def rt2tr(translation, rotation):
"""Change the transformation order from 1T2R to 1R2T.
"""
from pytom.tools.maths import TransformationMatrix
from pytom.angles.angleFnc import matToZXZ
m = TransformationMatrix(rotation, [0, 0, 0]) * TransformationMatrix(
[0, 0, 0], translation)
return (matToZXZ(m.getRotationMatrix()).toList(), m.getTranslation())
def nextRotation(self):
"""
nextRotation :
@return: [z1 z2 x] for the next rotation or [None,None,None] after all rotations were sampled
@author: Friedrich Foerster
@change: Local Rotation had a bug causing too large rotations in Phi
@date: 07/07/2014
"""
if self._finished:
return [None, None, None]
from math import sin, ceil, pi, sqrt, atan2 #,modf
from pytom.basic.structures import Rotation
from pytom.angles.angleFnc import matToZXZ
phi = self._currentZ1
if self._currentX == 0:
npsi = 1
dpsi = 360.
else:
dpsi = self._increment / sin(
float(self._currentX * self._increment) / 180. * pi)
npsi = ceil(360. / dpsi)
#make dpsi equidistant again
dpsi = 360. / npsi
localRotation = Rotation(z1=phi - self._currentZ2 * dpsi,
z2=self._currentZ2 * dpsi,
x=self._currentX * self._increment,
paradigm='ZXZ')
globalMatrix = localRotation.toMatrix() * self._startMatrix
[phi, psi, theta] = matToZXZ(globalMatrix)
if self._currentZ2 >= npsi - 1:
self._currentZ2 = 0
if self._currentX >= ceil(self._shells / 2):
self._currentX = 0
if self._currentZ1 >= self._shells * self._increment:
self._finished = True
return [self._startZ1, self._startZ2, self._startX]
else:
self._currentZ1 = self._currentZ1 + self._increment
else:
self._currentX = self._currentX + 1
else:
self._currentZ2 = self._currentZ2 + 1
return [phi % 360, psi % 360, theta % 360]
def matPoleTest1(self):
"""
check that conversion to angle from matrix works for x == 0
"""
z1 = 9
z2 = 360. - 114
x = 0.
self.rot1 = Rotation(z1=z1, z2=z2, x=x)
self.rot2 = Rotation(z1=0., z2=0., x=0.)
newrot = self.rot2 * self.rot1
[nz1, nz2, nx] = matToZXZ(newrot.toMatrix(), inRad=False)
self.assertTrue(nx == 0.0, 'Pole Test 1 failed: wrong x-angle')
self.assertTrue(
abs(nz2 + nz1 - z2 - z1) < 0.00001,
'Pole Test 2 failed: wrong assignment z1 and z2')
def matTestQ4(self):
"""
test that matToZXZ works for 180<z2<360
"""
z1 = 169.
z2 = 190.
x = 10.
self.rot1 = Rotation(z1=z1, z2=z2, x=x)
self.rot2 = Rotation(z1=0., z2=0., x=0.)
newrot = self.rot2 * self.rot1
[nz1, nz2, nx] = matToZXZ(newrot.toMatrix(), inRad=False)
self.assertTrue(abs(nx - x) < self.eps, 'matTestQ3: nx and x differ')
self.assertTrue(
abs(nz1 - z1) < self.eps, 'matTestQ3: nz1 and z1 differ')
self.assertTrue(
abs(nz2 - z2) < self.eps, 'matTestQ3: nz2 and z2 differ')
def zxzToMatToZXZ_T(self, z1, z2, x):
from pytom.angles.angleFnc import zxzToMat, matToZXZ
m = zxzToMat(z1=z1, z2=z2, x=x)
r = matToZXZ(m)
self.assertAlmostEqual(first=r.getZ1(),
second=z1,
places=3,
msg='numerical issue in z1')
self.assertAlmostEqual(first=r.getZ2(),
second=z2,
places=3,
msg='numerical issue in z2')
self.assertAlmostEqual(first=r.getX(),
second=x,
places=3,
msg='numerical issue in x')
def matPoleTest2(self):
"""
check that conversion to angle from matrix works for x == 180
"""
z1 = 9
z2 = -114
x = 180.
self.rot1 = Rotation(z1=z1, z2=z2, x=x)
self.rot2 = Rotation(z1=0., z2=0., x=0.)
newrot = self.rot2 * self.rot1
[nz1, nz2, nx] = matToZXZ(newrot.toMatrix(), inRad=False)
self.assertTrue(nx == 180.0, 'Pole Test 2 failed: wrong x-angle')
self.assertTrue(
abs(
modf((nz2 - nz1 + 360.) / 360.)[0] * 360 -
modf((z2 - z1 + 360.) / 360.)[0] * 360) < 0.00001,
'Pole Test 2 failed: z2 z1 not correct')
def test_conversion(self,
phi1=0,
psi1=0,
the1=0,
phi2=90,
psi2=90,
the2=90):
from pytom.angles.angleFnc import zxzToMat
m = zxzToMat(phi1, psi1, the1, False)
self.assertTrue(m.trace() == 3.0, msg='trace of matrix is wrong')
self.assertTrue(
m.getRow(0)[0] == 1.0 and m.getRow(1)[1] == 1.0
and m.getRow(2)[2] == 1.0)
m = zxzToMat(phi2, psi2, the2, False)
from pytom.angles.angleFnc import matToZXZ
a = matToZXZ(m)
self.assertTrue(a[0] == phi2 and a[1] == psi2 and a[2] == the2)