., 0., 0.],
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[ 0., 1., 0.] ]),
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'improper':np.array([ [ 0., 0., 1.],
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'proper':np.array([ [ 0., 0., 1.],
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[-1., 0., 0.],
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[ 0., 1., 0.] ]),
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}
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else:
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basis = {'proper':np.zeros((3,3),dtype=float),
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'improper':np.zeros((3,3),dtype=float),
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basis = {'improper':np.zeros((3,3),dtype=float),
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'proper':np.zeros((3,3),dtype=float),
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}
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if np.all(basis == 0.0):
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@ -751,15 +751,15 @@ class Symmetry:
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inSST = np.all(theComponents >= 0.0)
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else:
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v = np.array(vector,dtype = float)
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if improper: # check both proper ...
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theComponents = np.dot(basis['proper'],v)
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inSST = np.all(theComponents >= 0.0)
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if not inSST: # ... and improper SST
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if proper: # check both improper ...
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theComponents = np.dot(basis['improper'],v)
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inSST = np.all(theComponents >= 0.0)
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if not inSST: # ... and proper SST
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theComponents = np.dot(basis['proper'],v)
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inSST = np.all(theComponents >= 0.0)
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else:
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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['proper'],v)
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theComponents = np.dot(basis['improper'],v)
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inSST = np.all(theComponents >= 0.0)
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if color: # have to return color array
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@ -906,7 +906,7 @@ class Orientation:
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def inversePole(self,
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axis,
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improper = False,
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proper = False,
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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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@ -915,7 +915,7 @@ class Orientation:
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if SST: # pole requested to be within SST
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for i,q in enumerate(self.symmetry.equivalentQuaternions(self.quaternion)): # test all symmetric equivalent quaternions
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pole = q.conjugated()*axis # align crystal direction to axis
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if self.symmetry.inSST(pole,improper): break # found SST version
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if self.symmetry.inSST(pole,proper): break # found SST version
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else:
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pole = self.quaternion.conjugated()*axis # align crystal direction to axis
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