Merge branch 'no-python-quaternion' into 'development'
No python quaternion See merge request damask/DAMASK!122
This commit is contained in:
Philip Eisenlohr
commit
87767f0cc2
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@ -3,9 +3,8 @@ import math
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import numpy as np
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from . import Lambert
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from .quaternion import Quaternion
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from .quaternion import P
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P = -1
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####################################################################################################
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class Rotation:
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@ -50,10 +49,7 @@ class Rotation:
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Unit quaternion that follows the conventions. Use .fromQuaternion to perform a sanity check.
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"""
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if isinstance(quaternion,Quaternion):
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self.quaternion = quaternion.copy()
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else:
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self.quaternion = Quaternion(q=quaternion[0],p=quaternion[1:4])
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self.quaternion = quaternion.copy()
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def __copy__(self):
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"""Copy."""
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@ -65,9 +61,9 @@ class Rotation:
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def __repr__(self):
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"""Orientation displayed as unit quaternion, rotation matrix, and Bunge-Euler angles."""
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return '\n'.join([
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'{}'.format(self.quaternion),
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'Matrix:\n{}'.format( '\n'.join(['\t'.join(list(map(str,self.asMatrix()[i,:]))) for i in range(3)]) ),
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'Bunge Eulers / deg: {}'.format('\t'.join(list(map(str,self.asEulers(degrees=True)))) ),
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'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
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'Matrix:\n{}'.format(self.asMatrix()),
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'Bunge Eulers / deg: ({:3.2f}, {:3.2f}, {:3.2f})'.format(*self.asEulers(degrees=True)),
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])
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def __mul__(self, other):
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@ -86,19 +82,25 @@ class Rotation:
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"""
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if isinstance(other, Rotation): # rotate a rotation
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return self.__class__(self.quaternion * other.quaternion).standardize()
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elif isinstance(other, np.ndarray):
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if other.shape == (3,): # rotate a single (3)-vector
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( x, y, z) = self.quaternion.p
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(Vx,Vy,Vz) = other[0:3]
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A = self.quaternion.q*self.quaternion.q - np.dot(self.quaternion.p,self.quaternion.p)
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B = 2.0 * (x*Vx + y*Vy + z*Vz)
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C = 2.0 * P*self.quaternion.q
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self_q = self.quaternion[0]
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self_p = self.quaternion[1:]
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other_q = other.quaternion[0]
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other_p = other.quaternion[1:]
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R = self.__class__(np.append(self_q*other_q - np.dot(self_p,other_p),
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self_q*other_p + other_q*self_p + P * np.cross(self_p,other_p)))
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return R.standardize()
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elif isinstance(other, (tuple,np.ndarray)):
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if isinstance(other,tuple) or other.shape == (3,): # rotate a single (3)-vector or meshgrid
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A = self.quaternion[0]**2.0 - np.dot(self.quaternion[1:],self.quaternion[1:])
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B = 2.0 * ( self.quaternion[1]*other[0]
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+ self.quaternion[2]*other[1]
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+ self.quaternion[3]*other[2])
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C = 2.0 * P*self.quaternion[0]
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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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A*other[0] + B*self.quaternion[1] + C*(self.quaternion[2]*other[2] - self.quaternion[3]*other[1]),
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A*other[1] + B*self.quaternion[2] + C*(self.quaternion[3]*other[0] - self.quaternion[1]*other[2]),
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A*other[2] + B*self.quaternion[3] + C*(self.quaternion[1]*other[1] - self.quaternion[2]*other[0]),
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])
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elif other.shape == (3,3,): # rotate a single (3x3)-matrix
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return np.dot(self.asMatrix(),np.dot(other,self.asMatrix().T))
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@ -106,25 +108,13 @@ class Rotation:
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raise NotImplementedError
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else:
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return NotImplemented
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elif isinstance(other, tuple): # used to rotate a meshgrid-tuple
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( x, y, z) = self.quaternion.p
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(Vx,Vy,Vz) = other[0:3]
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A = self.quaternion.q*self.quaternion.q - np.dot(self.quaternion.p,self.quaternion.p)
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B = 2.0 * (x*Vx + y*Vy + z*Vz)
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C = 2.0 * P*self.quaternion.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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else:
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return NotImplemented
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def inverse(self):
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"""In-place inverse rotation/backward rotation."""
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self.quaternion.conjugate()
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self.quaternion[1:] *= -1
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return self
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def inversed(self):
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@ -134,7 +124,7 @@ class Rotation:
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def standardize(self):
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"""In-place quaternion representation with positive q."""
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if self.quaternion.q < 0.0: self.quaternion.homomorph()
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if self.quaternion[0] < 0.0: self.quaternion*=-1
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return self
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def standardized(self):
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@ -171,8 +161,7 @@ class Rotation:
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################################################################################################
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# convert to different orientation representations (numpy arrays)
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def asQuaternion(self,
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quaternion = False):
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def asQuaternion(self):
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"""
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Unit quaternion [q, p_1, p_2, p_3] unless quaternion == True: damask.quaternion object.
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@ -182,7 +171,7 @@ class Rotation:
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return quaternion as DAMASK object.
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"""
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return self.quaternion if quaternion else self.quaternion.asArray()
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return self.quaternion
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def asEulers(self,
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degrees = False):
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@ -195,7 +184,7 @@ class Rotation:
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return angles in degrees.
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"""
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eu = qu2eu(self.quaternion.asArray())
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eu = qu2eu(self.quaternion)
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if degrees: eu = np.degrees(eu)
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return eu
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@ -213,13 +202,13 @@ class Rotation:
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return tuple of axis and angle.
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"""
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ax = qu2ax(self.quaternion.asArray())
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ax = qu2ax(self.quaternion)
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if degrees: ax[3] = np.degrees(ax[3])
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return (ax[:3],np.degrees(ax[3])) if pair else ax
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def asMatrix(self):
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"""Rotation matrix."""
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return qu2om(self.quaternion.asArray())
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return qu2om(self.quaternion)
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def asRodrigues(self,
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vector = False):
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@ -232,16 +221,16 @@ class Rotation:
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return as actual Rodrigues--Frank vector, i.e. rotation axis scaled by tan(ω/2).
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"""
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ro = qu2ro(self.quaternion.asArray())
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ro = qu2ro(self.quaternion)
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return ro[:3]*ro[3] if vector else ro
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def asHomochoric(self):
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"""Homochoric vector: (h_1, h_2, h_3)."""
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return qu2ho(self.quaternion.asArray())
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return qu2ho(self.quaternion)
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def asCubochoric(self):
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"""Cubochoric vector: (c_1, c_2, c_3)."""
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return qu2cu(self.quaternion.asArray())
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return qu2cu(self.quaternion)
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def asM(self):
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"""
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@ -253,19 +242,18 @@ class Rotation:
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https://doi.org/10.2514/1.28949
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"""
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return self.quaternion.asM()
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return np.outer(self.quaternion,self.quaternion)
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################################################################################################
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# static constructors. The input data needs to follow the convention, options allow to
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# relax these convections
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@classmethod
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def fromQuaternion(cls,
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quaternion,
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@staticmethod
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def fromQuaternion(quaternion,
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acceptHomomorph = False,
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P = -1):
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qu = quaternion if isinstance(quaternion, np.ndarray) and quaternion.dtype == np.dtype(float) \
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qu = quaternion if isinstance(quaternion,np.ndarray) and quaternion.dtype == np.dtype(float) \
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else np.array(quaternion,dtype=float)
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if P > 0: qu[1:4] *= -1 # convert from P=1 to P=-1
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if qu[0] < 0.0:
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@ -276,11 +264,10 @@ class Rotation:
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if not np.isclose(np.linalg.norm(qu), 1.0):
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raise ValueError('Quaternion is not of unit length.\n{} {} {} {}'.format(*qu))
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return cls(qu)
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return Rotation(qu)
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@classmethod
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def fromEulers(cls,
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eulers,
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@staticmethod
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def fromEulers(eulers,
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degrees = False):
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eu = eulers if isinstance(eulers, np.ndarray) and eulers.dtype == np.dtype(float) \
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@ -289,11 +276,10 @@ class Rotation:
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if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or eu[1] > np.pi:
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raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].\n{} {} {}.'.format(*eu))
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return cls(eu2qu(eu))
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return Rotation(eu2qu(eu))
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@classmethod
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def fromAxisAngle(cls,
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angleAxis,
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@staticmethod
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def fromAxisAngle(angleAxis,
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degrees = False,
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normalise = False,
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P = -1):
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@ -308,11 +294,10 @@ class Rotation:
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if not np.isclose(np.linalg.norm(ax[0:3]), 1.0):
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raise ValueError('Axis angle rotation axis is not of unit length.\n{} {} {}'.format(*ax[0:3]))
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return cls(ax2qu(ax))
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return Rotation(ax2qu(ax))
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@classmethod
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def fromBasis(cls,
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basis,
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@staticmethod
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def fromBasis(basis,
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orthonormal = True,
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reciprocal = False,
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):
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@ -331,18 +316,16 @@ class Rotation:
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or not np.isclose(np.dot(om[2],om[0]), 0.0):
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raise ValueError('matrix is not orthogonal.\n{}'.format(om))
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return cls(om2qu(om))
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return Rotation(om2qu(om))
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@classmethod
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def fromMatrix(cls,
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om,
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@staticmethod
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def fromMatrix(om,
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):
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return cls.fromBasis(om)
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return Rotation.fromBasis(om)
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@classmethod
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def fromRodrigues(cls,
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rodrigues,
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@staticmethod
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def fromRodrigues(rodrigues,
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normalise = False,
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P = -1):
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@ -355,35 +338,32 @@ class Rotation:
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if ro[3] < 0.0:
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raise ValueError('Rodriques rotation angle not positive.\n'.format(ro[3]))
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return cls(ro2qu(ro))
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return Rotation(ro2qu(ro))
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@classmethod
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def fromHomochoric(cls,
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homochoric,
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P = -1):
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@staticmethod
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def fromHomochoric(homochoric,
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P = -1):
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ho = homochoric if isinstance(homochoric, np.ndarray) and homochoric.dtype == np.dtype(float) \
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else np.array(homochoric,dtype=float)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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return cls(ho2qu(ho))
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return Rotation(ho2qu(ho))
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@classmethod
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def fromCubochoric(cls,
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cubochoric,
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P = -1):
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@staticmethod
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def fromCubochoric(cubochoric,
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P = -1):
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cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \
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else np.array(cubochoric,dtype=float)
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ho = cu2ho(cu)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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return cls(ho2qu(ho))
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return Rotation(ho2qu(ho))
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@classmethod
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def fromAverage(cls,
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rotations,
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@staticmethod
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def fromAverage(rotations,
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weights = []):
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"""
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Average rotation.
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@ -413,19 +393,18 @@ class Rotation:
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else M + r.asM() * n # noqa add (multiples) of this rotation to average noqa
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eig, vec = np.linalg.eig(M/N)
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return cls.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
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return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
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@classmethod
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def fromRandom(cls):
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@staticmethod
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def fromRandom():
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r = np.random.random(3)
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A = np.sqrt(r[2])
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B = np.sqrt(1.0-r[2])
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w = np.cos(2.0*np.pi*r[0])*A
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x = np.sin(2.0*np.pi*r[1])*B
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y = np.cos(2.0*np.pi*r[1])*B
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z = np.sin(2.0*np.pi*r[0])*A
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return cls.fromQuaternion([w,x,y,z],acceptHomomorph=True)
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return Rotation(np.array([np.cos(2.0*np.pi*r[0])*A,
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np.sin(2.0*np.pi*r[1])*B,
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np.cos(2.0*np.pi*r[1])*B,
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np.sin(2.0*np.pi*r[0])*A])).standardize()
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|
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@ -1194,9 +1173,8 @@ class Orientation:
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return color
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@classmethod
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def fromAverage(cls,
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orientations,
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@staticmethod
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def fromAverage(orientations,
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weights = []):
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"""Create orientation from average of list of orientations."""
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if not all(isinstance(item, Orientation) for item in orientations):
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|
|
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|
|
@ -1,212 +0,0 @@
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import numpy as np
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P = -1 # convention (see DOI:10.1088/0965-0393/23/8/083501)
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|
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####################################################################################################
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class Quaternion:
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u"""
|
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Quaternion with basic operations
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q is the real part, p = (x, y, z) are the imaginary parts.
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Definition of multiplication depends on variable P, P ∈ {-1,1}.
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"""
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def __init__(self,
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q = 0.0,
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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 = float(q)
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self.p = np.array(p,dtype=float)
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|
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|
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def __copy__(self):
|
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"""Copy"""
|
||||
return self.__class__(q=self.q,
|
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p=self.p.copy())
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|
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copy = __copy__
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|
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|
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def __iter__(self):
|
||||
"""Components"""
|
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return iter(self.asList())
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|
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def __repr__(self):
|
||||
"""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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|
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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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|
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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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else:
|
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return NotImplemented
|
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|
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def __pos__(self):
|
||||
"""Unary positive operator"""
|
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return self
|
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|
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|
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def __sub__(self, other):
|
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"""Subtraction"""
|
||||
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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|
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def __isub__(self, other):
|
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"""In-place subtraction"""
|
||||
if isinstance(other, Quaternion):
|
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self.q -= other.q
|
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self.p -= other.p
|
||||
return self
|
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else:
|
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return NotImplemented
|
||||
|
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def __neg__(self):
|
||||
"""Unary negative operator"""
|
||||
return self * -1.0
|
||||
|
||||
|
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def __mul__(self, other):
|
||||
"""Multiplication with quaternion or scalar"""
|
||||
if isinstance(other, Quaternion):
|
||||
return self.__class__(q=self.q*other.q - np.dot(self.p,other.p),
|
||||
p=self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p))
|
||||
elif isinstance(other, (int, float)):
|
||||
return self.__class__(q=self.q*other,
|
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p=self.p*other)
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
def __imul__(self, other):
|
||||
"""In-place multiplication with quaternion or scalar"""
|
||||
if isinstance(other, Quaternion):
|
||||
self.q = self.q*other.q - np.dot(self.p,other.p)
|
||||
self.p = self.q*other.p + other.q*self.p + P * np.cross(self.p,other.p)
|
||||
return self
|
||||
elif isinstance(other, (int, float)):
|
||||
self.q *= other
|
||||
self.p *= other
|
||||
return self
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
|
||||
def __truediv__(self, other):
|
||||
"""Divsion with quaternion or scalar"""
|
||||
if isinstance(other, Quaternion):
|
||||
s = other.conjugate()/abs(other)**2.
|
||||
return self.__class__(q=self.q * s,
|
||||
p=self.p * s)
|
||||
elif isinstance(other, (int, float)):
|
||||
return self.__class__(q=self.q / other,
|
||||
p=self.p / other)
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
def __itruediv__(self, other):
|
||||
"""In-place divsion with quaternion or scalar"""
|
||||
if isinstance(other, Quaternion):
|
||||
s = other.conjugate()/abs(other)**2.
|
||||
self *= s
|
||||
return self
|
||||
elif isinstance(other, (int, float)):
|
||||
self.q /= other
|
||||
self.p /= other
|
||||
return self
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
|
||||
def __pow__(self, exponent):
|
||||
"""Power"""
|
||||
if isinstance(exponent, (int, float)):
|
||||
omega = np.acos(self.q)
|
||||
return self.__class__(q= np.cos(exponent*omega),
|
||||
p=self.p * np.sin(exponent*omega)/np.sin(omega))
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
def __ipow__(self, exponent):
|
||||
"""In-place power"""
|
||||
if isinstance(exponent, (int, float)):
|
||||
omega = np.acos(self.q)
|
||||
self.q = np.cos(exponent*omega)
|
||||
self.p *= np.sin(exponent*omega)/np.sin(omega)
|
||||
return self
|
||||
else:
|
||||
return NotImplemented
|
||||
|
||||
|
||||
def __abs__(self):
|
||||
"""Norm"""
|
||||
return np.sqrt(self.q ** 2 + np.dot(self.p,self.p))
|
||||
|
||||
magnitude = __abs__
|
||||
|
||||
|
||||
def __eq__(self,other):
|
||||
"""Equal (sufficiently close) to each other"""
|
||||
return np.isclose(( self-other).magnitude(),0.0) \
|
||||
or np.isclose((-self-other).magnitude(),0.0)
|
||||
|
||||
def __ne__(self,other):
|
||||
"""Not equal (sufficiently close) to each other"""
|
||||
return not self.__eq__(other)
|
||||
|
||||
|
||||
def asM(self):
|
||||
"""Intermediate representation useful for quaternion averaging (see F. Landis Markley et al.)"""
|
||||
return np.outer(self.asArray(),self.asArray())
|
||||
|
||||
def asArray(self):
|
||||
"""As numpy array"""
|
||||
return np.array((self.q,self.p[0],self.p[1],self.p[2]))
|
||||
|
||||
def asList(self):
|
||||
"""As list"""
|
||||
return [self.q]+list(self.p)
|
||||
|
||||
|
||||
def normalize(self):
|
||||
"""Normalizes in-place"""
|
||||
d = self.magnitude()
|
||||
if d > 0.0: self /= d
|
||||
return self
|
||||
|
||||
def normalized(self):
|
||||
"""Returns normalized copy"""
|
||||
return self.copy().normalize()
|
||||
|
||||
|
||||
def conjugate(self):
|
||||
"""Conjugates in-place"""
|
||||
self.p = -self.p
|
||||
return self
|
||||
|
||||
def conjugated(self):
|
||||
"""Returns conjugated copy"""
|
||||
return self.copy().conjugate()
|
||||
|
||||
|
||||
def homomorph(self):
|
||||
"""Homomorphs in-place"""
|
||||
self *= -1.0
|
||||
return self
|
||||
|
||||
def homomorphed(self):
|
||||
"""Returns homomorphed copy"""
|
||||
return self.copy().homomorph()
|
||||
|
|
@ -1,4 +1,5 @@
|
|||
import os
|
||||
from itertools import permutations
|
||||
|
||||
import pytest
|
||||
import numpy as np
|
||||
|
|
@ -6,6 +7,7 @@ import numpy as np
|
|||
import damask
|
||||
from damask import Rotation
|
||||
from damask import Orientation
|
||||
from damask import Lattice
|
||||
|
||||
n = 1000
|
||||
|
||||
|
|
@ -45,19 +47,37 @@ class TestRotation:
|
|||
def test_Homochoric(self,default):
|
||||
for rot in default:
|
||||
assert np.allclose(rot.asRodrigues(),
|
||||
Rotation.fromHomochoric(rot.asHomochoric()).asRodrigues(),rtol=5.e-5)
|
||||
Rotation.fromHomochoric(rot.asHomochoric()).asRodrigues(),rtol=1.e-4)
|
||||
|
||||
def test_Cubochoric(self,default):
|
||||
for rot in default:
|
||||
assert np.allclose(rot.asHomochoric(),
|
||||
Rotation.fromCubochoric(rot.asCubochoric()).asHomochoric(),rtol=5.e-5)
|
||||
Rotation.fromCubochoric(rot.asCubochoric()).asHomochoric())
|
||||
|
||||
def test_Quaternion(self,default):
|
||||
for rot in default:
|
||||
assert np.allclose(rot.asCubochoric(),
|
||||
Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric(),rtol=5.e-5)
|
||||
Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric())
|
||||
|
||||
|
||||
@pytest.mark.parametrize('color',[{'label':'red', 'RGB':[1,0,0],'direction':[0,0,1]},
|
||||
{'label':'green','RGB':[0,1,0],'direction':[0,1,1]},
|
||||
{'label':'blue', 'RGB':[0,0,1],'direction':[1,1,1]}])
|
||||
@pytest.mark.parametrize('lattice',['fcc','bcc'])
|
||||
def test_IPF_cubic(self,default,color,lattice):
|
||||
cube = damask.Orientation(damask.Rotation(),lattice)
|
||||
for direction in set(permutations(np.array(color['direction']))):
|
||||
assert np.allclose(cube.IPFcolor(direction),np.array(color['RGB']))
|
||||
|
||||
@pytest.mark.parametrize('lattice',Lattice.lattices)
|
||||
def test_IPF(self,lattice):
|
||||
direction = np.random.random(3)*2.0-1
|
||||
for rot in [Rotation.fromRandom() for r in range(n//100)]:
|
||||
R = damask.Orientation(rot,lattice)
|
||||
color = R.IPFcolor(direction)
|
||||
for equivalent in R.equivalentOrientations():
|
||||
assert np.allclose(color,R.IPFcolor(direction))
|
||||
|
||||
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
|
||||
@pytest.mark.parametrize('lattice',['fcc','bcc'])
|
||||
def test_relationship_forward_backward(self,model,lattice):
|
||||
|
|
|
|||
Loading…
Reference in New Issue