1277 lines
53 KiB
Cython
1277 lines
53 KiB
Cython
#!/usr/bin/env python
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# encoding: utf-8
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# filename: corientation.pyx
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# __ __ __________ ____ __ ____ ______ ____
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# / //_// ____/ __ \/ __ \/ //_/ / / / __ \/ __ \
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# / ,< / __/ / / / / / / / ,< / / / / / / / / / /
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# / /| |/ /___/ /_/ / /_/ / /| / /_/ / /_/ / /_/ /
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# /_/ |_/_____/_____/\____/_/ |_\____/_____/\____/
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######################################################
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# This is a Cython implementation of original DAMASK #
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# orientation class, mainly for speed improvement. #
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######################################################
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"""
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NOTE
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----
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The static method in Cython is different from Python, need more
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time to figure out details.
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"""
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import math, random, os
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import numpy as np
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cimport numpy as np
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##
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# This Rodrigues class is odd, not sure if it will function
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# properly or not
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cdef class Rodrigues:
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"""Rodrigues representation of orientation """
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cdef public double[3] r
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def __init__(self, vector):
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if isinstance(vector, Rodrigues):
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self.r[0] = vector.r[0]
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self.r[1] = vector.r[1]
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self.r[2] = vector.r[2]
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else:
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self.r[0] = vector[0]
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self.r[1] = vector[1]
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self.r[2] = vector[2]
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def asQuaternion(self):
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cdef double norm, halfAngle
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cdef double[4] q
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norm = np.linalg.norm(self.vector)
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halfAngle = np.arctan(norm)
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q[0] = np.cos(halfAngle)
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tmp = np.sin(halfAngle)*self.vector/norm
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q[1],q[2],q[3] = tmp[0],tmp[1],tmp[2]
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return Quaternion(q)
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def asAngleAxis(self):
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cdef double norm, halfAngle
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norm = np.linalg.norm(self.vector)
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halfAngle = np.arctan(norm)
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return (2.0*halfAngle,self.vector/norm)
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##
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# The Quaternion class do the heavy lifting of orientation
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# calculation
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cdef class Quaternion:
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""" Quaternion representation of orientation """
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# All methods and naming conventions based off
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# http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions
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cdef public double w,x,y,z
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def __init__(self, data):
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"""
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@description
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------------
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copy constructor friendly
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@parameters
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-----------
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data: array
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"""
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cdef double[4] q
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if isinstance(data, Quaternion):
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q[0] = data.w
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q[1] = data.x
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q[2] = data.y
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q[3] = data.z
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else:
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q[0] = data[0]
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q[1] = data[1]
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q[2] = data[2]
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q[3] = data[3]
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self.Quaternion(q)
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cdef Quaternion(self, double* quatArray):
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"""
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@description
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------------
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internal constructor for Quaternion
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@parameters
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-----------
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quatArray: double[4] // <w, x, y, z>
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w is the real part, (x, y, z) are the imaginary parts
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"""
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if quatArray[0] < 0:
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self.w = -quatArray[0]
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self.x = -quatArray[1]
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self.y = -quatArray[2]
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self.z = -quatArray[3]
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else:
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self.w = quatArray[0]
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self.x = quatArray[1]
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self.y = quatArray[2]
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self.z = quatArray[3]
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def __copy__(self):
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cdef double[4] q = [self.w,self.x,self.y,self.z]
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return Quaternion(q)
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copy = __copy__
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def __iter__(self):
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return iter([self.w,self.x,self.y,self.z])
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def __repr__(self):
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return 'Quaternion(real={:.4f},imag=<{:.4f},{:.4f}, {:.4f}>)'.format(self.w,
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self.x,
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self.y,
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self.z)
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def __pow__(self, exponent, modulo):
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# declare local var for speed gain
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cdef double omega, vRescale
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cdef double[4] q
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omega = math.acos(self.w)
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vRescale = math.sin(exponent*omega)/math.sin(omega)
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q[0] = math.cos(exponent*omega)
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q[1] = self.x*vRescale
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q[2] = self.y*vRescale
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q[3] = self.z*vRescale
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return Quaternion(q)
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def __ipow__(self, exponent):
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self = self.__pow__(self, exponent, 1.0)
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return self
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def __mul__(self, other):
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# declare local var for speed gain
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cdef double Aw,Ax,Ay,Az,Bw,Bx,By,Bz
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cdef double w,x,y,z,Vx,Vy,Vz
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cdef double[4] q
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# quaternion * quaternion
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try:
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Aw = self.w
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Ax = self.x
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Ay = self.y
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Az = self.z
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Bw = other.w
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Bx = other.x
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By = other.y
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Bz = other.z
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q[0] = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw
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q[1] = + Ax * Bw + Ay * Bz - Az * By + Aw * Bx
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q[2] = - Ax * Bz + Ay * Bw + Az * Bx + Aw * By
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q[3] = + Ax * By - Ay * Bx + Az * Bw + Aw * Bz
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return Quaternion(q)
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except:
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pass
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# vector (perform active rotation, i.e. q*v*q.conjugated)
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try:
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w = self.w
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x = self.x
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y = self.y
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z = self.z
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Vx = other[0]
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Vy = other[1]
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Vz = other[2]
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return np.array([\
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w * w * Vx + 2 * y * w * Vz - 2 * z * w * Vy + \
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x * x * Vx + 2 * y * x * Vy + 2 * z * x * Vz - \
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z * z * Vx - y * y * Vx,
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2 * x * y * Vx + y * y * Vy + 2 * z * y * Vz + \
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2 * w * z * Vx - z * z * Vy + w * w * Vy - \
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2 * x * w * Vz - x * x * Vy,
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2 * x * z * Vx + 2 * y * z * Vy + \
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z * z * Vz - 2 * w * y * Vx - y * y * Vz + \
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2 * w * x * Vy - x * x * Vz + w * w * Vz ])
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except:
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pass
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# quaternion * scalar
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try:
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Q = self.copy()
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Q.w *= other
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Q.x *= other
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Q.y *= other
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Q.z *= other
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return Q
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except:
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return self.copy()
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def __imul__(self, other):
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if isinstance(other, Quaternion):
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self = self.__mul__(other)
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return self
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else:
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return NotImplemented
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def __div__(self, other):
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cdef double[4] q
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if isinstance(other, (int,float,long)):
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q[0] = self.w / other
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q[1] = self.x / other
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q[2] = self.y / other
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q[3] = self.z / other
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return Quaternion(q)
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else:
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NotImplemented
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def __idiv__(self, other):
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self = self.__div__(other)
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return self
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def __add__(self, other):
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cdef double[4] q
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if isinstance(other, Quaternion):
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q[0] = self.w + other.w
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q[1] = self.x + other.x
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q[2] = self.y + other.y
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q[3] = self.z + other.z
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return self.__class__(q)
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else:
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return NotImplemented
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def __iadd__(self, other):
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self = self.__add__(other)
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return self
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def __sub__(self, other):
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cdef double[4] q
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if isinstance(other, Quaternion):
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q[0] = self.w - other.w
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q[1] = self.x - other.x
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q[2] = self.y - other.y
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q[3] = self.z - other.z
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return self.__class__(q)
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else:
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return NotImplemented
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def __isub__(self, other):
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self = self.__sub__(other)
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return self
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def __neg__(self):
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cdef double[4] q
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q[0] = -self.w
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q[1] = -self.x
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q[2] = -self.y
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q[3] = -self.z
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return self.__class__(q)
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def __abs__(self):
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cdef double tmp
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tmp = self.w**2 + self.x**2 + self.y**2 + self.z**2
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tmp = math.sqrt(tmp)
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return tmp
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magnitude = __abs__
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def __richcmp__(Quaternion self, Quaternion other, int op):
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cdef bint tmp
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tmp = (abs(self.w-other.w) < 1e-8 and \
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abs(self.x-other.x) < 1e-8 and \
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abs(self.y-other.y) < 1e-8 and \
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abs(self.z-other.z) < 1e-8) \
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or \
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(abs(-self.w-other.w) < 1e-8 and \
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abs(-self.x-other.x) < 1e-8 and \
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abs(-self.y-other.y) < 1e-8 and \
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abs(-self.z-other.z) < 1e-8)
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if op == 2: #__eq__
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return tmp
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elif op ==3: #__ne__
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return not tmp
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else:
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return NotImplemented
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def __cmp__(self,other):
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# not sure if this actually works or not
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return cmp(self.Rodrigues(),other.Rodrigues())
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def magnitude_squared(self):
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cdef double tmp
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tmp = self.w**2 + self.x**2 + self.y**2 + self.z**2
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return tmp
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def identity(self):
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self.w = 1.0
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self.x = 0.0
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self.y = 0.0
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self.z = 0.0
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return self
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def normalize(self):
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cdef double d
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d = self.magnitude()
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if d > 0.0:
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self /= d
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return self
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def conjugate(self):
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self.x = -self.x
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self.y = -self.y
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self.z = -self.z
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return self
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def inverse(self):
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cdef double d
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d = self.magnitude()
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if d > 0.0:
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self.conjugate()
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self /= d
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return self
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def homomorph(self):
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if self.w < 0.0:
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self.w = -self.w
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self.x = -self.x
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self.y = -self.y
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self.z = -self.z
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return self
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# return a copy of me
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def normalized(self):
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cdef Quaternion q
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q = Quaternion(self.normalize())
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return q
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def conjugated(self):
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cdef Quaternion q
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q = Quaternion(self.conjugate())
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return q
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def asList(self):
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cdef double[4] q = [self.w, self.x, self.y, self.z]
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return list(q)
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def asM(self): # to find Averaging Quaternions (see F. Landis Markley et al.)
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return np.outer([i for i in self],[i for i in self])
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def asMatrix(self):
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return np.array([[1.0-2.0*(self.y*self.y+self.z*self.z), 2.0*(self.x*self.y-self.z*self.w), 2.0*(self.x*self.z+self.y*self.w)],
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[ 2.0*(self.x*self.y+self.z*self.w), 1.0-2.0*(self.x*self.x+self.z*self.z), 2.0*(self.y*self.z-self.x*self.w)],
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[ 2.0*(self.x*self.z-self.y*self.w), 2.0*(self.x*self.w+self.y*self.z), 1.0-2.0*(self.x*self.x+self.y*self.y)]])
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def asAngleAxis(self):
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# keep the return as radians for simplicity
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cdef double s,x,y
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if self.w > 1:
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self.normalize()
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s = math.sqrt(1. - self.w**2)
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x = 2*self.w**2 - 1.
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y = 2*self.w * s
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angle = math.atan2(y,x)
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if angle < 0.0:
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angle *= -1.0
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s *= -1.0
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return (angle,
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np.array([1.0, 0.0, 0.0] if np.abs(angle) < 1e-3 else [self.x/s, self.y/s, self.z/s]) )
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def asRodrigues(self):
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if self.w != 0.0:
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return np.array([self.x, self.y, self.z])/self.w
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else:
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return np.array([float('inf')]*3)
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def asEulers(self,
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type='bunge',
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degrees=False,
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standardRange=False):
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"""
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CONVERSION TAKEN FROM:
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Melcher, A.; Unser, A.; Reichhardt, M.; Nestler, B.; Pötschke, M.; Selzer, M.
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Conversion of EBSD data by a quaternion based algorithm to be used for grain structure simulations
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Technische Mechanik 30 (2010) pp 401--413
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"""
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cdef double x,y
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angles = [0.0,0.0,0.0]
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if type.lower() == 'bunge' or type.lower() == 'zxz':
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if abs(self.x) < 1e-4 and abs(self.y) < 1e-4:
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x = self.w**2 - self.z**2
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y = 2.*self.w*self.z
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angles[0] = math.atan2(y,x)
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elif abs(self.w) < 1e-4 and abs(self.z) < 1e-4:
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x = self.x**2 - self.y**2
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y = 2.*self.x*self.y
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angles[0] = math.atan2(y,x)
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angles[1] = math.pi
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else:
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chi = math.sqrt((self.w**2 + self.z**2)*(self.x**2 + self.y**2))
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x = (self.w * self.x - self.y * self.z)/2./chi
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y = (self.w * self.y + self.x * self.z)/2./chi
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angles[0] = math.atan2(y,x)
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x = self.w**2 + self.z**2 - (self.x**2 + self.y**2)
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y = 2.*chi
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angles[1] = math.atan2(y,x)
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x = (self.w * self.x + self.y * self.z)/2./chi
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y = (self.z * self.x - self.y * self.w)/2./chi
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angles[2] = math.atan2(y,x)
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if standardRange:
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angles[0] %= 2*math.pi
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if angles[1] < 0.0:
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angles[1] += math.pi
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angles[2] *= -1.0
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angles[2] %= 2*math.pi
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return np.degrees(angles) if degrees else angles
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@staticmethod
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def fromIdentity():
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cdef double[4] q = [1.0, 0.0, 0.0, 0.0]
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return Quaternion(q)
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@staticmethod
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def fromRandom(randomSeed=None):
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cdef double r1,r2,r3
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cdef double[4] q
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if randomSeed == None:
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randomSeed = int(os.urandom(4).encode('hex'), 16)
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random.seed(randomSeed)
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r1 = random.random()
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r2 = random.random()
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r3 = random.random()
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q[0] = math.cos(2.0*math.pi*r1)*math.sqrt(r3)
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q[1] = math.sin(2.0*math.pi*r2)*math.sqrt(1.0-r3)
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q[2] = math.cos(2.0*math.pi*r2)*math.sqrt(1.0-r3)
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q[3] = math.sin(2.0*math.pi*r1)*math.sqrt(r3)
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return Quaternion(q)
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@staticmethod
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def fromRodrigues(rodrigues):
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if not isinstance(rodrigues, np.ndarray): rodrigues = np.array(rodrigues)
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halfangle = math.atan(np.linalg.norm(rodrigues))
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c = math.cos(halfangle)
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w = c
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x,y,z = c*rodrigues
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return Quaternion([w,x,y,z])
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@staticmethod
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def fromAngleAxis(angle, axis):
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if not isinstance(axis, np.ndarray): axis = np.array(axis)
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axis /= np.linalg.norm(axis)
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s = math.sin(angle / 2.0)
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w = math.cos(angle / 2.0)
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x = axis[0] * s
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y = axis[1] * s
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z = axis[2] * s
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return Quaternion([w,x,y,z])
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@staticmethod
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def fromEulers(eulers, type = 'Bunge'):
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cdef double c1,s1,c2,s2,c3,s3
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cdef double[4] q
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cdef double[3] halfEulers
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cdef int i
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for i in range(3):
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halfEulers[i] = eulers[i] * 0.5 # reduce to half angles
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c1 = math.cos(halfEulers[0])
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s1 = math.sin(halfEulers[0])
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c2 = math.cos(halfEulers[1])
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s2 = math.sin(halfEulers[1])
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c3 = math.cos(halfEulers[2])
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s3 = math.sin(halfEulers[2])
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if type.lower() == 'bunge' or type.lower() == 'zxz':
|
|
q[0] = c1 * c2 * c3 - s1 * c2 * s3
|
|
q[1] = c1 * s2 * c3 + s1 * s2 * s3
|
|
q[2] = - c1 * s2 * s3 + s1 * s2 * c3
|
|
q[3] = c1 * c2 * s3 + s1 * c2 * c3
|
|
else:
|
|
q[0] = c1 * c2 * c3 - s1 * s2 * s3
|
|
q[1] = s1 * s2 * c3 + c1 * c2 * s3
|
|
q[2] = s1 * c2 * c3 + c1 * s2 * s3
|
|
q[3] = c1 * s2 * c3 - s1 * c2 * s3
|
|
return Quaternion(q)
|
|
|
|
## Modified Method to calculate Quaternion from Orientation Matrix, Source: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
|
|
|
|
@staticmethod
|
|
def fromMatrix(m):
|
|
# This is a slow implementation
|
|
if m.shape != (3,3) and np.prod(m.shape) == 9:
|
|
m = m.reshape(3,3)
|
|
|
|
tr=np.trace(m)
|
|
if tr > 0.00000001:
|
|
s = math.sqrt(tr + 1.0)*2.0
|
|
|
|
return Quaternion(
|
|
[ s*0.25,
|
|
(m[2,1] - m[1,2])/s,
|
|
(m[0,2] - m[2,0])/s,
|
|
(m[1,0] - m[0,1])/s
|
|
])
|
|
|
|
elif m[0,0] > m[1,1] and m[0,0] > m[2,2]:
|
|
t = m[0,0] - m[1,1] - m[2,2] + 1.0
|
|
s = 2.0*math.sqrt(t)
|
|
|
|
return Quaternion(
|
|
[ (m[2,1] - m[1,2])/s,
|
|
s*0.25,
|
|
(m[0,1] + m[1,0])/s,
|
|
(m[2,0] + m[0,2])/s,
|
|
])
|
|
|
|
elif m[1,1] > m[2,2]:
|
|
t = -m[0,0] + m[1,1] - m[2,2] + 1.0
|
|
s = 2.0*math.sqrt(t)
|
|
|
|
return Quaternion(
|
|
[ (m[0,2] - m[2,0])/s,
|
|
(m[0,1] + m[1,0])/s,
|
|
s*0.25,
|
|
(m[1,2] + m[2,1])/s,
|
|
])
|
|
|
|
else:
|
|
t = -m[0,0] - m[1,1] + m[2,2] + 1.0
|
|
s = 2.0*math.sqrt(t)
|
|
|
|
return Quaternion(
|
|
[ (m[1,0] - m[0,1])/s,
|
|
(m[2,0] + m[0,2])/s,
|
|
(m[1,2] + m[2,1])/s,
|
|
s*0.25,
|
|
])
|
|
|
|
@staticmethod
|
|
def new_interpolate(q1, q2, t):
|
|
# see http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070017872_2007014421.pdf for (another?) way to interpolate quaternions
|
|
|
|
assert isinstance(q1, Quaternion) and isinstance(q2, Quaternion)
|
|
Q = Quaternion.fromIdentity()
|
|
|
|
costheta = q1.w * q2.w + q1.x * q2.x + q1.y * q2.y + q1.z * q2.z
|
|
if costheta < 0.:
|
|
costheta = -costheta
|
|
q1 = q1.conjugated()
|
|
elif costheta > 1:
|
|
costheta = 1
|
|
|
|
theta = math.acos(costheta)
|
|
if abs(theta) < 0.01:
|
|
Q.w = q2.w
|
|
Q.x = q2.x
|
|
Q.y = q2.y
|
|
Q.z = q2.z
|
|
return Q
|
|
|
|
sintheta = math.sqrt(1.0 - costheta * costheta)
|
|
if abs(sintheta) < 0.01:
|
|
Q.w = (q1.w + q2.w) * 0.5
|
|
Q.x = (q1.x + q2.x) * 0.5
|
|
Q.y = (q1.y + q2.y) * 0.5
|
|
Q.z = (q1.z + q2.z) * 0.5
|
|
return Q
|
|
|
|
ratio1 = math.sin((1 - t) * theta) / sintheta
|
|
ratio2 = math.sin(t * theta) / sintheta
|
|
|
|
Q.w = q1.w * ratio1 + q2.w * ratio2
|
|
Q.x = q1.x * ratio1 + q2.x * ratio2
|
|
Q.y = q1.y * ratio1 + q2.y * ratio2
|
|
Q.z = q1.z * ratio1 + q2.z * ratio2
|
|
return Q
|
|
|
|
##
|
|
# Define lattice_type to make it easier for future
|
|
# development
|
|
cdef enum lattice_type:
|
|
NONE = 0
|
|
ORTHORHOMBIC= 1
|
|
TETRAGONAL = 2
|
|
HEXAGONAL = 3
|
|
CUBIC = 4
|
|
##
|
|
# Symmetry class
|
|
cdef class Symmetry:
|
|
cdef public lattice_type lattice
|
|
# cdef enum LATTICES:
|
|
# NONE = 0
|
|
# ORTHORHOMBIC= 1
|
|
# TETRAGONAL = 2
|
|
# HEXAGONAL = 3
|
|
# CUBIC = 4
|
|
|
|
def __init__(self, symmetry):
|
|
if symmetry == 0 or symmetry == None:
|
|
self.lattice = NONE
|
|
elif symmetry == 1 or symmetry == 'orthorhombic':
|
|
self.lattice = ORTHORHOMBIC
|
|
elif symmetry == 2 or symmetry == 'tetragonal':
|
|
self.lattice = TETRAGONAL
|
|
elif symmetry == 3 or symmetry == 'hexagonal':
|
|
self.lattice = HEXAGONAL
|
|
elif symmetry == 4 or symmetry == 'cubic':
|
|
self.lattice = CUBIC
|
|
else:
|
|
self.lattice = NONE
|
|
|
|
def __copy__(self):
|
|
return self.__class__(self.lattice)
|
|
|
|
copy = __copy__
|
|
|
|
def __repr__(self):
|
|
return '{}'.format(self.lattice)
|
|
|
|
def __richcmp__(Symmetry self, Symmetry other, int op):
|
|
cdef bint tmp
|
|
|
|
tmp = self.lattice == other.lattice
|
|
if op == 2: #__eq__
|
|
return tmp
|
|
elif op ==3: #__ne__
|
|
return not tmp
|
|
else:
|
|
return NotImplemented
|
|
|
|
def __cmp__(self,other):
|
|
return cmp(self.lattice,other.lattice)
|
|
|
|
def symmetryQuats(self):
|
|
'''
|
|
List of symmetry operations as quaternions.
|
|
'''
|
|
if self.lattice == 'cubic':
|
|
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, 0.0, 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) ],
|
|
[ 0.0, 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, 0.5, 0.5, 0.5 ],
|
|
[-0.5, 0.5, 0.5, 0.5 ],
|
|
[-0.5, 0.5, 0.5, -0.5 ],
|
|
[-0.5, 0.5, -0.5, 0.5 ],
|
|
[-0.5, -0.5, 0.5, 0.5 ],
|
|
[-0.5, -0.5, 0.5, -0.5 ],
|
|
[-0.5, -0.5, -0.5, 0.5 ],
|
|
[-0.5, 0.5, -0.5, -0.5 ],
|
|
[-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 map(Quaternion,symQuats)
|
|
|
|
def equivalentQuaternions(self,quaternion):
|
|
'''
|
|
List of symmetrically equivalent quaternions based on own symmetry.
|
|
'''
|
|
return [quaternion*Quaternion(q) for q in self.symmetryQuats()]
|
|
|
|
def inFZ(self,R):
|
|
'''
|
|
Check whether given Rodrigues vector falls into fundamental zone of own symmetry.
|
|
'''
|
|
if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentially passed quaternion
|
|
R = abs(R) # fundamental zone in Rodrigues space is point symmetric around origin
|
|
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 accidentally passed quaternion
|
|
|
|
cdef double 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,
|
|
color = False):
|
|
'''
|
|
Check whether given vector falls into standard stereographic triangle of own symmetry.
|
|
Return inverse pole figure color if requested.
|
|
'''
|
|
# basis = {4 : 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
|
|
# 3 : 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
|
|
# 2 : 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
|
|
# 1 : 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 = np.array([ [-1. , 0. , 1. ],
|
|
[ np.sqrt(2.), -np.sqrt(2.), 0. ],
|
|
[ 0. , np.sqrt(3.), 0. ] ])
|
|
elif self.lattice == HEXAGONAL:
|
|
basis = np.array([ [ 0. , 0. , 1. ],
|
|
[ 1. , -np.sqrt(3.), 0. ],
|
|
[ 0. , 2. , 0. ] ])
|
|
elif self.lattice == TETRAGONAL:
|
|
basis = np.array([ [ 0. , 0. , 1. ],
|
|
[ 1. , -1. , 0. ],
|
|
[ 0. , np.sqrt(2.), 0. ] ])
|
|
elif self.lattice == ORTHORHOMBIC:
|
|
basis = np.array([ [ 0., 0., 1.],
|
|
[ 1., 0., 0.],
|
|
[ 0., 1., 0.] ])
|
|
else:
|
|
basis = np.zeros((3,3),dtype=float)
|
|
|
|
if np.all(basis == 0.0):
|
|
theComponents = -np.ones(3,'d')
|
|
else:
|
|
v = np.array(vector,dtype = float)
|
|
v[2] = abs(v[2]) # z component projects identical for positive and negative values
|
|
theComponents = np.dot(basis,v)
|
|
|
|
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,'d'),rgb) # limit to maximum intensity
|
|
rgb /= max(rgb) # normalize to (HS)V = 1
|
|
else:
|
|
rgb = np.zeros(3,'d')
|
|
return (inSST,rgb)
|
|
else:
|
|
return inSST
|
|
|
|
# code derived from http://pyeuclid.googlecode.com/svn/trunk/euclid.py
|
|
# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
|
|
|
|
|
|
##
|
|
# Orientation class is a composite class of Symmetry and Quaternion
|
|
cdef class Orientation:
|
|
cdef public Quaternion quaternion
|
|
cdef public Symmetry symmetry
|
|
|
|
def __init__(self,
|
|
quaternion = Quaternion.fromIdentity(),
|
|
Rodrigues = None,
|
|
angleAxis = None,
|
|
matrix = None,
|
|
Eulers = None,
|
|
random = False, # put any integer to have a fixed seed or True for real random
|
|
symmetry = None
|
|
):
|
|
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, type='bunge')
|
|
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])
|
|
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.homomorph()
|
|
elif isinstance(quaternion, np.ndarray) and quaternion.shape == (4,): # based on given quaternion
|
|
self.quaternion = Quaternion(quaternion).homomorph()
|
|
|
|
self.symmetry = Symmetry(symmetry)
|
|
|
|
def __copy__(self):
|
|
return self.__class__(quaternion=self.quaternion,symmetry=self.symmetry.lattice)
|
|
|
|
copy = __copy__
|
|
|
|
def __repr__(self):
|
|
return 'Symmetry: %s\n' % (self.symmetry) + \
|
|
'Quaternion: %s\n' % (self.quaternion) + \
|
|
'Matrix:\n%s\n' % ( '\n'.join(['\t'.join(map(str,self.asMatrix()[i,:])) for i in range(3)]) ) + \
|
|
'Bunge Eulers / deg: %s' % ('\t'.join(map(lambda x:str(np.degrees(x)),self.asEulers('bunge'))) )
|
|
|
|
def asQuaternion(self):
|
|
return self.quaternion.asList()
|
|
|
|
def asEulers(self,type='bunge'):
|
|
return self.quaternion.asEulers(type)
|
|
|
|
def asRodrigues(self):
|
|
return self.quaternion.asRodrigues()
|
|
|
|
def asAngleAxis(self):
|
|
return self.quaternion.asAngleAxis()
|
|
|
|
def asMatrix(self):
|
|
return self.quaternion.asMatrix()
|
|
|
|
def inFZ(self):
|
|
return self.symmetry.inFZ(self.quaternion.asRodrigues())
|
|
|
|
def equivalentQuaternions(self):
|
|
return self.symmetry.equivalentQuaternions(self.quaternion)
|
|
|
|
def equivalentOrientations(self):
|
|
return map(lambda q: Orientation(quaternion=q,symmetry=self.symmetry.lattice),
|
|
self.equivalentQuaternions())
|
|
|
|
|
|
def reduced(self):
|
|
'''Transform orientation to fall into fundamental zone according to symmetry'''
|
|
for me in self.symmetry.equivalentQuaternions(self.quaternion):
|
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if self.symmetry.inFZ(me.asRodrigues()): break
|
|
|
|
return Orientation(quaternion=me,symmetry=self.symmetry.lattice)
|
|
|
|
def disorientation_old(self,other):
|
|
'''
|
|
Disorientation between myself and given other orientation
|
|
(either reduced according to my own symmetry or given one)
|
|
'''
|
|
|
|
lowerSymmetry = min(self.symmetry,other.symmetry)
|
|
breaker = False
|
|
|
|
for me in self.symmetry.equivalentQuaternions(self.quaternion):
|
|
me.conjugate()
|
|
for they in other.symmetry.equivalentQuaternions(other.quaternion):
|
|
theQ = they * me
|
|
breaker = lowerSymmetry.inDisorientationSST(theQ.asRodrigues()) #\
|
|
# or lowerSymmetry.inDisorientationSST(theQ.conjugated().asRodrigues())
|
|
if breaker: break
|
|
if breaker: break
|
|
|
|
return Orientation(quaternion=theQ,symmetry=self.symmetry.lattice) #, me.conjugated(), they
|
|
|
|
def disorientation(self,other):
|
|
'''
|
|
Disorientation between myself and given other orientation
|
|
(currently needs to be of same symmetry.
|
|
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 = self.quaternion.conjugated()*other.quaternion
|
|
|
|
for i,sA in enumerate(self.symmetry.symmetryQuats()):
|
|
for j,sB in enumerate(other.symmetry.symmetryQuats()):
|
|
theQ = sA.conjugated()*misQ*sB
|
|
for k in xrange(2):
|
|
theQ.conjugate()
|
|
hitSST = other.symmetry.inDisorientationSST(theQ)
|
|
hitFZ = self.symmetry.inFZ(theQ)
|
|
breaker = hitSST and hitFZ
|
|
if breaker: break
|
|
if breaker: break
|
|
if breaker: break
|
|
return Orientation(quaternion=theQ,symmetry=self.symmetry.lattice) # disorientation, own sym, other sym, self-->other: True, self<--other: False
|
|
|
|
def inversePole(self,axis,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.conjugated()*axis # align crystal direction to axis
|
|
if self.symmetry.inSST(pole): break # found SST version
|
|
else:
|
|
pole = self.quaternion.conjugated()*axis # align crystal direction to axis
|
|
|
|
return pole
|
|
|
|
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.conjugated()*axis # align crystal direction to axis
|
|
inSST,color = self.symmetry.inSST(pole,color=True)
|
|
if inSST: break
|
|
|
|
return color
|
|
|
|
@staticmethod
|
|
def getAverageOrientation(orientationList):
|
|
"""
|
|
RETURN THE 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
|
|
sample usage:
|
|
a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry=3)
|
|
b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry=3)
|
|
avg = Orientation.getAverageOrientation([a,b])
|
|
NOTE
|
|
----
|
|
No symmetry information is available for the average orientation.
|
|
"""
|
|
|
|
if not all(isinstance(item, Orientation) for item in orientationList):
|
|
raise TypeError("Only instances of Orientation can be averaged.")
|
|
|
|
N = len(orientationList)
|
|
M = orientationList.pop(0).quaternion.asM()
|
|
for o in orientationList:
|
|
M += o.quaternion.asM()
|
|
eig, vec = np.linalg.eig(M/N)
|
|
|
|
return Orientation(quaternion = Quaternion(vec.T[eig.argmax()]))
|
|
|
|
def related(self, relationModel, direction, targetSymmetry = None):
|
|
|
|
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
|
|
# 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([myPlane,myNormal,np.cross(myPlane,myNormal)])
|
|
|
|
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([otherPlane,otherNormal,np.cross(otherPlane,otherNormal)])
|
|
|
|
rot=np.dot(otherMatrix.T,myMatrix)
|
|
|
|
return Orientation(matrix=np.dot(rot,self.asMatrix())) # no symmetry information ?? |