fixed serious disorientation bug; sorted transformation functions
This commit is contained in:
Philip Eisenlohr
parent
b8285d5749
commit
2190c3ef46
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@ -286,9 +286,9 @@ class Rotation:
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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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def asRodrigues(self,vector=False):
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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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return qu2ro(self.quaternion.asArray(),vector)
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def asHomochoric(self):
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"""Homochoric vector: (h_1, h_2, h_3)"""
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@ -1072,15 +1072,16 @@ class Orientation:
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#if self.lattice.symmetry != other.lattice.symmetry:
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# raise NotImplementedError('disorientation between different symmetry classes not supported yet.')
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mis = other.rotation*self.rotation.inversed()
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mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations()[:1] # take all or only first sym operation
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mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation
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otherSymEqs = other.equivalentOrientations()
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for i,sA in enumerate(mySymEqs):
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aInv = sA.rotation.inversed()
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for j,sB in enumerate(otherSymEqs):
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r = sB.rotation*mis*sA.rotation.inversed()
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b = sB.rotation
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r = b*aInv
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for k in range(2):
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r.inversed()
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r.inverse()
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breaker = self.lattice.symmetry.inFZ(r.asRodrigues()) \
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and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues()))
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if breaker: break
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@ -1211,94 +1212,7 @@ def isone(a):
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def iszero(a):
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return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
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def eu2om(eu):
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"""Euler angles to orientation matrix"""
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c = np.cos(eu)
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s = np.sin(eu)
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om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]],
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[-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]],
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[+s[0]*s[1], -c[0]*s[1], +c[1] ]])
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om[np.where(iszero(om))] = 0.0
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return om
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def eu2ax(eu):
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"""Euler angles to axis angle"""
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t = np.tan(eu[1]*0.5)
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sigma = 0.5*(eu[0]+eu[2])
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delta = 0.5*(eu[0]-eu[2])
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tau = np.linalg.norm([t,np.sin(sigma)])
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alpha = np.pi if iszero(np.cos(sigma)) else \
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2.0*np.arctan(tau/np.cos(sigma))
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if iszero(alpha):
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ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
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else:
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ax = -P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis-angle pair so a minus sign in front
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ax = np.append(ax,alpha)
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if alpha < 0.0: ax *= -1.0 # ensure alpha is positive
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return ax
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def eu2ro(eu):
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"""Euler angles to Rodrigues vector"""
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ro = eu2ax(eu) # convert to axis angle representation
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if ro[3] >= np.pi: # Differs from original implementation. check convention 5
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ro[3] = np.inf
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elif iszero(ro[3]):
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ro = np.array([ 0.0, 0.0, P, 0.0 ])
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else:
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ro[3] = np.tan(ro[3]*0.5)
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return ro
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def eu2qu(eu):
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"""Euler angles to quaternion"""
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ee = 0.5*eu
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cPhi = np.cos(ee[1])
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sPhi = np.sin(ee[1])
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qu = np.array([ cPhi*np.cos(ee[0]+ee[2]),
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-P*sPhi*np.cos(ee[0]-ee[2]),
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-P*sPhi*np.sin(ee[0]-ee[2]),
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-P*cPhi*np.sin(ee[0]+ee[2]) ])
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#if qu[0] < 0.0: qu.homomorph() !ToDo: Check with original
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return qu
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def om2eu(om):
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"""Euler angles to orientation matrix"""
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if isone(om[2,2]**2):
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eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
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else:
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zeta = 1.0/np.sqrt(1.0-om[2,2]**2)
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eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta),
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np.arccos(om[2,2]),
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np.arctan2(om[0,2]*zeta, om[1,2]*zeta)])
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# reduce Euler angles to definition range, i.e a lower limit of 0.0
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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def ax2om(ax):
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"""Axis angle to orientation matrix"""
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c = np.cos(ax[3])
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s = np.sin(ax[3])
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omc = 1.0-c
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om=np.diag(ax[0:3]**2*omc + c)
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for idx in [[0,1,2],[1,2,0],[2,0,1]]:
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q = omc*ax[idx[0]] * ax[idx[1]]
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om[idx[0],idx[1]] = q + s*ax[idx[2]]
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om[idx[1],idx[0]] = q - s*ax[idx[2]]
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return om if P < 0.0 else om.T
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#---------- quaternion ----------
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def qu2eu(qu):
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"""Quaternion to Euler angles"""
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@ -1318,113 +1232,6 @@ def qu2eu(qu):
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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def ax2ho(ax):
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"""Axis angle to homochoric"""
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f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
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ho = ax[0:3] * f
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return ho
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def ho2ax(ho):
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"""Homochoric to axis angle"""
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tfit = np.array([+1.0000000000018852, -0.5000000002194847,
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-0.024999992127593126, -0.003928701544781374,
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-0.0008152701535450438, -0.0002009500426119712,
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-0.00002397986776071756, -0.00008202868926605841,
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+0.00012448715042090092, -0.0001749114214822577,
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+0.0001703481934140054, -0.00012062065004116828,
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+0.000059719705868660826, -0.00001980756723965647,
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+0.000003953714684212874, -0.00000036555001439719544])
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# normalize h and store the magnitude
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hmag_squared = np.sum(ho**2.)
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if iszero(hmag_squared):
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ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
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else:
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hm = hmag_squared
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# convert the magnitude to the rotation angle
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s = tfit[0] + tfit[1] * hmag_squared
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for i in range(2,16):
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hm *= hmag_squared
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s += tfit[i] * hm
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ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0)))
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return ax
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def om2ax(om):
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"""Orientation matrix to axis angle"""
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ax=np.empty(4)
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# first get the rotation angle
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t = 0.5*(om.trace() -1.0)
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ax[3] = np.arccos(np.clip(t,-1.0,1.0))
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if iszero(ax[3]):
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ax = [ 0.0, 0.0, 1.0, 0.0]
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else:
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w,vr = np.linalg.eig(om)
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# next, find the eigenvalue (1,0j)
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i = np.where(np.isclose(w,1.0+0.0j))[0][0]
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ax[0:3] = np.real(vr[0:3,i])
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diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
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ax[0:3] = np.where(iszero(diagDelta), ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
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return np.array(ax)
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def ro2ax(ro):
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"""Rodrigues vector to axis angle"""
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ta = ro[3]
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if iszero(ta):
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ax = [ 0.0, 0.0, 1.0, 0.0 ]
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elif not np.isfinite(ta):
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ax = [ ro[0], ro[1], ro[2], np.pi ]
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else:
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angle = 2.0*np.arctan(ta)
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ta = 1.0/np.linalg.norm(ro[0:3])
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ax = [ ro[0]/ta, ro[1]/ta, ro[2]/ta, angle ]
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return np.array(ax)
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def ax2ro(ax):
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"""Axis angle to Rodrigues vector"""
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if iszero(ax[3]):
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ro = [ 0.0, 0.0, P, 0.0 ]
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else:
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ro = [ax[0], ax[1], ax[2]]
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# 180 degree case
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ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
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[np.tan(ax[3]*0.5)]
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return np.array(ro)
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def ax2qu(ax):
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"""Axis angle to quaternion"""
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if iszero(ax[3]):
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qu = np.array([ 1.0, 0.0, 0.0, 0.0 ])
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else:
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c = np.cos(ax[3]*0.5)
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s = np.sin(ax[3]*0.5)
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qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
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return qu
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def ro2ho(ro):
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"""Rodrigues vector to homochoric"""
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if iszero(np.sum(ro[0:3]**2.0)):
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ho = [ 0.0, 0.0, 0.0 ]
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else:
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f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi
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ho = ro[0:3] * (0.75*f)**(1.0/3.0)
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return np.array(ho)
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def qu2om(qu):
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"""Quaternion to orientation matrix"""
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qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2)
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@ -1457,7 +1264,7 @@ def qu2ax(qu):
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return np.array(ax)
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def qu2ro(qu):
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def qu2ro(qu,vector=False):
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"""Quaternion to Rodrigues vector"""
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if iszero(qu[0]):
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ro = [qu[1], qu[2], qu[3], np.inf]
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@ -1466,7 +1273,7 @@ def qu2ro(qu):
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ro = [0.0,0.0,P,0.0] if iszero(s) else \
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[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))] # avoid numerical difficulties
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return np.array(ro)
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return np.array(ro[:3])*ro[3] if vector else np.array(ro)
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def qu2ho(qu):
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@ -1483,29 +1290,67 @@ def qu2ho(qu):
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return ho
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def ho2cu(ho):
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"""Homochoric to cubochoric"""
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return Lambert.BallToCube(ho)
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def qu2cu(qu):
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"""Quaternion to cubochoric"""
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return ho2cu(qu2ho(qu))
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def cu2ho(cu):
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"""Cubochoric to homochoric"""
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return Lambert.CubeToBall(cu)
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#---------- orientation matrix ----------
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def ro2eu(ro):
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"""Rodrigues vector to orientation matrix"""
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return om2eu(ro2om(ro))
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def om2eu(om):
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"""Euler angles to orientation matrix"""
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if isone(om[2,2]**2):
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eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
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else:
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zeta = 1.0/np.sqrt(1.0-om[2,2]**2)
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eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta),
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np.arccos(om[2,2]),
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np.arctan2(om[0,2]*zeta, om[1,2]*zeta)])
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# reduce Euler angles to definition range, i.e a lower limit of 0.0
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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def eu2ho(eu):
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"""Euler angles to homochoric"""
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return ax2ho(eu2ax(eu))
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def om2ax(om):
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"""Orientation matrix to axis angle"""
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ax=np.empty(4)
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# first get the rotation angle
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t = 0.5*(om.trace() -1.0)
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ax[3] = np.arccos(np.clip(t,-1.0,1.0))
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if iszero(ax[3]):
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ax = [ 0.0, 0.0, 1.0, 0.0]
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else:
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w,vr = np.linalg.eig(om)
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# next, find the eigenvalue (1,0j)
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i = np.where(np.isclose(w,1.0+0.0j))[0][0]
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ax[0:3] = np.real(vr[0:3,i])
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diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
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ax[0:3] = np.where(iszero(diagDelta), ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
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return np.array(ax)
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def om2ro(om):
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def om2qu(om):
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"""
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Orientation matrix to quaternion
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The original formulation (direct conversion) had numerical issues
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"""
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return ax2qu(om2ax(om))
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def om2ro(om,vector=False):
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"""Orientation matrix to Rodriques vector"""
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return eu2ro(om2eu(om))
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return eu2ro(om2eu(om,vector))
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def om2cu(om):
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"""Orientation matrix to cubochoric"""
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return ho2cu(om2ho(om))
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def om2ho(om):
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@ -1513,11 +1358,161 @@ def om2ho(om):
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return ax2ho(om2ax(om))
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#---------- Euler angles ----------
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def eu2om(eu):
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"""Euler angles to orientation matrix"""
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c = np.cos(eu)
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s = np.sin(eu)
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om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]],
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[-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]],
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[+s[0]*s[1], -c[0]*s[1], +c[1] ]])
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om[np.where(iszero(om))] = 0.0
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return om
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def eu2ax(eu):
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"""Euler angles to axis angle"""
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t = np.tan(eu[1]*0.5)
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sigma = 0.5*(eu[0]+eu[2])
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delta = 0.5*(eu[0]-eu[2])
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tau = np.linalg.norm([t,np.sin(sigma)])
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alpha = np.pi if iszero(np.cos(sigma)) else \
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2.0*np.arctan(tau/np.cos(sigma))
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if iszero(alpha):
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ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
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else:
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ax = -P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis-angle pair so a minus sign in front
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ax = np.append(ax,alpha)
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if alpha < 0.0: ax *= -1.0 # ensure alpha is positive
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return ax
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def eu2ro(eu,vector=False):
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"""Euler angles to Rodrigues vector"""
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ro = eu2ax(eu) # convert to axis angle representation
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if ro[3] >= np.pi: # Differs from original implementation. check convention 5
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ro[3] = np.inf
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elif iszero(ro[3]):
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ro = np.array([ 0.0, 0.0, P, 0.0 ])
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else:
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ro[3] = np.tan(ro[3]*0.5)
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return ro[:3] * ro[3] if vector else ro
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def eu2ho(eu):
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"""Euler angles to homochoric"""
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return ax2ho(eu2ax(eu))
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def eu2qu(eu):
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"""Euler angles to quaternion"""
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ee = 0.5*eu
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cPhi = np.cos(ee[1])
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sPhi = np.sin(ee[1])
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qu = np.array([ cPhi*np.cos(ee[0]+ee[2]),
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-P*sPhi*np.cos(ee[0]-ee[2]),
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-P*sPhi*np.sin(ee[0]-ee[2]),
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-P*cPhi*np.sin(ee[0]+ee[2]) ])
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#if qu[0] < 0.0: qu.homomorph() !ToDo: Check with original
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return qu
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def eu2cu(eu):
|
||||
"""Euler angles to cubochoric"""
|
||||
return ho2cu(eu2ho(eu))
|
||||
|
||||
|
||||
#---------- axis angle ----------
|
||||
|
||||
|
||||
def ax2eu(ax):
|
||||
"""Orientation matrix to Euler angles"""
|
||||
return om2eu(ax2om(ax))
|
||||
|
||||
|
||||
def ax2om(ax):
|
||||
"""Axis angle to orientation matrix"""
|
||||
c = np.cos(ax[3])
|
||||
s = np.sin(ax[3])
|
||||
omc = 1.0-c
|
||||
om=np.diag(ax[0:3]**2*omc + c)
|
||||
|
||||
for idx in [[0,1,2],[1,2,0],[2,0,1]]:
|
||||
q = omc*ax[idx[0]] * ax[idx[1]]
|
||||
om[idx[0],idx[1]] = q + s*ax[idx[2]]
|
||||
om[idx[1],idx[0]] = q - s*ax[idx[2]]
|
||||
|
||||
return om if P < 0.0 else om.T
|
||||
|
||||
|
||||
def ax2ro(ax,vector=False):
|
||||
"""Axis angle to Rodrigues vector"""
|
||||
if iszero(ax[3]):
|
||||
ro = [ 0.0, 0.0, P, 0.0 ]
|
||||
else:
|
||||
ro = [ax[0], ax[1], ax[2]]
|
||||
# 180 degree case
|
||||
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
|
||||
[np.tan(ax[3]*0.5)]
|
||||
|
||||
return np.array(ro[:3])*ro[3] if vector else np.array(ro)
|
||||
|
||||
|
||||
def ax2qu(ax):
|
||||
"""Axis angle to quaternion"""
|
||||
if iszero(ax[3]):
|
||||
qu = np.array([ 1.0, 0.0, 0.0, 0.0 ])
|
||||
else:
|
||||
c = np.cos(ax[3]*0.5)
|
||||
s = np.sin(ax[3]*0.5)
|
||||
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
|
||||
|
||||
return qu
|
||||
|
||||
|
||||
def ax2ho(ax):
|
||||
"""Axis angle to homochoric"""
|
||||
f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
|
||||
ho = ax[0:3] * f
|
||||
return ho
|
||||
|
||||
|
||||
def ax2cu(ax):
|
||||
"""Axis angle to cubochoric"""
|
||||
return ho2cu(ax2ho(ax))
|
||||
|
||||
|
||||
#---------- Rodrigues--Frank ----------
|
||||
|
||||
|
||||
def ro2ax(ro):
|
||||
"""Rodrigues vector to axis angle"""
|
||||
ta = ro[3]
|
||||
|
||||
if iszero(ta):
|
||||
ax = [ 0.0, 0.0, 1.0, 0.0 ]
|
||||
elif not np.isfinite(ta):
|
||||
ax = [ ro[0], ro[1], ro[2], np.pi ]
|
||||
else:
|
||||
angle = 2.0*np.arctan(ta)
|
||||
ta = 1.0/np.linalg.norm(ro[0:3])
|
||||
ax = [ ro[0]/ta, ro[1]/ta, ro[2]/ta, angle ]
|
||||
|
||||
return np.array(ax)
|
||||
|
||||
|
||||
def ro2eu(ro):
|
||||
"""Rodrigues vector to orientation matrix"""
|
||||
return om2eu(ro2om(ro))
|
||||
|
||||
|
||||
def ro2om(ro):
|
||||
"""Rodgrigues vector to orientation matrix"""
|
||||
return ax2om(ro2ax(ro))
|
||||
|
|
@ -1528,6 +1523,56 @@ def ro2qu(ro):
|
|||
return ax2qu(ro2ax(ro))
|
||||
|
||||
|
||||
def ro2ho(ro):
|
||||
"""Rodrigues vector to homochoric"""
|
||||
if iszero(np.sum(ro[0:3]**2.0)):
|
||||
ho = [ 0.0, 0.0, 0.0 ]
|
||||
else:
|
||||
f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi
|
||||
ho = ro[0:3] * (0.75*f)**(1.0/3.0)
|
||||
|
||||
return np.array(ho)
|
||||
|
||||
|
||||
def ro2cu(ro):
|
||||
"""Rodrigues vector to cubochoric"""
|
||||
return ho2cu(ro2ho(ro))
|
||||
|
||||
|
||||
#---------- homochoric ----------
|
||||
|
||||
|
||||
def ho2ax(ho):
|
||||
"""Homochoric to axis angle"""
|
||||
tfit = np.array([+1.0000000000018852, -0.5000000002194847,
|
||||
-0.024999992127593126, -0.003928701544781374,
|
||||
-0.0008152701535450438, -0.0002009500426119712,
|
||||
-0.00002397986776071756, -0.00008202868926605841,
|
||||
+0.00012448715042090092, -0.0001749114214822577,
|
||||
+0.0001703481934140054, -0.00012062065004116828,
|
||||
+0.000059719705868660826, -0.00001980756723965647,
|
||||
+0.000003953714684212874, -0.00000036555001439719544])
|
||||
# normalize h and store the magnitude
|
||||
hmag_squared = np.sum(ho**2.)
|
||||
if iszero(hmag_squared):
|
||||
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
|
||||
else:
|
||||
hm = hmag_squared
|
||||
|
||||
# convert the magnitude to the rotation angle
|
||||
s = tfit[0] + tfit[1] * hmag_squared
|
||||
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(np.clip(s,-1.0,1.0)))
|
||||
return ax
|
||||
|
||||
|
||||
def ho2cu(ho):
|
||||
"""Homochoric to cubochoric"""
|
||||
return Lambert.BallToCube(ho)
|
||||
|
||||
|
||||
def ho2eu(ho):
|
||||
"""Homochoric to Euler angles"""
|
||||
return ax2eu(ho2ax(ho))
|
||||
|
|
@ -1538,9 +1583,9 @@ def ho2om(ho):
|
|||
return ax2om(ho2ax(ho))
|
||||
|
||||
|
||||
def ho2ro(ho):
|
||||
def ho2ro(ho,vector=False):
|
||||
"""Axis angle to Rodriques vector"""
|
||||
return ax2ro(ho2ax(ho))
|
||||
return ax2ro(ho2ax(ho,vector))
|
||||
|
||||
|
||||
def ho2qu(ho):
|
||||
|
|
@ -1548,40 +1593,6 @@ def ho2qu(ho):
|
|||
return ax2qu(ho2ax(ho))
|
||||
|
||||
|
||||
def eu2cu(eu):
|
||||
"""Euler angles to cubochoric"""
|
||||
return ho2cu(eu2ho(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"""
|
||||
return ho2cu(ax2ho(ax))
|
||||
|
||||
|
||||
def ro2cu(ro):
|
||||
"""Rodrigues vector to cubochoric"""
|
||||
return ho2cu(ro2ho(ro))
|
||||
|
||||
|
||||
def qu2cu(qu):
|
||||
"""Quaternion to cubochoric"""
|
||||
return ho2cu(qu2ho(qu))
|
||||
|
||||
|
||||
def cu2eu(cu):
|
||||
"""Cubochoric to Euler angles"""
|
||||
return ho2eu(cu2ho(cu))
|
||||
|
|
@ -1597,11 +1608,18 @@ def cu2ax(cu):
|
|||
return ho2ax(cu2ho(cu))
|
||||
|
||||
|
||||
def cu2ro(cu):
|
||||
def cu2ro(cu,vector=False):
|
||||
"""Cubochoric to Rodrigues vector"""
|
||||
return ho2ro(cu2ho(cu))
|
||||
return ho2ro(cu2ho(cu,vector))
|
||||
|
||||
|
||||
def cu2qu(cu):
|
||||
"""Cubochoric to quaternion"""
|
||||
return ho2qu(cu2ho(cu))
|
||||
|
||||
|
||||
def cu2ho(cu):
|
||||
"""Cubochoric to homochoric"""
|
||||
return Lambert.CubeToBall(cu)
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue