conversion routines from Marc de Graefs 3D rotation repository
Python version available on https://github.com/MarDiehl/3Drotations
This commit is contained in:
Martin Diehl
parent
453f4556e5
commit
e931b716fd
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@ -0,0 +1,122 @@
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####################################################################################################
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# Code below available according to below conditions on https://github.com/MarDiehl/3Drotations
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####################################################################################################
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# Copyright (c) 2017-2019, Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without modification, are
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# permitted provided that the following conditions are met:
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#
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# - Redistributions of source code must retain the above copyright notice, this list
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# of conditions and the following disclaimer.
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# - Redistributions in binary form must reproduce the above copyright notice, this
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# list of conditions and the following disclaimer in the documentation and/or
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# other materials provided with the distribution.
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# - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
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# of its contributors may be used to endorse or promote products derived from
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# this software without specific prior written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
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# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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####################################################################################################
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import numpy as np
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sc = np.pi**(1./6.)/6.**(1./6.)
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beta = np.pi**(5./6.)/6.**(1./6.)/2.
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R1 = (3.*np.pi/4.)**(1./3.)
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def CubeToBall(cube):
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if np.abs(np.max(cube))>np.pi**(2./3.) * 0.5:
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raise ValueError
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# transform to the sphere grid via the curved square, and intercept the zero point
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if np.allclose(cube,0.0,rtol=0.0,atol=1.0e-300):
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ball = np.zeros(3)
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else:
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# get pyramide and scale by grid parameter ratio
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p = GetPyramidOrder(cube)
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XYZ = cube[p] * sc
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# intercept all the points along the z-axis
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if np.allclose(XYZ[0:2],0.0,rtol=0.0,atol=1.0e-300):
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ball = np.array([0.0, 0.0, np.sqrt(6.0/np.pi) * XYZ[2]])
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else:
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order = [1,0] if np.abs(XYZ[1]) <= np.abs(XYZ[0]) else [0,1]
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q = np.pi/12.0 * XYZ[order[0]]/XYZ[order[1]]
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c = np.cos(q)
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s = np.sin(q)
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q = R1*2.0**0.25/beta * XYZ[order[1]] / np.sqrt(np.sqrt(2.0)-c)
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T = np.array([ (np.sqrt(2.0)*c - 1.0), np.sqrt(2.0) * s]) * q
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# transform to sphere grid (inverse Lambert)
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# note that there is no need to worry about dividing by zero, since XYZ[2] can not become zero
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c = np.sum(T**2)
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s = c * np.pi/24.0 /XYZ[2]**2
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c = c * np.sqrt(np.pi/24.0)/XYZ[2]
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q = np.sqrt( 1.0 - s )
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ball = np.array([ T[order[1]] * q, T[order[0]] * q, np.sqrt(6.0/np.pi) * XYZ[2] - c ])
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# reverse the coordinates back to the regular order according to the original pyramid number
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ball = ball[p]
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return ball
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def BallToCube(ball):
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rs = np.linalg.norm(ball)
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if rs > R1:
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raise ValueError
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if np.allclose(ball,0.0,rtol=0.0,atol=1.0e-300):
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cube = np.zeros(3)
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else:
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p = GetPyramidOrder(ball)
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xyz3 = ball[p]
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# inverse M_3
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xyz2 = xyz3[0:2] * np.sqrt( 2.0*rs/(rs+np.abs(xyz3[2])) )
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# inverse M_2
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qxy = np.sum(xyz2**2)
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if np.isclose(qxy,0.0,rtol=0.0,atol=1.0e-300):
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Tinv = np.zeros(2)
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else:
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q2 = qxy + np.max(np.abs(xyz2))**2
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sq2 = np.sqrt(q2)
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q = (beta/np.sqrt(2.0)/R1) * np.sqrt(q2*qxy/(q2-np.max(np.abs(xyz2))*sq2))
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tt = np.clip((np.min(np.abs(xyz2))**2+np.max(np.abs(xyz2))*sq2)/np.sqrt(2.0)/qxy,-1.0,1.0)
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Tinv = np.array([1.0,np.arccos(tt)/np.pi*12.0]) if np.abs(xyz2[1]) <= np.abs(xyz2[0]) else \
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np.array([np.arccos(tt)/np.pi*12.0,1.0])
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Tinv = q * np.where(xyz2<0.0,-Tinv,Tinv)
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# inverse M_1
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cube = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /sc
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# reverst the coordinates back to the regular order according to the original pyramid number
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cube = cube[p]
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return cube
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def GetPyramidOrder(xyz):
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if (abs(xyz[0])<= xyz[2]) and (abs(xyz[1])<= xyz[2]) or \
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(abs(xyz[0])<=-xyz[2]) and (abs(xyz[1])<=-xyz[2]):
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return [0,1,2]
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elif (abs(xyz[2])<= xyz[0]) and (abs(xyz[1])<= xyz[0]) or \
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(abs(xyz[2])<=-xyz[0]) and (abs(xyz[1])<=-xyz[0]):
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return [1,2,0]
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elif (abs(xyz[0])<= xyz[1]) and (abs(xyz[2])<= xyz[1]) or \
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(abs(xyz[0])<=-xyz[1]) and (abs(xyz[2])<=-xyz[1]):
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return [2,0,1]
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@ -6,6 +6,9 @@
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import math,os
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import math,os
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import numpy as np
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import numpy as np
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from . import Lambert
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P = -1
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# ******************************************************************************************
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# ******************************************************************************************
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class Quaternion:
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class Quaternion:
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@ -1093,3 +1096,443 @@ class Orientation:
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rot=np.dot(otherMatrix,myMatrix.T)
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rot=np.dot(otherMatrix,myMatrix.T)
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return Orientation(matrix=np.dot(rot,self.asMatrix()),symmetry=targetSymmetry)
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return Orientation(matrix=np.dot(rot,self.asMatrix()),symmetry=targetSymmetry)
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####################################################################################################
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# Code below available according to below conditions on https://github.com/MarDiehl/3Drotations
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####################################################################################################
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# Copyright (c) 2017-2019, Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without modification, are
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# permitted provided that the following conditions are met:
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#
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# - Redistributions of source code must retain the above copyright notice, this list
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# of conditions and the following disclaimer.
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# - Redistributions in binary form must reproduce the above copyright notice, this
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# list of conditions and the following disclaimer in the documentation and/or
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# other materials provided with the distribution.
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# - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
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# of its contributors may be used to endorse or promote products derived from
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# this software without specific prior written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
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# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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####################################################################################################
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def isone(a):
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return np.isclose(a,1.0,atol=1.0e-15,rtol=0.0)
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def iszero(a):
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return np.isclose(a,0.0,atol=1.0e-300,rtol=0.0)
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def eu2om(eu):
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"""Euler angles to orientation matrix"""
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c = np.cos(eu)
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s = np.sin(eu)
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om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]],
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[-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]],
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[+s[0]*s[1], -c[0]*s[1], +c[1] ]])
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om[np.where(iszero(om))] = 0.0
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return om
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def eu2ax(eu):
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"""Euler angles to axis angle"""
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t = np.tan(eu[1]*0.5)
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sigma = 0.5*(eu[0]+eu[2])
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delta = 0.5*(eu[0]-eu[2])
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tau = np.linalg.norm([t,np.sin(sigma)])
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alpha = np.pi if iszero(np.cos(sigma)) else \
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2.0*np.arctan(tau/np.cos(sigma))
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if iszero(alpha):
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ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
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else:
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ax = -P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis-angle pair so a minus sign in front
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ax = np.append(ax,alpha)
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if alpha < 0.0: ax *= -1.0 # ensure alpha is positive
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return ax
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def eu2ro(eu):
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"""Euler angles to Rodrigues vector"""
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ro = eu2ax(eu) # convert to axis angle representation
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if ro[3] >= np.pi: # Differs from original implementation. check convention 5
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ro[3] = np.inf
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elif iszero(ro[3]):
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ro = np.array([ 0.0, 0.0, P, 0.0 ])
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else:
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ro[3] = np.tan(ro[3]*0.5)
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return ro
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def eu2qu(eu):
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"""Euler angles to quaternion"""
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ee = 0.5*eu
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cPhi = np.cos(ee[1])
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sPhi = np.sin(ee[1])
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qu = np.array([ cPhi*np.cos(ee[0]+ee[2]),
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-P*sPhi*np.cos(ee[0]-ee[2]),
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-P*sPhi*np.sin(ee[0]-ee[2]),
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-P*cPhi*np.sin(ee[0]+ee[2]) ])
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#if qu[0] < 0.0: qu.homomorph() !ToDo: Check with original
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return qu
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def om2eu(om):
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"""Euler angles to orientation matrix"""
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if isone(om[2,2]**2):
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eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
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else:
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zeta = 1.0/np.sqrt(1.0-om[2,2]**2)
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eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta),
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np.arccos(om[2,2]),
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np.arctan2(om[0,2]*zeta, om[1,2]*zeta)])
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# reduce Euler angles to definition range, i.e a lower limit of 0.0
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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def ax2om(ax):
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"""Axis angle to orientation matrix"""
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c = np.cos(ax[3])
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s = np.sin(ax[3])
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omc = 1.0-c
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om=np.diag(ax[0:3]**2*omc + c)
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for idx in [[0,1,2],[1,2,0],[2,0,1]]:
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q = omc*ax[idx[0]] * ax[idx[1]]
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om[idx[0],idx[1]] = q + s*ax[idx[2]]
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om[idx[1],idx[0]] = q - s*ax[idx[2]]
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return om if P < 0.0 else om.T
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def qu2eu(qu):
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"""Quaternion to Euler angles"""
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q03 = qu[0]**2+qu[3]**2
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q12 = qu[1]**2+qu[2]**2
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chi = np.sqrt(q03*q12)
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if iszero(chi):
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eu = np.array([np.arctan2(-P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0]) if iszero(q12) else \
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np.array([np.arctan2(2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
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else:
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#chiInv = 1.0/chi ToDo: needed for what?
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eu = np.array([np.arctan2((-P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]-qu[2]*qu[3])*chi ),
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np.arctan2( 2.0*chi, q03-q12 ),
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np.arctan2(( P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]+qu[2]*qu[3])*chi )])
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# reduce Euler angles to definition range, i.e a lower limit of 0.0
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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def ax2ho(ax):
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"""Axis angle to homochoric"""
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f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
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ho = ax[0:3] * f
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return ho
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def ho2ax(ho):
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"""Homochoric to axis angle"""
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tfit = np.array([+1.0000000000018852, -0.5000000002194847,
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-0.024999992127593126, -0.003928701544781374,
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-0.0008152701535450438, -0.0002009500426119712,
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-0.00002397986776071756, -0.00008202868926605841,
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+0.00012448715042090092, -0.0001749114214822577,
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+0.0001703481934140054, -0.00012062065004116828,
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+0.000059719705868660826, -0.00001980756723965647,
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+0.000003953714684212874, -0.00000036555001439719544])
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# normalize h and store the magnitude
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hmag_squared = np.sum(ho**2.)
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if iszero(hmag_squared):
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ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
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else:
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hm = hmag_squared
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# convert the magnitude to the rotation angle
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s = tfit[0] + tfit[1] * hmag_squared
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for i in range(2,16):
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hm *= hmag_squared
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s += tfit[i] * hm
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ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(s)) # ToDo: Check sanity check in reference implementation
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return ax
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||||||
|
|
||||||
|
def om2ax(om):
|
||||||
|
"""Orientation matrix to axis angle"""
|
||||||
|
ax=np.empty(4)
|
||||||
|
|
||||||
|
# first get the rotation angle
|
||||||
|
t = 0.5*(om.trace() -1.0)
|
||||||
|
ax[3] = np.arccos(np.clip(t,-1.0,1.0))
|
||||||
|
|
||||||
|
if iszero(ax[3]):
|
||||||
|
ax = [ 0.0, 0.0, 1.0, 0.0]
|
||||||
|
else:
|
||||||
|
w,vr = np.linalg.eig(om)
|
||||||
|
# next, find the eigenvalue (1,0j)
|
||||||
|
i = np.where(np.isclose(w,1.0+0.0j))[0][0]
|
||||||
|
ax[0:3] = np.real(vr[0:3,i])
|
||||||
|
diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
|
||||||
|
ax[0:3] = np.where(iszero(diagDelta), ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
|
||||||
|
|
||||||
|
return np.array(ax)
|
||||||
|
|
||||||
|
|
||||||
|
def ro2ax(ro):
|
||||||
|
"""Rodrigues vector to axis angle"""
|
||||||
|
ta = ro[3]
|
||||||
|
|
||||||
|
if iszero(ta):
|
||||||
|
ax = [ 0.0, 0.0, 1.0, 0.0 ]
|
||||||
|
elif not np.isfinite(ta):
|
||||||
|
ax = [ ro[0], ro[1], ro[2], np.pi ]
|
||||||
|
else:
|
||||||
|
angle = 2.0*np.arctan(ta)
|
||||||
|
ta = 1.0/np.linalg.norm(ro[0:3])
|
||||||
|
ax = [ ro[0]/ta, ro[1]/ta, ro[2]/ta, angle ]
|
||||||
|
|
||||||
|
return np.array(ax)
|
||||||
|
|
||||||
|
|
||||||
|
def ax2ro(ax):
|
||||||
|
"""Axis angle to Rodrigues vector"""
|
||||||
|
if iszero(ax[3]):
|
||||||
|
ro = [ 0.0, 0.0, P, 0.0 ]
|
||||||
|
else:
|
||||||
|
ro = [ax[0], ax[1], ax[2]]
|
||||||
|
# 180 degree case
|
||||||
|
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
|
||||||
|
[np.tan(ax[3]*0.5)]
|
||||||
|
|
||||||
|
return np.array(ro)
|
||||||
|
|
||||||
|
|
||||||
|
def ax2qu(ax):
|
||||||
|
"""Axis angle to quaternion"""
|
||||||
|
if iszero(ax[3]):
|
||||||
|
qu = np.array([ 1.0, 0.0, 0.0, 0.0 ])
|
||||||
|
else:
|
||||||
|
c = np.cos(ax[3]*0.5)
|
||||||
|
s = np.sin(ax[3]*0.5)
|
||||||
|
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
|
||||||
|
|
||||||
|
return qu
|
||||||
|
|
||||||
|
|
||||||
|
def ro2ho(ro):
|
||||||
|
"""Rodrigues vector to homochoric"""
|
||||||
|
if iszero(np.sum(ro[0:3]**2.0)):
|
||||||
|
ho = [ 0.0, 0.0, 0.0 ]
|
||||||
|
else:
|
||||||
|
f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi
|
||||||
|
ho = ro[0:3] * (0.75*f)**(1.0/3.0)
|
||||||
|
|
||||||
|
return np.array(ho)
|
||||||
|
|
||||||
|
|
||||||
|
def qu2om(qu):
|
||||||
|
"""Quaternion to orientation matrix"""
|
||||||
|
qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2)
|
||||||
|
om = np.diag(qq + 2.0*np.array([qu[1],qu[2],qu[3]])**2)
|
||||||
|
|
||||||
|
om[1,0] = 2.0*(qu[2]*qu[1]+qu[0]*qu[3])
|
||||||
|
om[0,1] = 2.0*(qu[1]*qu[2]-qu[0]*qu[3])
|
||||||
|
om[2,1] = 2.0*(qu[3]*qu[2]+qu[0]*qu[1])
|
||||||
|
om[1,2] = 2.0*(qu[2]*qu[3]-qu[0]*qu[1])
|
||||||
|
om[0,2] = 2.0*(qu[1]*qu[3]+qu[0]*qu[2])
|
||||||
|
om[2,0] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2])
|
||||||
|
return om if P > 0.0 else om.T
|
||||||
|
|
||||||
|
|
||||||
|
def om2qu(om):
|
||||||
|
"""Orientation matrix to quaternion"""
|
||||||
|
s = [+om[0,0] +om[1,1] +om[2,2] +1.0,
|
||||||
|
+om[0,0] -om[1,1] -om[2,2] +1.0,
|
||||||
|
-om[0,0] +om[1,1] -om[2,2] +1.0,
|
||||||
|
-om[0,0] -om[1,1] +om[2,2] +1.0]
|
||||||
|
s = np.maximum(np.zeros(4),s)
|
||||||
|
qu = np.sqrt(s)*0.5*np.array([1.0,P,P,P])
|
||||||
|
# verify the signs (q0 always positive)
|
||||||
|
#ToDo: Here I donot understand the original shortcut from paper to implementation
|
||||||
|
|
||||||
|
qu /= np.linalg.norm(qu)
|
||||||
|
if any(isone(abs(qu))): qu[np.where(np.logical_not(isone(qu)))] = 0.0
|
||||||
|
if om[2,1] < om[1,2]: qu[1] *= -1.0
|
||||||
|
if om[0,2] < om[2,0]: qu[2] *= -1.0
|
||||||
|
if om[1,0] < om[0,1]: qu[3] *= -1.0
|
||||||
|
if any(om2ax(om)[0:3]*qu[1:4] < 0.0): print(om2ax(om),qu) # something is wrong here
|
||||||
|
return qu
|
||||||
|
|
||||||
|
def qu2ax(qu):
|
||||||
|
"""Quaternion to axis angle"""
|
||||||
|
omega = 2.0 * np.arccos(qu[0])
|
||||||
|
if iszero(omega): # return axis as [001] if the angle is zero
|
||||||
|
ax = [ 0.0, 0.0, 1.0, 0.0 ]
|
||||||
|
elif not iszero(qu[0]):
|
||||||
|
s = np.sign(qu[0])/np.sqrt(qu[1]**2+qu[2]**2+qu[3]**2)
|
||||||
|
ax = [ qu[1]*s, qu[2]*s, qu[3]*s, omega ]
|
||||||
|
else:
|
||||||
|
ax = [ qu[1], qu[2], qu[3], np.pi]
|
||||||
|
|
||||||
|
return np.array(ax)
|
||||||
|
|
||||||
|
|
||||||
|
def qu2ro(qu):
|
||||||
|
"""Quaternion to Rodrigues vector"""
|
||||||
|
if iszero(qu[0]):
|
||||||
|
ro = [qu[1], qu[2], qu[3], np.inf]
|
||||||
|
else:
|
||||||
|
s = np.linalg.norm([qu[1],qu[2],qu[3]])
|
||||||
|
ro = [0.0,0.0,P,0.0] if iszero(s) else \
|
||||||
|
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(qu[0]))]
|
||||||
|
|
||||||
|
return np.array(ro)
|
||||||
|
|
||||||
|
|
||||||
|
def qu2ho(qu):
|
||||||
|
"""Quaternion to homochoric"""
|
||||||
|
omega = 2.0 * np.arccos(qu[0])
|
||||||
|
|
||||||
|
if iszero(omega):
|
||||||
|
ho = np.array([ 0.0, 0.0, 0.0 ])
|
||||||
|
else:
|
||||||
|
ho = np.array([qu[1], qu[2], qu[3]])
|
||||||
|
f = 0.75 * ( omega - np.sin(omega) )
|
||||||
|
ho = ho/np.linalg.norm(ho) * f**(1./3.)
|
||||||
|
|
||||||
|
return ho
|
||||||
|
|
||||||
|
|
||||||
|
def ho2cu(ho):
|
||||||
|
"""Homochoric to cubochoric"""
|
||||||
|
return Lambert.BallToCube(ho)
|
||||||
|
|
||||||
|
|
||||||
|
def cu2ho(cu):
|
||||||
|
"""Cubochoric to homochoric"""
|
||||||
|
return Lambert.CubeToBall(cu)
|
||||||
|
|
||||||
|
|
||||||
|
def ro2eu(ro):
|
||||||
|
"""Rodrigues vector to orientation matrix"""
|
||||||
|
return om2eu(ro2om(ro))
|
||||||
|
|
||||||
|
|
||||||
|
def eu2ho(eu):
|
||||||
|
"""Euler angles to homochoric"""
|
||||||
|
return ax2ho(eu2ax(eu))
|
||||||
|
|
||||||
|
|
||||||
|
def om2ro(om):
|
||||||
|
"""Orientation matrix to Rodriques vector"""
|
||||||
|
return eu2ro(om2eu(om))
|
||||||
|
|
||||||
|
|
||||||
|
def om2ho(om):
|
||||||
|
"""Orientation matrix to homochoric"""
|
||||||
|
return ax2ho(om2ax(om))
|
||||||
|
|
||||||
|
|
||||||
|
def ax2eu(ax):
|
||||||
|
"""Orientation matrix to Euler angles"""
|
||||||
|
return om2eu(ax2om(ax))
|
||||||
|
|
||||||
|
|
||||||
|
def ro2om(ro):
|
||||||
|
"""Rodgrigues vector to orientation matrix"""
|
||||||
|
return ax2om(ro2ax(ro))
|
||||||
|
|
||||||
|
|
||||||
|
def ro2qu(ro):
|
||||||
|
"""Rodrigues vector to quaternion"""
|
||||||
|
return ax2qu(ro2ax(ro))
|
||||||
|
|
||||||
|
|
||||||
|
def ho2eu(ho):
|
||||||
|
"""Homochoric to Euler angles"""
|
||||||
|
return ax2eu(ho2ax(ho))
|
||||||
|
|
||||||
|
|
||||||
|
def ho2om(ho):
|
||||||
|
"""Homochoric to orientation matrix"""
|
||||||
|
return ax2om(ho2ax(ho))
|
||||||
|
|
||||||
|
|
||||||
|
def ho2ro(ho):
|
||||||
|
"""Axis angle to Rodriques vector"""
|
||||||
|
return ax2ro(ho2ax(ho))
|
||||||
|
|
||||||
|
|
||||||
|
def ho2qu(ho):
|
||||||
|
"""Homochoric to quaternion"""
|
||||||
|
return ax2qu(ho2ax(ho))
|
||||||
|
|
||||||
|
|
||||||
|
def eu2cu(eu):
|
||||||
|
"""Euler angles to cubochoric"""
|
||||||
|
return ho2cu(eu2ho(eu))
|
||||||
|
|
||||||
|
|
||||||
|
def om2cu(om):
|
||||||
|
"""Orientation matrix to cubochoric"""
|
||||||
|
return ho2cu(om2ho(om))
|
||||||
|
|
||||||
|
|
||||||
|
def ax2cu(ax):
|
||||||
|
"""Axis angle to cubochoric"""
|
||||||
|
return ho2cu(ax2ho(ax))
|
||||||
|
|
||||||
|
|
||||||
|
def ro2cu(ro):
|
||||||
|
"""Rodrigues vector to cubochoric"""
|
||||||
|
return ho2cu(ro2ho(ro))
|
||||||
|
|
||||||
|
|
||||||
|
def qu2cu(qu):
|
||||||
|
"""Quaternion to cubochoric"""
|
||||||
|
return ho2cu(qu2ho(qu))
|
||||||
|
|
||||||
|
|
||||||
|
def cu2eu(cu):
|
||||||
|
"""Cubochoric to Euler angles"""
|
||||||
|
return ho2eu(cu2ho(cu))
|
||||||
|
|
||||||
|
|
||||||
|
def cu2om(cu):
|
||||||
|
"""Cubochoric to orientation matrix"""
|
||||||
|
return ho2om(cu2ho(cu))
|
||||||
|
|
||||||
|
|
||||||
|
def cu2ax(cu):
|
||||||
|
"""Cubochoric to axis angle"""
|
||||||
|
return ho2ax(cu2ho(cu))
|
||||||
|
|
||||||
|
|
||||||
|
def cu2ro(cu):
|
||||||
|
"""Cubochoric to Rodrigues vector"""
|
||||||
|
return ho2ro(cu2ho(cu))
|
||||||
|
|
||||||
|
|
||||||
|
def cu2qu(cu):
|
||||||
|
"""Cubochoric to quaternion"""
|
||||||
|
return ho2qu(cu2ho(cu))
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue