def test_multiplicity(self):
"""Int Tables of Crystallography Vol. 1 p 32."""
self.assertEqual(
HklPlane(1, 0, 0).multiplicity(symmetry=Symmetry.cubic), 6)
for h in range(1, 4):
self.assertEqual(
HklPlane(h, 0, 0).multiplicity(symmetry=Symmetry.tetragonal),
4)
self.assertEqual(
HklPlane(0, h, 0).multiplicity(symmetry=Symmetry.tetragonal),
4)
self.assertEqual(
HklPlane(h, h, 0).multiplicity(symmetry=Symmetry.tetragonal),
4)
self.assertEqual(
HklPlane(-h, h, 0).multiplicity(symmetry=Symmetry.tetragonal),
4)
self.assertEqual(
HklPlane(h, h, 1).multiplicity(symmetry=Symmetry.tetragonal),
8)
self.assertEqual(
HklPlane(-h, h, 1).multiplicity(symmetry=Symmetry.tetragonal),
8)
self.assertEqual(
HklPlane(0, 0, 1).multiplicity(symmetry=Symmetry.tetragonal), 2)
self.assertEqual(
HklPlane(1, 0, 2).multiplicity(symmetry=Symmetry.tetragonal), 8)
self.assertEqual(
HklPlane(-1, 0, 2).multiplicity(symmetry=Symmetry.tetragonal), 8)
self.assertEqual(
HklPlane(0, 1, 2).multiplicity(symmetry=Symmetry.tetragonal), 8)
self.assertEqual(
HklPlane(0, -1, 2).multiplicity(symmetry=Symmetry.tetragonal), 8)
self.assertEqual(
HklPlane(1, 2, 0).multiplicity(symmetry=Symmetry.tetragonal), 8)
self.assertEqual(
HklPlane(-1, 2, 0).multiplicity(symmetry=Symmetry.tetragonal), 8)
self.assertEqual(
HklPlane(1, 2, 3).multiplicity(symmetry=Symmetry.tetragonal), 16)
def test_HklPlane(self):
p = HklPlane(1, 1, 1)
n = p.normal()
self.assertEqual(np.linalg.norm(n), 1)
def plot_sst(self, **kwargs):
""" Create the inverse pole figure in the unit standard triangle.
:param ax: a reference to a pyplot ax to draw the poles.
:param mk: marker used to plot the poles (square by default).
:param bool ann: Annotate the pole with the coordinates of the vector
if True (False by default).
"""
# first draw the boundary of the symmetry domain limited by 3 hkl plane
# normals, called here A, B and C
symmetry = self.lattice.get_symmetry()
ax = kwargs.get('ax')
if symmetry is Symmetry.cubic:
sst_poles = [(0, 0, 1), (1, 0, 1), (1, 1, 1)]
ax.axis([-0.05, 0.45, -0.05, 0.40])
elif symmetry is Symmetry.hexagonal:
sst_poles = [(0, 0, 1), (2, -1, 0), (1, 0, 0)]
ax.axis([-0.05, 1.05, -0.05, 0.6])
else:
print('unsuported symmetry: %s' % symmetry)
A = HklPlane(*sst_poles[0], lattice=self.lattice)
B = HklPlane(*sst_poles[1], lattice=self.lattice)
C = HklPlane(*sst_poles[2], lattice=self.lattice)
self.plot_line_between_crystal_dir(A.normal(),
B.normal(),
ax=ax,
col='k')
self.plot_line_between_crystal_dir(B.normal(),
C.normal(),
ax=ax,
col='k')
self.plot_line_between_crystal_dir(C.normal(),
A.normal(),
ax=ax,
col='k')
# display the 3 crystal axes
poles = [A, B, C]
v_align = ['top', 'top', 'bottom']
for i in range(3):
hkl = poles[i]
c_dir = hkl.normal()
c = c_dir + self.z
c /= c[2] # SP'/SP = r/z with r=1
pole_str = '%d%d%d' % hkl.miller_indices()
if symmetry is Symmetry.hexagonal:
pole_str = '%d%d%d%d' % HklPlane.three_to_four_indices(
*hkl.miller_indices())
ax.annotate(pole_str, (c[0], c[1] - (2 * (i < 2) - 1) * 0.01),
xycoords='data',
fontsize=12,
horizontalalignment='center',
verticalalignment=v_align[i])
# now plot the sample axis
if self.resize_markers:
# compute the max grain volume to normalize
volume_max = max(self.microstructure.get_grain_volumes())
for grain in self.microstructure.grains:
g = Orientation.Rodrigues2OrientationMatrix(grain['orientation'])
if self.resize_markers:
kwargs['mksize'] = 0.15 * np.sqrt(
grain['volume'] / volume_max) * 1000
# compute axis and apply SST symmetry
if self.axis == 'Z':
axis = self.z
elif self.axis == 'Y':
axis = self.y
else:
axis = self.x
axis_rot = self.sst_symmetry(g.dot(axis))
label = ''
if self.map_field == 'grain_id':
label = 'grain ' + str(grain['idnumber'])
kwargs['lab'] = label
kwargs['col'] = self.get_color_from_field(grain)
self.plot_crystal_dir(axis_rot, **kwargs)
if self.verbose:
print('plotting %s in crystal CS: %s' % (self.axis, axis_rot))
ax.axis('off')
ax.set_title('%s-axis SST inverse %s projection' %
(self.axis, self.proj))
def test_SchimdFactor(self):
o = Orientation.from_euler([0., 0., 0.])
ss = SlipSystem(HklPlane(1, 1, 1), HklDirection(0, 1, -1))
self.assertAlmostEqual(o.schmid_factor(ss), 0.4082, 4)
# create a python Grain object from the image data
orientation = Orientation.from_rodrigues(np.array([0.3889, -0.0885, 0.3268]))
grain = Grain(1, orientation)
grain_data = HST_read(im_file,
header_size=0,
autoparse_filename=True,
verbose=True)
grain.position = ndimage.measurements.center_of_mass(grain_data, grain_data)
print('grain position:', grain.position)
grain.volume = ndimage.measurements.sum(grain_data) # label is 1.0 here
grain.add_vtk_mesh(grain_data, contour=False)
print('adding bounding box')
grain_bbox = box_3d(size=np.shape(grain_data), line_color=white)
print('adding grain with slip planes')
hklplanes = [HklPlane(1, 1, 1)]
grain_with_planes = grain_3d(grain, hklplanes, show_normal=False, \
plane_opacity=1.0, show_orientation=True)
tr = vtk.vtkTransform()
tr.Translate(grain.position)
grain_with_planes.SetUserTransform(tr)
print('adding a lattice to picture the grain orientation')
lat_size = 20
l = Lattice.face_centered_cubic(lat_size)
cubic = lattice_3d_with_planes(l, hklplanes, crystal_orientation=grain.orientation, \
show_normal=True, plane_opacity=1.0, origin='mid', sphereColor=grey,
sphereRadius=0.1)
apply_translation_to_actor(cubic, (lat_size, lat_size, lat_size))
print('adding axes')
