WIP (broken?): vectorized calculation of IPF color
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Martin Diehl
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1648963b57
commit
13bf7515ce
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@ -374,8 +374,93 @@ class Symmetry:
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else:
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else:
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return inSST
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return inSST
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# code derived from https://github.com/ezag/pyeuclid
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# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
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def in_SST(self,
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vector,
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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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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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Bases are computed from
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>>> basis = {'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,1.]/np.sqrt(2.), # direction of green
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... [1.,1.,1.]/np.sqrt(3.)]).T), # direction of blue
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... 'hexagonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # direction of green
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... [np.sqrt(3.),1.,0.]/np.sqrt(4.)]).T), # direction of blue
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... 'tetragonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # direction of green
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... [1.,1.,0.]/np.sqrt(2.)]).T), # direction of blue
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... 'orthorhombic': np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # direction of green
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... [0.,1.,0.]]).T), # direction of blue
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... }
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"""
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if self.lattice == 'cubic':
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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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'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 = {'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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'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 = {'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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'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 = {'improper':np.array([ [ 0., 0., 1.],
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[ 1., 0., 0.],
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[ 0., 1., 0.] ]),
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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: # direct exit for unspecified symmetry
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if color:
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return (np.ones_like(vector[...,0],bool),np.zeros_like(vector))
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else:
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return np.ones_like(vector[...,0],bool)
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b_p = np.broadcast_to(basis['proper'], vector.shape+(3,))
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if proper:
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b_i = np.broadcast_to(basis['improper'],vector.shape+(3,))
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improper = np.all(np.around(np.einsum('...ji,...i',b_i,vector),12)>=0.0,axis=-1,keepdims=True)
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theComponents = np.where(np.broadcast_to(improper,vector.shape),
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np.around(np.einsum('...ji,...i',b_i,vector),12),
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np.around(np.einsum('...ji,...i',b_p,vector),12))
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else:
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vector_ = np.block([vector[...,0:2],np.abs(vector[...,2:3])]) # z component projects identical
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theComponents = np.around(np.einsum('...ji,...i',b_p,vector_),12)
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in_SST = np.all(theComponents >= 0.0,axis=-1)
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if color: # have to return color array
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with np.errstate(invalid='ignore',divide='ignore'):
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rgb = (theComponents/np.linalg.norm(theComponents,axis=-1,keepdims=True))**0.5 # smoothen color ramps
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rgb = np.minimum(1.,rgb) # limit to maximum intensity
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rgb /= np.max(rgb,axis=-1,keepdims=True) # normalize to (HS)V = 1
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rgb[np.invert(np.broadcast_to(in_SST.reshape(vector[...,0].shape+(1,)),vector.shape))] = 0.0
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return (in_SST,rgb)
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else:
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return in_SST
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# ******************************************************************************************
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# ******************************************************************************************
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@ -176,6 +176,16 @@ class Orientation: # make subclass or Rotation?
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return color
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return color
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def IPF_color(self,axis):
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"""TSL color of inverse pole figure for given axis."""
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color = np.zeros(self.rotation.shape)
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eq = self.equivalent
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pole = eq.rotation @ np.broadcast_to(axis,eq.rotation.shape+(3,))
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in_SST, color = self.lattice.symmetry.in_SST(pole,color=True)
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return color[in_SST]
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@staticmethod
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@staticmethod
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def fromAverage(orientations,
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def fromAverage(orientations,
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weights = []):
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weights = []):
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