transition to new orientation class
forward-backward conversion quite stable
This commit is contained in:
Martin Diehl
parent
affe65eb55
commit
b3455c825e
2
PRIVATE
2
PRIVATE
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@ -1 +1 @@
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Subproject commit 35bed9722ddecc342719bafac32590e9ab94d053
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Subproject commit f0090997df817f0a0b5a480a60e81929875b1010
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@ -109,8 +109,8 @@ if np.sum(input) != 1: parser.error('needs exactly one input format.')
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crystalrotation = np.array(options.crystalrotation[1:4] + (options.crystalrotation[0],)) # Compatibility hack
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labrotation = np.array(options.labrotation[1:4] + (options.labrotation[0],)) # Compatibility hack
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r = damask.Rotation.fromAngleAxis(crystalrotation,options.degrees) # crystal frame rotation
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R = damask.Rotation.fromAngleAxis(labrotation,options.degrees) # lab frame rotation
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r = damask.Rotation.fromAxisAngle(crystalrotation,options.degrees) # crystal frame rotation
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R = damask.Rotation.fromAxisAngle(labrotation,options.degrees) # lab frame rotation
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# --- loop over input files ------------------------------------------------------------------------
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@ -183,7 +183,7 @@ for name in filenames:
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elif output == 'rodrigues': table.data_append(o.asRodrigues())
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elif output == 'eulers': table.data_append(o.asEulers(degrees=options.degrees))
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elif output == 'matrix': table.data_append(o.asMatrix())
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elif output == 'angleaxis': table.data_append(o.asAngleAxis(degrees=options.degrees))
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elif output == 'angleaxis': table.data_append(o.asAxisAngle(degrees=options.degrees))
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outputAlive = table.data_write() # output processed line
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# ------------------------------------------ output finalization -----------------------------------
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@ -41,7 +41,7 @@ if options.data is None:
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parser.error('no data column specified.')
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rotation = np.array(options.rotation[1:4]+(options.rotation[0],)) # Compatibility hack
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r = damask.Rotation.fromAngleAxis(rotation,options.degrees,normalise=True)
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r = damask.Rotation.fromAxisAngle(rotation,options.degrees,normalise=True)
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# --- loop over input files -------------------------------------------------------------------------
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@ -64,7 +64,7 @@ if options.dimension is None:
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parser.error('no dimension specified.')
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if options.angleaxis is not None:
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ax = np.array(options.angleaxis[1:4] + (options.angleaxis[0],)) # Compatibility hack
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rotation = damask.Rotation.fromAngleAxis(ax,options.degrees,normalise=True)
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rotation = damask.Rotation.fromAxisAngle(ax,options.degrees,normalise=True)
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elif options.quaternion is not None:
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rotation = damask.Rotation.fromQuaternion(options.quaternion)
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else:
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@ -261,32 +261,34 @@ class Rotation:
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# convert to different orientation representations (numpy arrays)
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def asQuaternion(self):
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"""Unit quaternion: (q, [p_1, p_2, p_3])"""
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return self.quaternion.asArray()
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def asEulers(self,
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degrees = False):
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"""Bunge-Euler angles: (φ_1, ϕ, φ_2)"""
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eu = qu2eu(self.quaternion.asArray())
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if degrees: eu = np.degrees(eu)
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return eu
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def asAngleAxis(self,
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def asAxisAngle(self,
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degrees = False):
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"""Axis-angle pair: ([n_1, n_2, n_3], ω)"""
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ax = qu2ax(self.quaternion.asArray())
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if degrees: ax[3] = np.degrees(ax[3])
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return ax
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def asMatrix(self):
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"""Rotation matrix"""
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return qu2om(self.quaternion.asArray())
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def asRodrigues(self):
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"""Rodrigues-Frank vector: ([n_1, n_2, n_3], tan(ω/2))"""
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return qu2ro(self.quaternion.asArray())
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def asHomochoric(self):
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return qu2ho(self.quaternion.asArray())
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"""Homochoric vector: (h_1, h_2, h_3)"""
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return qu2ho(self.quaternion.asArray())
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def asCubochoric(self):
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return qu2cu(self.quaternion.asArray())
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@ -322,7 +324,7 @@ class Rotation:
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return cls(eu2qu(eu))
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@classmethod
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def fromAngleAxis(cls,
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def fromAxisAngle(cls,
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angleAxis,
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degrees = False,
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normalise = False,
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@ -372,6 +374,27 @@ class Rotation:
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raise ValueError('Rodriques rotation angle not positive.\n'.format(ro[3]))
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return cls(ro2qu(ro))
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@classmethod
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def fromHomochoric(cls,
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homochoric,
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P = -1):
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ho = homochoric if isinstance(homochoric, np.ndarray) else np.array(homochoric)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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return cls(ho2qu(ho))
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@classmethod
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def fromCubochoric(cls,
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cubochoric,
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P = -1):
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cu = cubochoric if isinstance(cubochoric, np.ndarray) else np.array(cubochoric)
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ho = cu2ho(cu)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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return cls(ho2qu(ho))
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def __mul__(self, other):
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@ -672,28 +695,6 @@ class Quaternion:
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def asRodrigues(self):
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return np.inf*np.ones(3) if np.isclose(self.q,0.0) else self.p/self.q
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def asEulers(self,
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degrees = False):
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"""Orientation as Bunge-Euler angles."""
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# Rowenhorst_etal2015 MSMSE: value of P is selected as -1
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P = -1.0
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q03 = self.q**2 + self.p[2]**2
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q12 = self.p[0]**2 + self.p[1]**2
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chi = np.sqrt(q03*q12)
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if np.isclose(chi,0.0) and np.isclose(q12,0.0):
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eulers = np.array([math.atan2(-2*P*self.q*self.p[2],self.q**2-self.p[2]**2),0,0])
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elif np.isclose(chi,0.0) and np.isclose(q03,0.0):
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eulers = np.array([math.atan2( 2 *self.p[0]*self.p[1],self.p[0]**2-self.p[1]**2),np.pi,0])
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else:
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eulers = np.array([math.atan2((self.p[0]*self.p[2]-P*self.q*self.p[1])/chi,(-P*self.q*self.p[0]-self.p[1]*self.p[2])/chi),
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math.atan2(2*chi,q03-q12),
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math.atan2((P*self.q*self.p[1]+self.p[0]*self.p[2])/chi,( self.p[1]*self.p[2]-P*self.q*self.p[0])/chi),
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])
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eulers %= 2.0*math.pi # enforce positive angles
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return np.degrees(eulers) if degrees else eulers
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# # Static constructors
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@classmethod
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@ -1506,18 +1507,8 @@ class Orientation:
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'Symmetry: {}'.format(self.symmetry),
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'Quaternion: {}'.format(self.quaternion),
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'Matrix:\n{}'.format( '\n'.join(['\t'.join(list(map(str,self.asMatrix()[i,:]))) for i in range(3)]) ),
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'Bunge Eulers / deg: {}'.format('\t'.join(list(map(str,self.asEulers(degrees=True)))) ),
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])
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def asQuaternion(self):
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return self.quaternion.asList()
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def asEulers(self,
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degrees = False,
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):
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return self.quaternion.asEulers(degrees)
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eulers = property(asEulers)
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def asRodrigues(self):
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return self.quaternion.asRodrigues()
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rodrigues = property(asRodrigues)
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@ -1526,7 +1517,6 @@ class Orientation:
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degrees = False,
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flat = False):
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return self.quaternion.asAngleAxis(degrees,flat)
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angleAxis = property(asAngleAxis)
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def asMatrix(self):
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return self.quaternion.asMatrix()
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@ -1643,251 +1633,6 @@ class Orientation:
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symmetry = reference.symmetry.lattice)
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def related(self,
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relationModel,
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direction,
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targetSymmetry = 'cubic'):
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"""
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Orientation relationship
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positive number: fcc --> bcc
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negative number: bcc --> fcc
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"""
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if relationModel not in ['KS','GT','GTdash','NW','Pitsch','Bain']: return None
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if int(direction) == 0: return None
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variant = int(abs(direction))-1
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(me,other) = (0,1) if direction > 0 else (1,0)
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planes = {'KS': \
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np.array([[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]]]),
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'GT': \
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np.array([[[ 1, 1, 1],[ 1, 0, 1]],
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[[ 1, 1, 1],[ 1, 1, 0]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ -1, 0, 1]],
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[[ -1, -1, 1],[ -1, -1, 0]],
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[[ -1, -1, 1],[ 0, -1, 1]],
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[[ -1, 1, 1],[ -1, 0, 1]],
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[[ -1, 1, 1],[ -1, 1, 0]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 1, 0, 1]],
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[[ 1, -1, 1],[ 1, -1, 0]],
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[[ 1, -1, 1],[ 0, -1, 1]],
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[[ 1, 1, 1],[ 1, 1, 0]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 1, 0, 1]],
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[[ -1, -1, 1],[ -1, -1, 0]],
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[[ -1, -1, 1],[ 0, -1, 1]],
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[[ -1, -1, 1],[ -1, 0, 1]],
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[[ -1, 1, 1],[ -1, 1, 0]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ -1, 0, 1]],
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[[ 1, -1, 1],[ 1, -1, 0]],
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[[ 1, -1, 1],[ 0, -1, 1]],
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[[ 1, -1, 1],[ 1, 0, 1]]]),
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'GTdash': \
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np.array([[[ 7, 17, 17],[ 12, 5, 17]],
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[[ 17, 7, 17],[ 17, 12, 5]],
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[[ 17, 17, 7],[ 5, 17, 12]],
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[[ -7,-17, 17],[-12, -5, 17]],
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[[-17, -7, 17],[-17,-12, 5]],
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[[-17,-17, 7],[ -5,-17, 12]],
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[[ 7,-17,-17],[ 12, -5,-17]],
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[[ 17, -7,-17],[ 17,-12, -5]],
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[[ 17,-17, -7],[ 5,-17,-12]],
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[[ -7, 17,-17],[-12, 5,-17]],
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[[-17, 7,-17],[-17, 12, -5]],
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[[-17, 17, -7],[ -5, 17,-12]],
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[[ 7, 17, 17],[ 12, 17, 5]],
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[[ 17, 7, 17],[ 5, 12, 17]],
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[[ 17, 17, 7],[ 17, 5, 12]],
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[[ -7,-17, 17],[-12,-17, 5]],
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[[-17, -7, 17],[ -5,-12, 17]],
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[[-17,-17, 7],[-17, -5, 12]],
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[[ 7,-17,-17],[ 12,-17, -5]],
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[[ 17, -7,-17],[ 5, -12,-17]],
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[[ 17,-17, 7],[ 17, -5,-12]],
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[[ -7, 17,-17],[-12, 17, -5]],
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[[-17, 7,-17],[ -5, 12,-17]],
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[[-17, 17, -7],[-17, 5,-12]]]),
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'NW': \
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np.array([[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]]]),
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'Pitsch': \
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np.array([[[ 0, 1, 0],[ -1, 0, 1]],
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[[ 0, 0, 1],[ 1, -1, 0]],
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[[ 1, 0, 0],[ 0, 1, -1]],
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[[ 1, 0, 0],[ 0, -1, -1]],
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[[ 0, 1, 0],[ -1, 0, -1]],
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[[ 0, 0, 1],[ -1, -1, 0]],
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[[ 0, 1, 0],[ -1, 0, -1]],
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[[ 0, 0, 1],[ -1, -1, 0]],
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[[ 1, 0, 0],[ 0, -1, -1]],
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[[ 1, 0, 0],[ 0, -1, 1]],
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[[ 0, 1, 0],[ 1, 0, -1]],
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[[ 0, 0, 1],[ -1, 1, 0]]]),
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'Bain': \
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np.array([[[ 1, 0, 0],[ 1, 0, 0]],
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[[ 0, 1, 0],[ 0, 1, 0]],
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[[ 0, 0, 1],[ 0, 0, 1]]]),
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}
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normals = {'KS': \
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np.array([[[ -1, 0, 1],[ -1, -1, 1]],
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[[ -1, 0, 1],[ -1, 1, -1]],
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[[ 0, 1, -1],[ -1, -1, 1]],
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[[ 0, 1, -1],[ -1, 1, -1]],
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[[ 1, -1, 0],[ -1, -1, 1]],
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[[ 1, -1, 0],[ -1, 1, -1]],
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[[ 1, 0, -1],[ -1, -1, 1]],
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[[ 1, 0, -1],[ -1, 1, -1]],
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[[ -1, -1, 0],[ -1, -1, 1]],
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[[ -1, -1, 0],[ -1, 1, -1]],
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[[ 0, 1, 1],[ -1, -1, 1]],
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[[ 0, 1, 1],[ -1, 1, -1]],
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[[ 0, -1, 1],[ -1, -1, 1]],
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[[ 0, -1, 1],[ -1, 1, -1]],
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[[ -1, 0, -1],[ -1, -1, 1]],
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[[ -1, 0, -1],[ -1, 1, -1]],
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[[ 1, 1, 0],[ -1, -1, 1]],
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[[ 1, 1, 0],[ -1, 1, -1]],
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[[ -1, 1, 0],[ -1, -1, 1]],
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[[ -1, 1, 0],[ -1, 1, -1]],
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[[ 0, -1, -1],[ -1, -1, 1]],
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[[ 0, -1, -1],[ -1, 1, -1]],
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[[ 1, 0, 1],[ -1, -1, 1]],
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[[ 1, 0, 1],[ -1, 1, -1]]]),
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'GT': \
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np.array([[[ -5,-12, 17],[-17, -7, 17]],
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[[ 17, -5,-12],[ 17,-17, -7]],
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[[-12, 17, -5],[ -7, 17,-17]],
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[[ 5, 12, 17],[ 17, 7, 17]],
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[[-17, 5,-12],[-17, 17, -7]],
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[[ 12,-17, -5],[ 7,-17,-17]],
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[[ -5, 12,-17],[-17, 7,-17]],
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[[ 17, 5, 12],[ 17, 17, 7]],
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[[-12,-17, 5],[ -7,-17, 17]],
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[[ 5,-12,-17],[ 17, -7,-17]],
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[[-17, -5, 12],[-17,-17, 7]],
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[[ 12, 17, 5],[ 7, 17, 17]],
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[[ -5, 17,-12],[-17, 17, -7]],
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[[-12, -5, 17],[ -7,-17, 17]],
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[[ 17,-12, -5],[ 17, -7,-17]],
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[[ 5,-17,-12],[ 17,-17, -7]],
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[[ 12, 5, 17],[ 7, 17, 17]],
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[[-17, 12, -5],[-17, 7,-17]],
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[[ -5,-17, 12],[-17,-17, 7]],
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[[-12, 5,-17],[ -7, 17,-17]],
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[[ 17, 12, 5],[ 17, 7, 17]],
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[[ 5, 17, 12],[ 17, 17, 7]],
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[[ 12, -5,-17],[ 7,-17,-17]],
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[[-17,-12, 5],[-17, 7, 17]]]),
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'GTdash': \
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np.array([[[ 0, 1, -1],[ 1, 1, -1]],
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[[ -1, 0, 1],[ -1, 1, 1]],
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[[ 1, -1, 0],[ 1, -1, 1]],
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[[ 0, -1, -1],[ -1, -1, -1]],
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[[ 1, 0, 1],[ 1, -1, 1]],
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[[ 1, -1, 0],[ 1, -1, -1]],
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[[ 0, 1, -1],[ -1, 1, -1]],
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[[ 1, 0, 1],[ 1, 1, 1]],
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[[ -1, -1, 0],[ -1, -1, 1]],
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[[ 0, -1, -1],[ 1, -1, -1]],
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[[ -1, 0, 1],[ -1, -1, 1]],
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[[ -1, -1, 0],[ -1, -1, -1]],
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[[ 0, -1, 1],[ 1, -1, 1]],
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[[ 1, 0, -1],[ 1, 1, -1]],
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[[ -1, 1, 0],[ -1, 1, 1]],
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[[ 0, 1, 1],[ -1, 1, 1]],
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[[ -1, 0, -1],[ -1, -1, -1]],
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[[ -1, 1, 0],[ -1, 1, -1]],
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[[ 0, -1, 1],[ -1, -1, 1]],
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[[ -1, 0, -1],[ -1, 1, -1]],
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[[ 1, 1, 0],[ 1, 1, 1]],
|
||||
[[ 0, 1, 1],[ 1, 1, 1]],
|
||||
[[ 1, 0, -1],[ 1, -1, -1]],
|
||||
[[ 1, 1, 0],[ 1, 1, -1]]]),
|
||||
'NW': \
|
||||
np.array([[[ 2, -1, -1],[ 0, -1, 1]],
|
||||
[[ -1, 2, -1],[ 0, -1, 1]],
|
||||
[[ -1, -1, 2],[ 0, -1, 1]],
|
||||
[[ -2, -1, -1],[ 0, -1, 1]],
|
||||
[[ 1, 2, -1],[ 0, -1, 1]],
|
||||
[[ 1, -1, 2],[ 0, -1, 1]],
|
||||
[[ 2, 1, -1],[ 0, -1, 1]],
|
||||
[[ -1, -2, -1],[ 0, -1, 1]],
|
||||
[[ -1, 1, 2],[ 0, -1, 1]],
|
||||
[[ -1, 2, 1],[ 0, -1, 1]],
|
||||
[[ -1, 2, 1],[ 0, -1, 1]],
|
||||
[[ -1, -1, -2],[ 0, -1, 1]]]),
|
||||
'Pitsch': \
|
||||
np.array([[[ 1, 0, 1],[ 1, -1, 1]],
|
||||
[[ 1, 1, 0],[ 1, 1, -1]],
|
||||
[[ 0, 1, 1],[ -1, 1, 1]],
|
||||
[[ 0, 1, -1],[ -1, 1, -1]],
|
||||
[[ -1, 0, 1],[ -1, -1, 1]],
|
||||
[[ 1, -1, 0],[ 1, -1, -1]],
|
||||
[[ 1, 0, -1],[ 1, -1, -1]],
|
||||
[[ -1, 1, 0],[ -1, 1, -1]],
|
||||
[[ 0, -1, 1],[ -1, -1, 1]],
|
||||
[[ 0, 1, 1],[ -1, 1, 1]],
|
||||
[[ 1, 0, 1],[ 1, -1, 1]],
|
||||
[[ 1, 1, 0],[ 1, 1, -1]]]),
|
||||
'Bain': \
|
||||
np.array([[[ 0, 1, 0],[ 0, 1, 1]],
|
||||
[[ 0, 0, 1],[ 1, 0, 1]],
|
||||
[[ 1, 0, 0],[ 1, 1, 0]]]),
|
||||
}
|
||||
myPlane = [float(i) for i in planes[relationModel][variant,me]] # map(float, planes[...]) does not work in python 3
|
||||
myPlane /= np.linalg.norm(myPlane)
|
||||
myNormal = [float(i) for i in normals[relationModel][variant,me]] # map(float, planes[...]) does not work in python 3
|
||||
myNormal /= np.linalg.norm(myNormal)
|
||||
myMatrix = np.array([myNormal,np.cross(myPlane,myNormal),myPlane]).T
|
||||
|
||||
otherPlane = [float(i) for i in planes[relationModel][variant,other]] # map(float, planes[...]) does not work in python 3
|
||||
otherPlane /= np.linalg.norm(otherPlane)
|
||||
otherNormal = [float(i) for i in normals[relationModel][variant,other]] # map(float, planes[...]) does not work in python 3
|
||||
otherNormal /= np.linalg.norm(otherNormal)
|
||||
otherMatrix = np.array([otherNormal,np.cross(otherPlane,otherNormal),otherPlane]).T
|
||||
|
||||
rot=np.dot(otherMatrix,myMatrix.T)
|
||||
|
||||
return Orientation(matrix=np.dot(rot,self.asMatrix()),symmetry=targetSymmetry)
|
||||
|
||||
####################################################################################################
|
||||
# Code below available according to the followin conditions on https://github.com/MarDiehl/3Drotations
|
||||
####################################################################################################
|
||||
|
|
@ -1920,10 +1665,10 @@ class Orientation:
|
|||
####################################################################################################
|
||||
|
||||
def isone(a):
|
||||
return np.isclose(a,1.0,atol=1.0e-15,rtol=0.0)
|
||||
return np.isclose(a,1.0,atol=1.0e-7,rtol=0.0)
|
||||
|
||||
def iszero(a):
|
||||
return np.isclose(a,0.0,atol=1.0e-300,rtol=0.0)
|
||||
return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
|
||||
|
||||
|
||||
def eu2om(eu):
|
||||
|
|
@ -2063,8 +1808,7 @@ def ho2ax(ho):
|
|||
for i in range(2,16):
|
||||
hm *= hmag_squared
|
||||
s += tfit[i] * hm
|
||||
ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(s)) # ToDo: Check sanity check in reference implementation
|
||||
|
||||
ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0)))
|
||||
return ax
|
||||
|
||||
|
||||
|
|
@ -2155,32 +1899,16 @@ def qu2om(qu):
|
|||
return om if P > 0.0 else om.T
|
||||
|
||||
|
||||
def om2qu(om):
|
||||
"""Orientation matrix to quaternion"""
|
||||
s = [+om[0,0] +om[1,1] +om[2,2] +1.0,
|
||||
+om[0,0] -om[1,1] -om[2,2] +1.0,
|
||||
-om[0,0] +om[1,1] -om[2,2] +1.0,
|
||||
-om[0,0] -om[1,1] +om[2,2] +1.0]
|
||||
s = np.maximum(np.zeros(4),s)
|
||||
qu = np.sqrt(s)*0.5*np.array([1.0,P,P,P])
|
||||
# verify the signs (q0 always positive)
|
||||
#ToDo: Here I donot understand the original shortcut from paper to implementation
|
||||
|
||||
qu /= np.linalg.norm(qu)
|
||||
if any(isone(abs(qu))): qu[np.where(np.logical_not(isone(qu)))] = 0.0
|
||||
if om[2,1] < om[1,2]: qu[1] *= -1.0
|
||||
if om[0,2] < om[2,0]: qu[2] *= -1.0
|
||||
if om[1,0] < om[0,1]: qu[3] *= -1.0
|
||||
if any(om2ax(om)[0:3]*qu[1:4] < 0.0): print('sign problem',om2ax(om),qu) # something is wrong here
|
||||
return qu
|
||||
|
||||
|
||||
def qu2ax(qu):
|
||||
"""Quaternion to axis angle"""
|
||||
omega = 2.0 * np.arccos(qu[0])
|
||||
if iszero(omega): # return axis as [001] if the angle is zero
|
||||
"""
|
||||
Quaternion to axis angle
|
||||
|
||||
Modified version of the original formulation, should be numerically more stable
|
||||
"""
|
||||
if isone(abs(qu[0])): # set axis to [001] if the angle is 0/360
|
||||
ax = [ 0.0, 0.0, 1.0, 0.0 ]
|
||||
elif not iszero(qu[0]):
|
||||
omega = 2.0 * np.arccos(qu[0])
|
||||
s = np.sign(qu[0])/np.sqrt(qu[1]**2+qu[2]**2+qu[3]**2)
|
||||
ax = [ qu[1]*s, qu[2]*s, qu[3]*s, omega ]
|
||||
else:
|
||||
|
|
@ -2196,14 +1924,14 @@ def qu2ro(qu):
|
|||
else:
|
||||
s = np.linalg.norm([qu[1],qu[2],qu[3]])
|
||||
ro = [0.0,0.0,P,0.0] if iszero(s) else \
|
||||
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(qu[0]))]
|
||||
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))] # avoid numerical difficulties
|
||||
|
||||
return np.array(ro)
|
||||
|
||||
|
||||
def qu2ho(qu):
|
||||
"""Quaternion to homochoric"""
|
||||
omega = 2.0 * np.arccos(qu[0])
|
||||
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0)) # avoid numerical difficulties
|
||||
|
||||
if iszero(omega):
|
||||
ho = np.array([ 0.0, 0.0, 0.0 ])
|
||||
|
|
@ -2288,7 +2016,16 @@ def eu2cu(eu):
|
|||
def om2cu(om):
|
||||
"""Orientation matrix to cubochoric"""
|
||||
return ho2cu(om2ho(om))
|
||||
|
||||
|
||||
def om2qu(om):
|
||||
"""
|
||||
Orientation matrix to quaternion
|
||||
|
||||
The original formulation (direct conversion) had numerical issues
|
||||
"""
|
||||
return ax2qu(om2ax(om))
|
||||
|
||||
|
||||
def ax2cu(ax):
|
||||
"""Axis angle to cubochoric"""
|
||||
|
|
|
|||
Loading…
Reference in New Issue