1094 lines
48 KiB
Python
1094 lines
48 KiB
Python
# -*- coding: UTF-8 no BOM -*-
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###################################################
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# NOTE: everything here needs to be a np array #
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###################################################
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import math,os
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import numpy as np
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# ******************************************************************************************
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class Quaternion:
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u"""
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Orientation represented as unit quaternion.
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All methods and naming conventions based on Rowenhorst_etal2015
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Convention 1: coordinate frames are right-handed
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Convention 2: a rotation angle ω is taken to be positive for a counterclockwise rotation
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when viewing from the end point of the rotation axis towards the origin
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Convention 3: rotations will be interpreted in the passive sense
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Convention 4: Euler angle triplets are implemented using the Bunge convention,
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with the angular ranges as [0, 2π],[0, π],[0, 2π]
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Convention 5: the rotation angle ω is limited to the interval [0, π]
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w is the real part, (x, y, z) are the imaginary parts.
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Vector "a" (defined in coordinate system "A") is passively rotated
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resulting in new coordinates "b" when expressed in system "B".
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b = Q * a
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b = np.dot(Q.asMatrix(),a)
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"""
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def __init__(self,
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quat = None,
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q = 1.0,
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p = np.zeros(3,dtype=float)):
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"""Initializes to identity unless specified"""
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self.q = quat[0] if quat is not None else q
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self.p = np.array(quat[1:4]) if quat is not None else p
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self.homomorph()
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def __iter__(self):
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"""Components"""
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return iter(self.asList())
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def __copy__(self):
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"""Copy"""
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return self.__class__(q=self.q,p=self.p.copy())
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copy = __copy__
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def __repr__(self):
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"""Readable string"""
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return 'Quaternion(real={q:+.6f}, imag=<{p[0]:+.6f}, {p[1]:+.6f}, {p[2]:+.6f}>)'.format(q=self.q,p=self.p)
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def __pow__(self, exponent):
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"""Power"""
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omega = math.acos(self.q)
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return self.__class__(q= math.cos(exponent*omega),
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p=self.p * math.sin(exponent*omega)/math.sin(omega))
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def __ipow__(self, exponent):
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"""In-place power"""
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omega = math.acos(self.q)
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self.q = math.cos(exponent*omega)
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self.p *= math.sin(exponent*omega)/math.sin(omega)
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return self
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def __mul__(self, other):
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"""Multiplication"""
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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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try: # quaternion
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return self.__class__(q=self.q*other.q - np.dot(self.p,other.p),
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p=self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p))
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except: pass
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try: # vector (perform passive rotation)
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( x, y, z) = self.p
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(Vx,Vy,Vz) = other[0:3]
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A = self.q*self.q - np.dot(self.p,self.p)
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B = 2.0 * (x*Vx + y*Vy + z*Vz)
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C = 2.0 * P*self.q
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return np.array([
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A*Vx + B*x + C*(y*Vz - z*Vy),
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A*Vy + B*y + C*(z*Vx - x*Vz),
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A*Vz + B*z + C*(x*Vy - y*Vx),
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])
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except: pass
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try: # scalar
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return self.__class__(q=self.q*other,
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p=self.p*other)
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except:
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return self.copy()
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def __imul__(self, other):
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"""In-place multiplication"""
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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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try: # Quaternion
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self.q = self.q*other.q - np.dot(self.p,other.p)
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self.p = self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p)
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except: pass
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return self
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def __div__(self, other):
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"""Division"""
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if isinstance(other, (int,float)):
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return self.__class__(q=self.q / other,
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p=self.p / other)
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else:
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return NotImplemented
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def __idiv__(self, other):
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"""In-place division"""
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if isinstance(other, (int,float)):
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self.q /= other
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self.p /= other
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return self
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def __add__(self, other):
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"""Addition"""
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if isinstance(other, Quaternion):
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return self.__class__(q=self.q + other.q,
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p=self.p + other.p)
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else:
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return NotImplemented
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def __iadd__(self, other):
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"""In-place addition"""
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if isinstance(other, Quaternion):
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self.q += other.q
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self.p += other.p
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return self
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def __sub__(self, other):
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"""Subtraction"""
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if isinstance(other, Quaternion):
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return self.__class__(q=self.q - other.q,
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p=self.p - other.p)
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else:
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return NotImplemented
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def __isub__(self, other):
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"""In-place subtraction"""
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if isinstance(other, Quaternion):
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self.q -= other.q
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self.p -= other.p
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return self
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def __neg__(self):
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"""Additive inverse"""
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self.q = -self.q
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self.p = -self.p
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return self
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def __abs__(self):
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"""Norm"""
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return math.sqrt(self.q ** 2 + np.dot(self.p,self.p))
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magnitude = __abs__
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def __eq__(self,other):
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"""Equal (sufficiently close) to each other"""
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return np.isclose(( self-other).magnitude(),0.0) \
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or np.isclose((-self-other).magnitude(),0.0)
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def __ne__(self,other):
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"""Not equal (sufficiently close) to each other"""
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return not self.__eq__(other)
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def __cmp__(self,other):
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"""Linear ordering"""
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return (1 if np.linalg.norm(self.asRodrigues()) > np.linalg.norm(other.asRodrigues()) else 0) \
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- (1 if np.linalg.norm(self.asRodrigues()) < np.linalg.norm(other.asRodrigues()) else 0)
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def magnitude_squared(self):
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return self.q ** 2 + np.dot(self.p,self.p)
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def normalize(self):
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d = self.magnitude()
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if d > 0.0:
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self.q /= d
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self.p /= d
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return self
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def conjugate(self):
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self.p = -self.p
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return self
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def homomorph(self):
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if self.q < 0.0:
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self.q = -self.q
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self.p = -self.p
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return self
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def normalized(self):
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return self.copy().normalize()
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def conjugated(self):
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return self.copy().conjugate()
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def homomorphed(self):
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return self.copy().homomorph()
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def asList(self):
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return [self.q]+list(self.p)
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def asM(self): # to find Averaging Quaternions (see F. Landis Markley et al.)
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return np.outer(self.asList(),self.asList())
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def asMatrix(self):
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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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qbarhalf = 0.5*(self.q**2 - np.dot(self.p,self.p))
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return 2.0*np.array(
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[[ qbarhalf + self.p[0]**2 ,
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self.p[0]*self.p[1] -P* self.q*self.p[2],
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self.p[0]*self.p[2] +P* self.q*self.p[1] ],
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[ self.p[0]*self.p[1] +P* self.q*self.p[2],
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qbarhalf + self.p[1]**2 ,
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self.p[1]*self.p[2] -P* self.q*self.p[0] ],
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[ self.p[0]*self.p[2] -P* self.q*self.p[1],
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self.p[1]*self.p[2] +P* self.q*self.p[0],
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qbarhalf + self.p[2]**2 ],
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])
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def asAngleAxis(self,
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degrees = False,
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flat = False):
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angle = 2.0*math.acos(self.q)
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if np.isclose(angle,0.0):
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angle = 0.0
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axis = np.array([0.0,0.0,1.0])
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elif np.isclose(self.q,0.0):
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angle = math.pi
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axis = self.p
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else:
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axis = np.sign(self.q)*self.p/np.linalg.norm(self.p)
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angle = np.degrees(angle) if degrees else angle
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return np.hstack((angle,axis)) if flat else (angle,axis)
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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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def fromIdentity(cls):
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return cls()
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@classmethod
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def fromRandom(cls,randomSeed = None):
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import binascii
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if randomSeed is None:
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randomSeed = int(binascii.hexlify(os.urandom(4)),16)
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np.random.seed(randomSeed)
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r = np.random.random(3)
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A = math.sqrt(max(0.0,r[2]))
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B = math.sqrt(max(0.0,1.0-r[2]))
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w = math.cos(2.0*math.pi*r[0])*A
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x = math.sin(2.0*math.pi*r[1])*B
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y = math.cos(2.0*math.pi*r[1])*B
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z = math.sin(2.0*math.pi*r[0])*A
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return cls(quat=[w,x,y,z])
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@classmethod
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def fromRodrigues(cls, rodrigues):
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if not isinstance(rodrigues, np.ndarray): rodrigues = np.array(rodrigues)
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norm = np.linalg.norm(rodrigues)
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halfangle = math.atan(norm)
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s = math.sin(halfangle)
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c = math.cos(halfangle)
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return cls(q=c,p=s*rodrigues/norm)
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@classmethod
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def fromAngleAxis(cls,
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angle,
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axis,
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degrees = False):
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if not isinstance(axis, np.ndarray): axis = np.array(axis,dtype=float)
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axis = axis.astype(float)/np.linalg.norm(axis)
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angle = np.radians(angle) if degrees else angle
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s = math.sin(0.5 * angle)
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c = math.cos(0.5 * angle)
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return cls(q=c,p=axis*s)
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@classmethod
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def fromEulers(cls,
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eulers,
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degrees = False):
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if not isinstance(eulers, np.ndarray): eulers = np.array(eulers,dtype=float)
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eulers = np.radians(eulers) if degrees else eulers
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sigma = 0.5*(eulers[0]+eulers[2])
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delta = 0.5*(eulers[0]-eulers[2])
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c = np.cos(0.5*eulers[1])
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s = np.sin(0.5*eulers[1])
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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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w = c * np.cos(sigma)
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x = -P * s * np.cos(delta)
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y = -P * s * np.sin(delta)
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z = -P * c * np.sin(sigma)
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return cls(quat=[w,x,y,z])
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# Modified Method to calculate Quaternion from Orientation Matrix,
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# Source: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
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@classmethod
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def fromMatrix(cls, m):
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if m.shape != (3,3) and np.prod(m.shape) == 9:
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m = m.reshape(3,3)
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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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w = 0.5*math.sqrt(max(0.0,1.0+m[0,0]+m[1,1]+m[2,2]))
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x = P*0.5*math.sqrt(max(0.0,1.0+m[0,0]-m[1,1]-m[2,2]))
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y = P*0.5*math.sqrt(max(0.0,1.0-m[0,0]+m[1,1]-m[2,2]))
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z = P*0.5*math.sqrt(max(0.0,1.0-m[0,0]-m[1,1]+m[2,2]))
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x *= -1 if m[2,1] < m[1,2] else 1
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y *= -1 if m[0,2] < m[2,0] else 1
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z *= -1 if m[1,0] < m[0,1] else 1
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return cls(quat=np.array([w,x,y,z])/math.sqrt(w**2 + x**2 + y**2 + z**2))
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@classmethod
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def new_interpolate(cls, q1, q2, t):
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"""
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Interpolation
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See http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070017872_2007014421.pdf
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for (another?) way to interpolate quaternions.
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"""
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assert isinstance(q1, Quaternion) and isinstance(q2, Quaternion)
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Q = cls()
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costheta = q1.q*q2.q + np.dot(q1.p,q2.p)
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if costheta < 0.:
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costheta = -costheta
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q1 = q1.conjugated()
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elif costheta > 1.:
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costheta = 1.
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theta = math.acos(costheta)
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if abs(theta) < 0.01:
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Q.q = q2.q
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Q.p = q2.p
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return Q
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sintheta = math.sqrt(1.0 - costheta * costheta)
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if abs(sintheta) < 0.01:
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Q.q = (q1.q + q2.q) * 0.5
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Q.p = (q1.p + q2.p) * 0.5
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return Q
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ratio1 = math.sin((1.0 - t) * theta) / sintheta
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ratio2 = math.sin( t * theta) / sintheta
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Q.q = q1.q * ratio1 + q2.q * ratio2
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Q.p = q1.p * ratio1 + q2.p * ratio2
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return Q
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# ******************************************************************************************
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class Symmetry:
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lattices = [None,'orthorhombic','tetragonal','hexagonal','cubic',]
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def __init__(self, symmetry = None):
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"""Lattice with given symmetry, defaults to None"""
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if isinstance(symmetry, str) and symmetry.lower() in Symmetry.lattices:
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self.lattice = symmetry.lower()
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else:
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self.lattice = None
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def __copy__(self):
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"""Copy"""
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return self.__class__(self.lattice)
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copy = __copy__
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def __repr__(self):
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"""Readable string"""
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return '{}'.format(self.lattice)
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def __eq__(self, other):
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"""Equal to other"""
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return self.lattice == other.lattice
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def __neq__(self, other):
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"""Not equal to other"""
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return not self.__eq__(other)
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def __cmp__(self,other):
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"""Linear ordering"""
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myOrder = Symmetry.lattices.index(self.lattice)
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otherOrder = Symmetry.lattices.index(other.lattice)
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return (myOrder > otherOrder) - (myOrder < otherOrder)
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def symmetryQuats(self,who = []):
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"""List of symmetry operations as quaternions."""
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if self.lattice == 'cubic':
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symQuats = [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ],
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[ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2), 0.0, -0.5*math.sqrt(2) ],
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[ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
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[ 0.0, -0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
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[ 0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, -0.5 ],
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[-0.5, 0.5, -0.5, 0.5 ],
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[-0.5, -0.5, 0.5, 0.5 ],
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[-0.5, -0.5, 0.5, -0.5 ],
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[-0.5, -0.5, -0.5, 0.5 ],
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[-0.5, 0.5, -0.5, -0.5 ],
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[-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
|
|
[ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
|
|
[-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ],
|
|
[-0.5*math.sqrt(2), 0.0, -0.5*math.sqrt(2), 0.0 ],
|
|
[-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ],
|
|
[-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ],
|
|
]
|
|
elif self.lattice == 'hexagonal':
|
|
symQuats = [
|
|
[ 1.0,0.0,0.0,0.0 ],
|
|
[-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ],
|
|
[ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
|
|
[ 0.0,0.0,0.0,1.0 ],
|
|
[-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
|
|
[-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ],
|
|
[ 0.0,1.0,0.0,0.0 ],
|
|
[ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ],
|
|
[ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ],
|
|
[ 0.0,0.0,1.0,0.0 ],
|
|
[ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ],
|
|
[ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ],
|
|
]
|
|
elif self.lattice == 'tetragonal':
|
|
symQuats = [
|
|
[ 1.0,0.0,0.0,0.0 ],
|
|
[ 0.0,1.0,0.0,0.0 ],
|
|
[ 0.0,0.0,1.0,0.0 ],
|
|
[ 0.0,0.0,0.0,1.0 ],
|
|
[ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
|
|
[ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
|
|
[ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
|
|
[-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
|
|
]
|
|
elif self.lattice == 'orthorhombic':
|
|
symQuats = [
|
|
[ 1.0,0.0,0.0,0.0 ],
|
|
[ 0.0,1.0,0.0,0.0 ],
|
|
[ 0.0,0.0,1.0,0.0 ],
|
|
[ 0.0,0.0,0.0,1.0 ],
|
|
]
|
|
else:
|
|
symQuats = [
|
|
[ 1.0,0.0,0.0,0.0 ],
|
|
]
|
|
|
|
return list(map(Quaternion,
|
|
np.array(symQuats)[np.atleast_1d(np.array(who)) if who != [] else range(len(symQuats))]))
|
|
|
|
|
|
def equivalentQuaternions(self,
|
|
quaternion,
|
|
who = []):
|
|
"""List of symmetrically equivalent quaternions based on own symmetry."""
|
|
return [q*quaternion for q in self.symmetryQuats(who)]
|
|
|
|
|
|
def inFZ(self,R):
|
|
"""Check whether given Rodrigues vector falls into fundamental zone of own symmetry."""
|
|
if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentally passed quaternion
|
|
# fundamental zone in Rodrigues space is point symmetric around origin
|
|
R = abs(R)
|
|
if self.lattice == 'cubic':
|
|
return math.sqrt(2.0)-1.0 >= R[0] \
|
|
and math.sqrt(2.0)-1.0 >= R[1] \
|
|
and math.sqrt(2.0)-1.0 >= R[2] \
|
|
and 1.0 >= R[0] + R[1] + R[2]
|
|
elif self.lattice == 'hexagonal':
|
|
return 1.0 >= R[0] and 1.0 >= R[1] and 1.0 >= R[2] \
|
|
and 2.0 >= math.sqrt(3)*R[0] + R[1] \
|
|
and 2.0 >= math.sqrt(3)*R[1] + R[0] \
|
|
and 2.0 >= math.sqrt(3) + R[2]
|
|
elif self.lattice == 'tetragonal':
|
|
return 1.0 >= R[0] and 1.0 >= R[1] \
|
|
and math.sqrt(2.0) >= R[0] + R[1] \
|
|
and math.sqrt(2.0) >= R[2] + 1.0
|
|
elif self.lattice == 'orthorhombic':
|
|
return 1.0 >= R[0] and 1.0 >= R[1] and 1.0 >= R[2]
|
|
else:
|
|
return True
|
|
|
|
|
|
def inDisorientationSST(self,R):
|
|
"""
|
|
Check whether given Rodrigues vector (of misorientation) falls into standard stereographic triangle of own symmetry.
|
|
|
|
Determination of disorientations follow the work of A. Heinz and P. Neumann:
|
|
Representation of Orientation and Disorientation Data for Cubic, Hexagonal, Tetragonal and Orthorhombic Crystals
|
|
Acta Cryst. (1991). A47, 780-789
|
|
"""
|
|
if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentially passed quaternion
|
|
|
|
epsilon = 0.0
|
|
if self.lattice == 'cubic':
|
|
return R[0] >= R[1]+epsilon and R[1] >= R[2]+epsilon and R[2] >= epsilon
|
|
|
|
elif self.lattice == 'hexagonal':
|
|
return R[0] >= math.sqrt(3)*(R[1]-epsilon) and R[1] >= epsilon and R[2] >= epsilon
|
|
|
|
elif self.lattice == 'tetragonal':
|
|
return R[0] >= R[1]-epsilon and R[1] >= epsilon and R[2] >= epsilon
|
|
|
|
elif self.lattice == 'orthorhombic':
|
|
return R[0] >= epsilon and R[1] >= epsilon and R[2] >= epsilon
|
|
|
|
else:
|
|
return True
|
|
|
|
|
|
def inSST(self,
|
|
vector,
|
|
proper = False,
|
|
color = False):
|
|
"""
|
|
Check whether given vector falls into standard stereographic triangle of own symmetry.
|
|
|
|
proper considers only vectors with z >= 0, hence uses two neighboring SSTs.
|
|
Return inverse pole figure color if requested.
|
|
"""
|
|
# basis = {'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
|
|
# [1.,0.,1.]/np.sqrt(2.), # direction of green
|
|
# [1.,1.,1.]/np.sqrt(3.)]).transpose()), # direction of blue
|
|
# 'hexagonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
|
|
# [1.,0.,0.], # direction of green
|
|
# [np.sqrt(3.),1.,0.]/np.sqrt(4.)]).transpose()), # direction of blue
|
|
# 'tetragonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
|
|
# [1.,0.,0.], # direction of green
|
|
# [1.,1.,0.]/np.sqrt(2.)]).transpose()), # direction of blue
|
|
# 'orthorhombic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
|
|
# [1.,0.,0.], # direction of green
|
|
# [0.,1.,0.]]).transpose()), # direction of blue
|
|
# }
|
|
|
|
if self.lattice == 'cubic':
|
|
basis = {'improper':np.array([ [-1. , 0. , 1. ],
|
|
[ np.sqrt(2.) , -np.sqrt(2.) , 0. ],
|
|
[ 0. , np.sqrt(3.) , 0. ] ]),
|
|
'proper':np.array([ [ 0. , -1. , 1. ],
|
|
[-np.sqrt(2.) , np.sqrt(2.) , 0. ],
|
|
[ np.sqrt(3.) , 0. , 0. ] ]),
|
|
}
|
|
elif self.lattice == 'hexagonal':
|
|
basis = {'improper':np.array([ [ 0. , 0. , 1. ],
|
|
[ 1. , -np.sqrt(3.) , 0. ],
|
|
[ 0. , 2. , 0. ] ]),
|
|
'proper':np.array([ [ 0. , 0. , 1. ],
|
|
[-1. , np.sqrt(3.) , 0. ],
|
|
[ np.sqrt(3.) , -1. , 0. ] ]),
|
|
}
|
|
elif self.lattice == 'tetragonal':
|
|
basis = {'improper':np.array([ [ 0. , 0. , 1. ],
|
|
[ 1. , -1. , 0. ],
|
|
[ 0. , np.sqrt(2.) , 0. ] ]),
|
|
'proper':np.array([ [ 0. , 0. , 1. ],
|
|
[-1. , 1. , 0. ],
|
|
[ np.sqrt(2.) , 0. , 0. ] ]),
|
|
}
|
|
elif self.lattice == 'orthorhombic':
|
|
basis = {'improper':np.array([ [ 0., 0., 1.],
|
|
[ 1., 0., 0.],
|
|
[ 0., 1., 0.] ]),
|
|
'proper':np.array([ [ 0., 0., 1.],
|
|
[-1., 0., 0.],
|
|
[ 0., 1., 0.] ]),
|
|
}
|
|
else: # direct exit for unspecified symmetry
|
|
if color:
|
|
return (True,np.zeros(3,'d'))
|
|
else:
|
|
return True
|
|
|
|
v = np.array(vector,dtype=float)
|
|
if proper: # check both improper ...
|
|
theComponents = np.dot(basis['improper'],v)
|
|
inSST = np.all(theComponents >= 0.0)
|
|
if not inSST: # ... and proper SST
|
|
theComponents = np.dot(basis['proper'],v)
|
|
inSST = np.all(theComponents >= 0.0)
|
|
else:
|
|
v[2] = abs(v[2]) # z component projects identical
|
|
theComponents = np.dot(basis['improper'],v) # for positive and negative values
|
|
inSST = np.all(theComponents >= 0.0)
|
|
|
|
if color: # have to return color array
|
|
if inSST:
|
|
rgb = np.power(theComponents/np.linalg.norm(theComponents),0.5) # smoothen color ramps
|
|
rgb = np.minimum(np.ones(3,dtype=float),rgb) # limit to maximum intensity
|
|
rgb /= max(rgb) # normalize to (HS)V = 1
|
|
else:
|
|
rgb = np.zeros(3,dtype=float)
|
|
return (inSST,rgb)
|
|
else:
|
|
return inSST
|
|
|
|
# code derived from https://github.com/ezag/pyeuclid
|
|
# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
|
|
|
|
|
|
|
|
# ******************************************************************************************
|
|
class Orientation:
|
|
|
|
__slots__ = ['quaternion','symmetry']
|
|
|
|
def __init__(self,
|
|
quaternion = Quaternion.fromIdentity(),
|
|
Rodrigues = None,
|
|
angleAxis = None,
|
|
matrix = None,
|
|
Eulers = None,
|
|
random = False, # integer to have a fixed seed or True for real random
|
|
symmetry = None,
|
|
degrees = False,
|
|
):
|
|
if random: # produce random orientation
|
|
if isinstance(random, bool ):
|
|
self.quaternion = Quaternion.fromRandom()
|
|
else:
|
|
self.quaternion = Quaternion.fromRandom(randomSeed=random)
|
|
elif isinstance(Eulers, np.ndarray) and Eulers.shape == (3,): # based on given Euler angles
|
|
self.quaternion = Quaternion.fromEulers(Eulers,degrees=degrees)
|
|
elif isinstance(matrix, np.ndarray) : # based on given rotation matrix
|
|
self.quaternion = Quaternion.fromMatrix(matrix)
|
|
elif isinstance(angleAxis, np.ndarray) and angleAxis.shape == (4,): # based on given angle and rotation axis
|
|
self.quaternion = Quaternion.fromAngleAxis(angleAxis[0],angleAxis[1:4],degrees=degrees)
|
|
elif isinstance(Rodrigues, np.ndarray) and Rodrigues.shape == (3,): # based on given Rodrigues vector
|
|
self.quaternion = Quaternion.fromRodrigues(Rodrigues)
|
|
elif isinstance(quaternion, Quaternion): # based on given quaternion
|
|
self.quaternion = quaternion.homomorphed()
|
|
elif (isinstance(quaternion, np.ndarray) and quaternion.shape == (4,)) or \
|
|
(isinstance(quaternion, list) and len(quaternion) == 4 ): # based on given quaternion-like array
|
|
self.quaternion = Quaternion(quat=quaternion).homomorphed()
|
|
|
|
self.symmetry = Symmetry(symmetry)
|
|
|
|
def __copy__(self):
|
|
"""Copy"""
|
|
return self.__class__(quaternion=self.quaternion,symmetry=self.symmetry.lattice)
|
|
|
|
copy = __copy__
|
|
|
|
|
|
def __repr__(self):
|
|
"""Value as all implemented representations"""
|
|
return '\n'.join([
|
|
'Symmetry: {}'.format(self.symmetry),
|
|
'Quaternion: {}'.format(self.quaternion),
|
|
'Matrix:\n{}'.format( '\n'.join(['\t'.join(list(map(str,self.asMatrix()[i,:]))) for i in range(3)]) ),
|
|
'Bunge Eulers / deg: {}'.format('\t'.join(list(map(str,self.asEulers(degrees=True)))) ),
|
|
])
|
|
|
|
def asQuaternion(self):
|
|
return self.quaternion.asList()
|
|
|
|
def asEulers(self,
|
|
degrees = False,
|
|
):
|
|
return self.quaternion.asEulers(degrees)
|
|
eulers = property(asEulers)
|
|
|
|
def asRodrigues(self):
|
|
return self.quaternion.asRodrigues()
|
|
rodrigues = property(asRodrigues)
|
|
|
|
def asAngleAxis(self,
|
|
degrees = False,
|
|
flat = False):
|
|
return self.quaternion.asAngleAxis(degrees,flat)
|
|
angleAxis = property(asAngleAxis)
|
|
|
|
def asMatrix(self):
|
|
return self.quaternion.asMatrix()
|
|
matrix = property(asMatrix)
|
|
|
|
def inFZ(self):
|
|
return self.symmetry.inFZ(self.quaternion.asRodrigues())
|
|
infz = property(inFZ)
|
|
|
|
def equivalentQuaternions(self,
|
|
who = []):
|
|
return self.symmetry.equivalentQuaternions(self.quaternion,who)
|
|
|
|
def equivalentOrientations(self,
|
|
who = []):
|
|
return [Orientation(quaternion = q, symmetry = self.symmetry.lattice) for q in self.equivalentQuaternions(who)]
|
|
|
|
def reduced(self):
|
|
"""Transform orientation to fall into fundamental zone according to symmetry"""
|
|
for me in self.symmetry.equivalentQuaternions(self.quaternion):
|
|
if self.symmetry.inFZ(me.asRodrigues()): break
|
|
|
|
return Orientation(quaternion=me,symmetry=self.symmetry.lattice)
|
|
|
|
|
|
def disorientation(self,
|
|
other,
|
|
SST = True):
|
|
"""
|
|
Disorientation between myself and given other orientation.
|
|
|
|
Rotation axis falls into SST if SST == True.
|
|
(Currently requires same symmetry for both orientations.
|
|
Look into A. Heinz and P. Neumann 1991 for cases with differing sym.)
|
|
"""
|
|
if self.symmetry != other.symmetry: raise TypeError('disorientation between different symmetry classes not supported yet.')
|
|
|
|
misQ = other.quaternion*self.quaternion.conjugated()
|
|
mySymQs = self.symmetry.symmetryQuats() if SST else self.symmetry.symmetryQuats()[:1] # take all or only first sym operation
|
|
otherSymQs = other.symmetry.symmetryQuats()
|
|
|
|
for i,sA in enumerate(mySymQs):
|
|
for j,sB in enumerate(otherSymQs):
|
|
theQ = sB*misQ*sA.conjugated()
|
|
for k in range(2):
|
|
theQ.conjugate()
|
|
breaker = self.symmetry.inFZ(theQ) \
|
|
and (not SST or other.symmetry.inDisorientationSST(theQ))
|
|
if breaker: break
|
|
if breaker: break
|
|
if breaker: break
|
|
|
|
# disorientation, own sym, other sym, self-->other: True, self<--other: False
|
|
return (Orientation(quaternion = theQ,symmetry = self.symmetry.lattice),
|
|
i,j, k == 1)
|
|
|
|
|
|
def inversePole(self,
|
|
axis,
|
|
proper = False,
|
|
SST = True):
|
|
"""Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)"""
|
|
if SST: # pole requested to be within SST
|
|
for i,q in enumerate(self.symmetry.equivalentQuaternions(self.quaternion)): # test all symmetric equivalent quaternions
|
|
pole = q*axis # align crystal direction to axis
|
|
if self.symmetry.inSST(pole,proper): break # found SST version
|
|
else:
|
|
pole = self.quaternion*axis # align crystal direction to axis
|
|
|
|
return (pole,i if SST else 0)
|
|
|
|
def IPFcolor(self,axis):
|
|
"""TSL color of inverse pole figure for given axis"""
|
|
color = np.zeros(3,'d')
|
|
|
|
for q in self.symmetry.equivalentQuaternions(self.quaternion):
|
|
pole = q*axis # align crystal direction to axis
|
|
inSST,color = self.symmetry.inSST(pole,color=True)
|
|
if inSST: break
|
|
|
|
return color
|
|
|
|
@classmethod
|
|
def average(cls,
|
|
orientations,
|
|
multiplicity = []):
|
|
"""
|
|
Average orientation
|
|
|
|
ref: F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman.
|
|
Averaging Quaternions,
|
|
Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197.
|
|
doi: 10.2514/1.28949
|
|
usage:
|
|
a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry='hexagonal')
|
|
b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
|
|
avg = Orientation.average([a,b])
|
|
"""
|
|
if not all(isinstance(item, Orientation) for item in orientations):
|
|
raise TypeError("Only instances of Orientation can be averaged.")
|
|
|
|
N = len(orientations)
|
|
if multiplicity == [] or not multiplicity:
|
|
multiplicity = np.ones(N,dtype='i')
|
|
|
|
reference = orientations[0] # take first as reference
|
|
for i,(o,n) in enumerate(zip(orientations,multiplicity)):
|
|
closest = o.equivalentOrientations(reference.disorientation(o,SST = False)[2])[0] # select sym orientation with lowest misorientation
|
|
M = closest.quaternion.asM() * n if i == 0 else M + closest.quaternion.asM() * n # noqa add (multiples) of this orientation to average noqa
|
|
eig, vec = np.linalg.eig(M/N)
|
|
|
|
return Orientation(quaternion = Quaternion(quat = np.real(vec.T[eig.argmax()])),
|
|
symmetry = reference.symmetry.lattice)
|
|
|
|
|
|
def related(self,
|
|
relationModel,
|
|
direction,
|
|
targetSymmetry = 'cubic'):
|
|
"""
|
|
Orientation relationship
|
|
|
|
positive number: fcc --> bcc
|
|
negative number: bcc --> fcc
|
|
"""
|
|
if relationModel not in ['KS','GT','GTdash','NW','Pitsch','Bain']: return None
|
|
if int(direction) == 0: return None
|
|
|
|
# KS from S. Morito et al./Journal of Alloys and Compounds 5775 (2013) S587-S592
|
|
# for KS rotation matrices also check K. Kitahara et al./Acta Materialia 54 (2006) 1279-1288
|
|
# GT from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
|
# GT' from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
|
# NW from H. Kitahara et al./Materials Characterization 54 (2005) 378-386
|
|
# Pitsch from Y. He et al./Acta Materialia 53 (2005) 1179-1190
|
|
# Bain from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
|
|
|
variant = int(abs(direction))-1
|
|
(me,other) = (0,1) if direction > 0 else (1,0)
|
|
|
|
planes = {'KS': \
|
|
np.array([[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, -1],[ 0, 1, 1]],
|
|
[[ 1, 1, -1],[ 0, 1, 1]],
|
|
[[ 1, 1, -1],[ 0, 1, 1]],
|
|
[[ 1, 1, -1],[ 0, 1, 1]],
|
|
[[ 1, 1, -1],[ 0, 1, 1]],
|
|
[[ 1, 1, -1],[ 0, 1, 1]]]),
|
|
'GT': \
|
|
np.array([[[ 1, 1, 1],[ 1, 0, 1]],
|
|
[[ 1, 1, 1],[ 1, 1, 0]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, -1, 1],[ -1, 0, 1]],
|
|
[[ -1, -1, 1],[ -1, -1, 0]],
|
|
[[ -1, -1, 1],[ 0, -1, 1]],
|
|
[[ -1, 1, 1],[ -1, 0, 1]],
|
|
[[ -1, 1, 1],[ -1, 1, 0]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 1, 0, 1]],
|
|
[[ 1, -1, 1],[ 1, -1, 0]],
|
|
[[ 1, -1, 1],[ 0, -1, 1]],
|
|
[[ 1, 1, 1],[ 1, 1, 0]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 1, 0, 1]],
|
|
[[ -1, -1, 1],[ -1, -1, 0]],
|
|
[[ -1, -1, 1],[ 0, -1, 1]],
|
|
[[ -1, -1, 1],[ -1, 0, 1]],
|
|
[[ -1, 1, 1],[ -1, 1, 0]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ -1, 0, 1]],
|
|
[[ 1, -1, 1],[ 1, -1, 0]],
|
|
[[ 1, -1, 1],[ 0, -1, 1]],
|
|
[[ 1, -1, 1],[ 1, 0, 1]]]),
|
|
'GTdash': \
|
|
np.array([[[ 7, 17, 17],[ 12, 5, 17]],
|
|
[[ 17, 7, 17],[ 17, 12, 5]],
|
|
[[ 17, 17, 7],[ 5, 17, 12]],
|
|
[[ -7,-17, 17],[-12, -5, 17]],
|
|
[[-17, -7, 17],[-17,-12, 5]],
|
|
[[-17,-17, 7],[ -5,-17, 12]],
|
|
[[ 7,-17,-17],[ 12, -5,-17]],
|
|
[[ 17, -7,-17],[ 17,-12, -5]],
|
|
[[ 17,-17, -7],[ 5,-17,-12]],
|
|
[[ -7, 17,-17],[-12, 5,-17]],
|
|
[[-17, 7,-17],[-17, 12, -5]],
|
|
[[-17, 17, -7],[ -5, 17,-12]],
|
|
[[ 7, 17, 17],[ 12, 17, 5]],
|
|
[[ 17, 7, 17],[ 5, 12, 17]],
|
|
[[ 17, 17, 7],[ 17, 5, 12]],
|
|
[[ -7,-17, 17],[-12,-17, 5]],
|
|
[[-17, -7, 17],[ -5,-12, 17]],
|
|
[[-17,-17, 7],[-17, -5, 12]],
|
|
[[ 7,-17,-17],[ 12,-17, -5]],
|
|
[[ 17, -7,-17],[ 5, -12,-17]],
|
|
[[ 17,-17, 7],[ 17, -5,-12]],
|
|
[[ -7, 17,-17],[-12, 17, -5]],
|
|
[[-17, 7,-17],[ -5, 12,-17]],
|
|
[[-17, 17, -7],[-17, 5,-12]]]),
|
|
'NW': \
|
|
np.array([[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
|
[[ -1, -1, 1],[ 0, 1, 1]],
|
|
[[ -1, -1, 1],[ 0, 1, 1]],
|
|
[[ -1, -1, 1],[ 0, 1, 1]]]),
|
|
'Pitsch': \
|
|
np.array([[[ 0, 1, 0],[ -1, 0, 1]],
|
|
[[ 0, 0, 1],[ 1, -1, 0]],
|
|
[[ 1, 0, 0],[ 0, 1, -1]],
|
|
[[ 1, 0, 0],[ 0, -1, -1]],
|
|
[[ 0, 1, 0],[ -1, 0, -1]],
|
|
[[ 0, 0, 1],[ -1, -1, 0]],
|
|
[[ 0, 1, 0],[ -1, 0, -1]],
|
|
[[ 0, 0, 1],[ -1, -1, 0]],
|
|
[[ 1, 0, 0],[ 0, -1, -1]],
|
|
[[ 1, 0, 0],[ 0, -1, 1]],
|
|
[[ 0, 1, 0],[ 1, 0, -1]],
|
|
[[ 0, 0, 1],[ -1, 1, 0]]]),
|
|
'Bain': \
|
|
np.array([[[ 1, 0, 0],[ 1, 0, 0]],
|
|
[[ 0, 1, 0],[ 0, 1, 0]],
|
|
[[ 0, 0, 1],[ 0, 0, 1]]]),
|
|
}
|
|
|
|
normals = {'KS': \
|
|
np.array([[[ -1, 0, 1],[ -1, -1, 1]],
|
|
[[ -1, 0, 1],[ -1, 1, -1]],
|
|
[[ 0, 1, -1],[ -1, -1, 1]],
|
|
[[ 0, 1, -1],[ -1, 1, -1]],
|
|
[[ 1, -1, 0],[ -1, -1, 1]],
|
|
[[ 1, -1, 0],[ -1, 1, -1]],
|
|
[[ 1, 0, -1],[ -1, -1, 1]],
|
|
[[ 1, 0, -1],[ -1, 1, -1]],
|
|
[[ -1, -1, 0],[ -1, -1, 1]],
|
|
[[ -1, -1, 0],[ -1, 1, -1]],
|
|
[[ 0, 1, 1],[ -1, -1, 1]],
|
|
[[ 0, 1, 1],[ -1, 1, -1]],
|
|
[[ 0, -1, 1],[ -1, -1, 1]],
|
|
[[ 0, -1, 1],[ -1, 1, -1]],
|
|
[[ -1, 0, -1],[ -1, -1, 1]],
|
|
[[ -1, 0, -1],[ -1, 1, -1]],
|
|
[[ 1, 1, 0],[ -1, -1, 1]],
|
|
[[ 1, 1, 0],[ -1, 1, -1]],
|
|
[[ -1, 1, 0],[ -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, 0, 1],[ -1, 1, -1]]]),
|
|
'GT': \
|
|
np.array([[[ -5,-12, 17],[-17, -7, 17]],
|
|
[[ 17, -5,-12],[ 17,-17, -7]],
|
|
[[-12, 17, -5],[ -7, 17,-17]],
|
|
[[ 5, 12, 17],[ 17, 7, 17]],
|
|
[[-17, 5,-12],[-17, 17, -7]],
|
|
[[ 12,-17, -5],[ 7,-17,-17]],
|
|
[[ -5, 12,-17],[-17, 7,-17]],
|
|
[[ 17, 5, 12],[ 17, 17, 7]],
|
|
[[-12,-17, 5],[ -7,-17, 17]],
|
|
[[ 5,-12,-17],[ 17, -7,-17]],
|
|
[[-17, -5, 12],[-17,-17, 7]],
|
|
[[ 12, 17, 5],[ 7, 17, 17]],
|
|
[[ -5, 17,-12],[-17, 17, -7]],
|
|
[[-12, -5, 17],[ -7,-17, 17]],
|
|
[[ 17,-12, -5],[ 17, -7,-17]],
|
|
[[ 5,-17,-12],[ 17,-17, -7]],
|
|
[[ 12, 5, 17],[ 7, 17, 17]],
|
|
[[-17, 12, -5],[-17, 7,-17]],
|
|
[[ -5,-17, 12],[-17,-17, 7]],
|
|
[[-12, 5,-17],[ -7, 17,-17]],
|
|
[[ 17, 12, 5],[ 17, 7, 17]],
|
|
[[ 5, 17, 12],[ 17, 17, 7]],
|
|
[[ 12, -5,-17],[ 7,-17,-17]],
|
|
[[-17,-12, 5],[-17, 7, 17]]]),
|
|
'GTdash': \
|
|
np.array([[[ 0, 1, -1],[ 1, 1, -1]],
|
|
[[ -1, 0, 1],[ -1, 1, 1]],
|
|
[[ 1, -1, 0],[ 1, -1, 1]],
|
|
[[ 0, -1, -1],[ -1, -1, -1]],
|
|
[[ 1, 0, 1],[ 1, -1, 1]],
|
|
[[ 1, -1, 0],[ 1, -1, -1]],
|
|
[[ 0, 1, -1],[ -1, 1, -1]],
|
|
[[ 1, 0, 1],[ 1, 1, 1]],
|
|
[[ -1, -1, 0],[ -1, -1, 1]],
|
|
[[ 0, -1, -1],[ 1, -1, -1]],
|
|
[[ -1, 0, 1],[ -1, -1, 1]],
|
|
[[ -1, -1, 0],[ -1, -1, -1]],
|
|
[[ 0, -1, 1],[ 1, -1, 1]],
|
|
[[ 1, 0, -1],[ 1, 1, -1]],
|
|
[[ -1, 1, 0],[ -1, 1, 1]],
|
|
[[ 0, 1, 1],[ -1, 1, 1]],
|
|
[[ -1, 0, -1],[ -1, -1, -1]],
|
|
[[ -1, 1, 0],[ -1, 1, -1]],
|
|
[[ 0, -1, 1],[ -1, -1, 1]],
|
|
[[ -1, 0, -1],[ -1, 1, -1]],
|
|
[[ 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)
|