added optional keyword `degrees´ to q.asEulers().
added methods inFZ, equivalentQuaternions, and equivalentOrientations to Orientation class. general polishing…
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Philip Eisenlohr
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e310763c52
commit
2d8af638b0
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@ -58,36 +58,36 @@ class Quaternion:
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omega = math.acos(self.w)
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vRescale = math.sin(exponent*omega)/math.sin(omega)
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Q = Quaternion()
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Q.w = math.cos(exponent*omega)
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Q.x = self.x * vRescale
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Q.y = self.y * vRescale
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Q.z = self.z * vRescale
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Q.w = math.cos(exponent*omega)
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return Q
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def __ipow__(self, exponent):
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omega = math.acos(self.w)
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omega = math.acos(self.w)
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vRescale = math.sin(exponent*omega)/math.sin(omega)
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self.w = np.cos(exponent*omega)
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self.x *= vRescale
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self.y *= vRescale
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self.z *= vRescale
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self.w = np.cos(exponent*omega)
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return self
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def __mul__(self, other):
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try: # quaternion
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Aw = self.w
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Ax = self.x
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Ay = self.y
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Az = self.z
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Aw = self.w
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Bw = other.w
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Bx = other.x
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By = other.y
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Bz = other.z
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Bw = other.w
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Q = Quaternion()
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Q.w = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw
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Q.x = + Ax * Bw + Ay * Bz - Az * By + Aw * Bx
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Q.y = - Ax * Bz + Ay * Bw + Az * Bx + Aw * By
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Q.z = + Ax * By - Ay * Bx + Az * Bw + Aw * Bz
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Q.w = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw
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return Q
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except: pass
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try: # vector (perform active rotation, i.e. q*v*q.conjugated)
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@ -309,10 +309,7 @@ class Quaternion:
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angle = math.atan2(y,x)
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if angle < 1e-3:
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return angle, np.array([1.0, 0.0, 0.0])
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else:
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return angle, np.array([self.x / s, self.y / s, self.z / s])
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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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def asRodrigues(self):
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if self.w != 0.0:
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@ -320,7 +317,7 @@ 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'):
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def asEulers(self,type='bunge',degrees=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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@ -362,7 +359,7 @@ class Quaternion:
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# if angles[2] < 0.0:
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# angles[2] += 2*math.pi
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return angles
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return np.degrees(angles) if degrees else angles
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# # Static constructors
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@ -407,12 +404,15 @@ class Quaternion:
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@classmethod
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def fromEulers(cls, eulers, type = 'Bunge'):
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c1 = math.cos(eulers[0] / 2.0)
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s1 = math.sin(eulers[0] / 2.0)
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c2 = math.cos(eulers[1] / 2.0)
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s2 = math.sin(eulers[1] / 2.0)
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c3 = math.cos(eulers[2] / 2.0)
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s3 = math.sin(eulers[2] / 2.0)
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eulers *= 0.5 # reduce to half angles
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c1 = math.cos(eulers[0])
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s1 = math.sin(eulers[0])
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c2 = math.cos(eulers[1])
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s2 = math.sin(eulers[1])
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c3 = math.cos(eulers[2])
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s3 = math.sin(eulers[2])
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if type.lower() == 'bunge' or type.lower() == 'zxz':
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w = c1 * c2 * c3 - s1 * c2 * s3
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@ -797,10 +797,19 @@ class Orientation:
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def asMatrix(self):
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return self.quaternion.asMatrix()
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def inFZ(self):
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return self.symmetry.inFZ(self.quaternion.asRodrigues())
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def equivalentQuaternions(self):
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return self.symmetry.equivalentQuaternions(self.quaternion)
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def equivalentOrientations(self):
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return map(lambda q: Orientation(quaternion=q,symmetry=self.symmetry.lattice),
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self.equivalentQuaternions())
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def reduced(self):
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'''
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Transform orientation to fall into fundamental zone according to own (or given) symmetry
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Transform orientation to fall into fundamental zone according to symmetry
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'''
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for me in self.symmetry.equivalentQuaternions(self.quaternion):
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@ -821,9 +830,7 @@ class Orientation:
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for me in self.symmetry.equivalentQuaternions(self.quaternion):
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me.conjugate()
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for they in other.symmetry.equivalentQuaternions(other.quaternion):
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# theQ = me * they
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theQ = they * me
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# if theQ.x < 0.0 or theQ.y < 0.0 or theQ.z < 0.0: theQ.conjugate() # speed up scanning since minimum angle is usually found for positive x,y,z
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breaker = lowerSymmetry.inDisorientationSST(theQ.asRodrigues()) #\
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# or lowerSymmetry.inDisorientationSST(theQ.conjugated().asRodrigues())
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if breaker: break
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@ -838,9 +845,9 @@ class Orientation:
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'''
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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 orientations
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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): print i;break # found SST version
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if self.symmetry.inSST(pole): 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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@ -869,18 +876,18 @@ class Orientation:
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doi: 10.2514/1.28949
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usage:
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a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry='hexagonal')
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b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
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b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
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avg = Orientation.getAverageOrientation([a,b])
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"""
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if not all(isinstance(item, Orientation) for item in orientationList):
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raise TypeError("Only instances of Orientation can be averaged.")
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n = len(orientationList)
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tmp_m = orientationList.pop(0).quaternion.asM()
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for tmp_o in orientationList:
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tmp_m += tmp_o.quaternion.asM()
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eig, vec = np.linalg.eig(tmp_m/n)
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N = len(orientationList)
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M = orientationList.pop(0).quaternion.asM()
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for o in orientationList:
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M += o.quaternion.asM()
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eig, vec = np.linalg.eig(M/N)
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return Orientation(quaternion = Quaternion(quatArray = vec.T[eig.argmax()]))
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@ -1081,16 +1088,17 @@ class Orientation:
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[[ 0, 0, 1],[ 1, 0, 1]],
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[[ 1, 0, 0],[ 1, 1, 0]]]),
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}
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myPlane = planes [relationModel][variant,me]
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myNormal = normals[relationModel][variant,me]
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myPlane = myPlane/np.linalg.norm(myPlane)
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myNormal = myNormal/np.linalg.norm(myNormal)
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myMatrix = np.array([myPlane,myNormal,np.cross(myNormal,myPlane)])
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myPlane = planes [relationModel][variant,me]
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myPlane /= np.linalg.norm(myPlane)
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myNormal = normals[relationModel][variant,me]
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myNormal /= np.linalg.norm(myNormal)
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myMatrix = np.array([myPlane,myNormal,np.cross(myNormal,myPlane)])
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otherPlane = planes [relationModel][variant,other]
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otherNormal = normals[relationModel][variant,other]
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otherPlane = otherPlane/np.linalg.norm(otherPlane)
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otherNormal = otherNormal/np.linalg.norm(otherNormal)
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otherMatrix = np.array([otherPlane,otherNormal,np.cross(otherNormal,otherPlane)])
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myMatrix = np.dot(self.asMatrix(),myMatrix)
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return Orientation(matrix=np.dot(otherMatrix.T,myMatrix))
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otherPlane = planes [relationModel][variant,other]
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otherPlane /= np.linalg.norm(otherPlane)
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otherNormal = normals[relationModel][variant,other]
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otherNormal /= np.linalg.norm(otherNormal)
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otherMatrix = np.array([otherPlane,otherNormal,np.cross(otherNormal,otherPlane)])
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myMatrix = np.dot(self.asMatrix(),myMatrix)
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return Orientation(matrix=np.dot(otherMatrix.T,myMatrix)) # no symmetry information ??
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