diff --git a/Makefile b/Makefile index 1850f6cca..6c63d01f6 100755 --- a/Makefile +++ b/Makefile @@ -21,6 +21,7 @@ marc: processing: @if hash cython 2>/dev/null; then \ cd ./lib/damask; \ + ln -s orientation.py corientation.pyx; \ CC=gcc python setup_corientation.py build_ext --inplace; \ rm -rv build; \ rm *.c; \ diff --git a/lib/damask/.gitignore b/lib/damask/.gitignore index 00feaa11f..1b8936623 100644 --- a/lib/damask/.gitignore +++ b/lib/damask/.gitignore @@ -1,2 +1,3 @@ core.so corientation.so +*.pyx diff --git a/lib/damask/__init__.py b/lib/damask/__init__.py index c25fc0bd8..dc40920fa 100644 --- a/lib/damask/__init__.py +++ b/lib/damask/__init__.py @@ -10,12 +10,11 @@ from .environment import Environment # noqa from .asciitable import ASCIItable # noqa from .config import Material # noqa from .colormaps import Colormap, Color # noqa -from .orientation import Quaternion, Rodrigues, Symmetry, Orientation # noqa -# try: -# from .corientation import Quaternion, Rodrigues, Symmetry, Orientation -# print "Import Cython version of Orientation module" -# except: -# from .orientation import Quaternion, Rodrigues, Symmetry, Orientation +try: + from .corientation import Quaternion, Rodrigues, Symmetry, Orientation + print "Import Cython version of Orientation module" +except: + from .orientation import Quaternion, Rodrigues, Symmetry, Orientation #from .block import Block # only one class from .result import Result # noqa from .geometry import Geometry # noqa diff --git a/lib/damask/corientation.pyx b/lib/damask/corientation.pyx deleted file mode 100644 index 6da6ba8a5..000000000 --- a/lib/damask/corientation.pyx +++ /dev/null @@ -1,1277 +0,0 @@ -#!/usr/bin/env python -# encoding: utf-8 -# filename: corientation.pyx - -# __ __ __________ ____ __ ____ ______ ____ -# / //_// ____/ __ \/ __ \/ //_/ / / / __ \/ __ \ -# / ,< / __/ / / / / / / / ,< / / / / / / / / / / -# / /| |/ /___/ /_/ / /_/ / /| / /_/ / /_/ / /_/ / -# /_/ |_/_____/_____/\____/_/ |_\____/_____/\____/ - - -###################################################### -# This is a Cython implementation of original DAMASK # -# orientation class, mainly for speed improvement. # -###################################################### - -""" -NOTE ----- -The static method in Cython is different from Python, need more -time to figure out details. -""" - -import math, random, os -import numpy as np -cimport numpy as np - - -## -# This Rodrigues class is odd, not sure if it will function -# properly or not -cdef class Rodrigues: - """Rodrigues representation of orientation """ - cdef public double[3] r - - def __init__(self, vector): - if isinstance(vector, Rodrigues): - self.r[0] = vector.r[0] - self.r[1] = vector.r[1] - self.r[2] = vector.r[2] - else: - self.r[0] = vector[0] - self.r[1] = vector[1] - self.r[2] = vector[2] - - def asQuaternion(self): - cdef double norm, halfAngle - cdef double[4] q - - norm = np.linalg.norm(self.vector) - halfAngle = np.arctan(norm) - q[0] = np.cos(halfAngle) - tmp = np.sin(halfAngle)*self.vector/norm - q[1],q[2],q[3] = tmp[0],tmp[1],tmp[2] - - return Quaternion(q) - - def asAngleAxis(self): - cdef double norm, halfAngle - - norm = np.linalg.norm(self.vector) - halfAngle = np.arctan(norm) - - return (2.0*halfAngle,self.vector/norm) - - -## -# The Quaternion class do the heavy lifting of orientation -# calculation -cdef class Quaternion: - """ Quaternion representation of orientation """ - # All methods and naming conventions based off - # http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions - cdef public double w,x,y,z - - def __init__(self, data): - """ - @description - ------------ - copy constructor friendly - @parameters - ----------- - data: array - """ - cdef double[4] q - - if isinstance(data, Quaternion): - q[0] = data.w - q[1] = data.x - q[2] = data.y - q[3] = data.z - else: - q[0] = data[0] - q[1] = data[1] - q[2] = data[2] - q[3] = data[3] - - self.Quaternion(q) - - cdef Quaternion(self, double* quatArray): - """ - @description - ------------ - internal constructor for Quaternion - @parameters - ----------- - quatArray: double[4] // - w is the real part, (x, y, z) are the imaginary parts - """ - if quatArray[0] < 0: - self.w = -quatArray[0] - self.x = -quatArray[1] - self.y = -quatArray[2] - self.z = -quatArray[3] - else: - self.w = quatArray[0] - self.x = quatArray[1] - self.y = quatArray[2] - self.z = quatArray[3] - - def __copy__(self): - cdef double[4] q = [self.w,self.x,self.y,self.z] - return Quaternion(q) - - copy = __copy__ - - def __iter__(self): - return iter([self.w,self.x,self.y,self.z]) - - def __repr__(self): - return 'Quaternion(real={:.4f},imag=<{:.4f},{:.4f}, {:.4f}>)'.format(self.w, - self.x, - self.y, - self.z) - - def __pow__(self, exponent, modulo): - # declare local var for speed gain - cdef double omega, vRescale - cdef double[4] q - - omega = math.acos(self.w) - vRescale = math.sin(exponent*omega)/math.sin(omega) - - q[0] = math.cos(exponent*omega) - q[1] = self.x*vRescale - q[2] = self.y*vRescale - q[3] = self.z*vRescale - return Quaternion(q) - - def __ipow__(self, exponent): - self = self.__pow__(self, exponent, 1.0) - return self - - def __mul__(self, other): - # declare local var for speed gain - cdef double Aw,Ax,Ay,Az,Bw,Bx,By,Bz - cdef double w,x,y,z,Vx,Vy,Vz - cdef double[4] q - - # quaternion * quaternion - try: - Aw = self.w - Ax = self.x - Ay = self.y - Az = self.z - Bw = other.w - Bx = other.x - By = other.y - Bz = other.z - q[0] = - Ax * Bx - Ay * By - Az * Bz + Aw * Bw - q[1] = + Ax * Bw + Ay * Bz - Az * By + Aw * Bx - q[2] = - Ax * Bz + Ay * Bw + Az * Bx + Aw * By - q[3] = + Ax * By - Ay * Bx + Az * Bw + Aw * Bz - return Quaternion(q) - except: - pass - # vector (perform active rotation, i.e. q*v*q.conjugated) - try: - w = self.w - x = self.x - y = self.y - z = self.z - Vx = other[0] - Vy = other[1] - Vz = other[2] - return np.array([\ - w * w * Vx + 2 * y * w * Vz - 2 * z * w * Vy + \ - x * x * Vx + 2 * y * x * Vy + 2 * z * x * Vz - \ - z * z * Vx - y * y * Vx, - 2 * x * y * Vx + y * y * Vy + 2 * z * y * Vz + \ - 2 * w * z * Vx - z * z * Vy + w * w * Vy - \ - 2 * x * w * Vz - x * x * Vy, - 2 * x * z * Vx + 2 * y * z * Vy + \ - z * z * Vz - 2 * w * y * Vx - y * y * Vz + \ - 2 * w * x * Vy - x * x * Vz + w * w * Vz ]) - except: - pass - # quaternion * scalar - try: - Q = self.copy() - Q.w *= other - Q.x *= other - Q.y *= other - Q.z *= other - return Q - except: - return self.copy() - - def __imul__(self, other): - if isinstance(other, Quaternion): - self = self.__mul__(other) - return self - else: - return NotImplemented - - def __div__(self, other): - cdef double[4] q - - if isinstance(other, (int,float,long)): - q[0] = self.w / other - q[1] = self.x / other - q[2] = self.y / other - q[3] = self.z / other - return Quaternion(q) - else: - NotImplemented - - def __idiv__(self, other): - self = self.__div__(other) - return self - - def __add__(self, other): - cdef double[4] q - - if isinstance(other, Quaternion): - q[0] = self.w + other.w - q[1] = self.x + other.x - q[2] = self.y + other.y - q[3] = self.z + other.z - return self.__class__(q) - else: - return NotImplemented - - def __iadd__(self, other): - self = self.__add__(other) - return self - - def __sub__(self, other): - cdef double[4] q - - if isinstance(other, Quaternion): - q[0] = self.w - other.w - q[1] = self.x - other.x - q[2] = self.y - other.y - q[3] = self.z - other.z - return self.__class__(q) - else: - return NotImplemented - - def __isub__(self, other): - self = self.__sub__(other) - return self - - def __neg__(self): - cdef double[4] q - - q[0] = -self.w - q[1] = -self.x - q[2] = -self.y - q[3] = -self.z - - return self.__class__(q) - - def __abs__(self): - cdef double tmp - - tmp = self.w**2 + self.x**2 + self.y**2 + self.z**2 - tmp = math.sqrt(tmp) - return tmp - - magnitude = __abs__ - - def __richcmp__(Quaternion self, Quaternion other, int op): - cdef bint tmp - - tmp = (abs(self.w-other.w) < 1e-8 and \ - abs(self.x-other.x) < 1e-8 and \ - abs(self.y-other.y) < 1e-8 and \ - abs(self.z-other.z) < 1e-8) \ - or \ - (abs(-self.w-other.w) < 1e-8 and \ - abs(-self.x-other.x) < 1e-8 and \ - abs(-self.y-other.y) < 1e-8 and \ - abs(-self.z-other.z) < 1e-8) - if op == 2: #__eq__ - return tmp - elif op ==3: #__ne__ - return not tmp - else: - return NotImplemented - - def __cmp__(self,other): - # not sure if this actually works or not - return cmp(self.Rodrigues(),other.Rodrigues()) - - def magnitude_squared(self): - cdef double tmp - - tmp = self.w**2 + self.x**2 + self.y**2 + self.z**2 - return tmp - - def identity(self): - self.w = 1.0 - self.x = 0.0 - self.y = 0.0 - self.z = 0.0 - return self - - def normalize(self): - cdef double d - - d = self.magnitude() - if d > 0.0: - self /= d - return self - - def conjugate(self): - self.x = -self.x - self.y = -self.y - self.z = -self.z - return self - - def inverse(self): - cdef double d - - d = self.magnitude() - if d > 0.0: - self.conjugate() - self /= d - return self - - def homomorph(self): - if self.w < 0.0: - self.w = -self.w - self.x = -self.x - self.y = -self.y - self.z = -self.z - return self - - # return a copy of me - def normalized(self): - cdef Quaternion q - - q = Quaternion(self.normalize()) - return q - - def conjugated(self): - cdef Quaternion q - - q = Quaternion(self.conjugate()) - return q - - def asList(self): - cdef double[4] q = [self.w, self.x, self.y, self.z] - - return list(q) - - def asM(self): # to find Averaging Quaternions (see F. Landis Markley et al.) - return np.outer([i for i in self],[i for i in self]) - - def asMatrix(self): - 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)], - [ 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)], - [ 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)]]) - - def asAngleAxis(self): - # keep the return as radians for simplicity - cdef double s,x,y - - if self.w > 1: - self.normalize() - - s = math.sqrt(1. - self.w**2) - x = 2*self.w**2 - 1. - y = 2*self.w * s - - angle = math.atan2(y,x) - if angle < 0.0: - angle *= -1.0 - s *= -1.0 - - return (angle, - np.array([1.0, 0.0, 0.0] if np.abs(angle) < 1e-3 else [self.x/s, self.y/s, self.z/s]) ) - - def asRodrigues(self): - if self.w != 0.0: - return np.array([self.x, self.y, self.z])/self.w - else: - return np.array([float('inf')]*3) - - def asEulers(self, - type='bunge', - degrees=False, - standardRange=False): - """ - CONVERSION TAKEN FROM: - Melcher, A.; Unser, A.; Reichhardt, M.; Nestler, B.; Pötschke, M.; Selzer, M. - Conversion of EBSD data by a quaternion based algorithm to be used for grain structure simulations - Technische Mechanik 30 (2010) pp 401--413 - """ - cdef double x,y - - angles = [0.0,0.0,0.0] - - if type.lower() == 'bunge' or type.lower() == 'zxz': - if abs(self.x) < 1e-4 and abs(self.y) < 1e-4: - x = self.w**2 - self.z**2 - y = 2.*self.w*self.z - angles[0] = math.atan2(y,x) - elif abs(self.w) < 1e-4 and abs(self.z) < 1e-4: - x = self.x**2 - self.y**2 - y = 2.*self.x*self.y - angles[0] = math.atan2(y,x) - angles[1] = math.pi - else: - chi = math.sqrt((self.w**2 + self.z**2)*(self.x**2 + self.y**2)) - - x = (self.w * self.x - self.y * self.z)/2./chi - y = (self.w * self.y + self.x * self.z)/2./chi - angles[0] = math.atan2(y,x) - - x = self.w**2 + self.z**2 - (self.x**2 + self.y**2) - y = 2.*chi - angles[1] = math.atan2(y,x) - - x = (self.w * self.x + self.y * self.z)/2./chi - y = (self.z * self.x - self.y * self.w)/2./chi - angles[2] = math.atan2(y,x) - if standardRange: - angles[0] %= 2*math.pi - if angles[1] < 0.0: - angles[1] += math.pi - angles[2] *= -1.0 - angles[2] %= 2*math.pi - - return np.degrees(angles) if degrees else angles - - @staticmethod - def fromIdentity(): - cdef double[4] q = [1.0, 0.0, 0.0, 0.0] - - return Quaternion(q) - - @staticmethod - def fromRandom(randomSeed=None): - cdef double r1,r2,r3 - cdef double[4] q - - if randomSeed == None: - randomSeed = int(os.urandom(4).encode('hex'), 16) - random.seed(randomSeed) - - r1 = random.random() - r2 = random.random() - r3 = random.random() - q[0] = math.cos(2.0*math.pi*r1)*math.sqrt(r3) - q[1] = math.sin(2.0*math.pi*r2)*math.sqrt(1.0-r3) - q[2] = math.cos(2.0*math.pi*r2)*math.sqrt(1.0-r3) - q[3] = math.sin(2.0*math.pi*r1)*math.sqrt(r3) - return Quaternion(q) - - @staticmethod - def fromRodrigues(rodrigues): - if not isinstance(rodrigues, np.ndarray): rodrigues = np.array(rodrigues) - halfangle = math.atan(np.linalg.norm(rodrigues)) - c = math.cos(halfangle) - w = c - x,y,z = c*rodrigues - return Quaternion([w,x,y,z]) - - @staticmethod - def fromAngleAxis(angle, axis): - if not isinstance(axis, np.ndarray): axis = np.array(axis) - axis /= np.linalg.norm(axis) - s = math.sin(angle / 2.0) - w = math.cos(angle / 2.0) - x = axis[0] * s - y = axis[1] * s - z = axis[2] * s - return Quaternion([w,x,y,z]) - - @staticmethod - def fromEulers(eulers, type = 'Bunge'): - cdef double c1,s1,c2,s2,c3,s3 - cdef double[4] q - cdef double[3] halfEulers - cdef int i - - for i in range(3): - halfEulers[i] = eulers[i] * 0.5 # reduce to half angles - - - c1 = math.cos(halfEulers[0]) - s1 = math.sin(halfEulers[0]) - c2 = math.cos(halfEulers[1]) - s2 = math.sin(halfEulers[1]) - c3 = math.cos(halfEulers[2]) - s3 = math.sin(halfEulers[2]) - - 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): - 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 ?? \ No newline at end of file