def test_add_grains(self):
micro = Microstructure(name='test', autodelete=True)
self.assertEqual(micro.get_number_of_grains(), 0)
micro.add_grains(self.test_eulers)
self.assertEqual(micro.get_number_of_grains(), 3)
del micro
class PoleFigure:
"""A class to create pole figures.
A pole figure is a useful tool to plot multiple crystal orientations,
either in the sample coordinate system (direct pole figure) or
alternatively plotting a particular direction in the crystal
coordinate system (inverse pole figure).
"""
def __init__(self,
microstructure=None,
lattice=None,
axis='Z',
hkl='111',
proj='stereo',
verbose=False):
"""
Create an empty PoleFigure object associated with a Microstructure.
.. warning::
Any crystal structure is now supported (you have to set the proper
crystal lattice) but it has only really be tested for cubic.
:param microstructure: the :py:class:`~pymicro.crystal.microstructure.Microstructure`
containing the collection of orientations to plot (None by default).
:param lattice: the crystal :py:class:`~pymicro.crystal.lattice.Lattice`.
:param str axis: the pole figure axis ('Z' by default), vertical axis in
the direct pole figure and direction plotted on the inverse pole figure.
:param str hkl: slip plane family ('111' by default)
:param str proj: projection type, can be either 'stereo' (default) or 'flat'
:param bool verbose: verbose mode (False by default)
"""
self.proj = proj
self.axis = axis
self.map_field = None
if microstructure:
self.microstructure = microstructure
else:
self.microstructure = Microstructure()
if lattice:
self.lattice = lattice
else:
self.lattice = Lattice.cubic(1.0)
self.family = None
self.poles = []
self.set_hkl_poles(hkl)
self.verbose = verbose
self.resize_markers = False
self.mksize = 50
self.pflegend = False
self.x = np.array([1., 0., 0.])
self.y = np.array([0., 1., 0.])
self.z = np.array([0., 0., 1.])
# list all crystal directions
#self.c001s = np.array([[0, 0, 1], [0, 1, 0], [1, 0, 0]], dtype=np.float)
#self.c011s = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0], [0, -1, 1], [-1, 0, 1], [-1, 1, 0]],
# dtype=np.float) / np.sqrt(2)
#self.c111s = np.array([[1, 1, 1], [-1, -1, 1], [1, -1, 1], [-1, 1, 1]], dtype=np.float) / np.sqrt(3)
def get_orientations(self):
"""Get the list of orientations in the PoleFigure.
:return: a list of `Orientation` instances.
"""
return self.microstructure.get_grain_orientations()
def set_hkl_poles(self, hkl='111'):
"""Set the pole (aka hkl planes) list to to use in the `PoleFigure`.
The list of poles can be given by the family type or directly by a list
of `HklPlanes` objects.
:params str/list hkl: slip plane family ('111' by default)
"""
if type(hkl) is str:
self.family = hkl # keep a record of this
hkl_planes = self.lattice.get_hkl_family(self.family)
elif type(hkl) is list:
self.family = None
hkl_planes = hkl
self.poles = hkl_planes
def set_map_field(self,
field_name,
field=None,
field_min_level=None,
field_max_level=None,
lut='hot'):
"""Set the PoleFigure to color poles with the given field.
This method activates a mode where each symbol in the pole figure
is color coded with respect to a field, which can be either the
grain id, or a given field given in form of a list. If the grain
volume or strain. For the grain id, the color is set according the
each grain id in the :py:class:`~pymicro.crystal.microstructure.Microstructure`
and the :py:meth:`~pymicro.crystal.microstructure.rand_cmap` function.
For a given field, the color is set from the lookup table and
according to the value in the given list. The list must contain a
record for each grain. Minimum and maximum value to map the field
values and the colors can be specify, if not they are directly taken
as the min() and max() of the field.
:param str field_name: The field name, could be 'grain_id', 'ipf',
'grain_size' or any other name describing the field.
:param list field: A list containing a record for each grain.
:param float field_min_level: The minimum value to use for this field.
:param float field_max_level: The maximum value to use for this field.
:param str lut: A string describing the colormap to use (among
matplotlib ones available).
:raise ValueError: If the given field does not contain enough values.
"""
self.map_field = field_name
self.lut = lut
if field_name in ['grain_id', 'ipf']:
self.field = self.microstructure.get_grain_ids()
elif field_name in ['grain_size', 'volume']:
self.field = self.microstructure.get_grain_volumes()
else:
if len(field) != self.microstructure.get_number_of_grains():
raise ValueError('The field must contain exactly one record '
'for each grain in the microstructure')
self.field = field
if not field_min_level:
self.field_min_level = self.field.min()
else:
self.field_min_level = field_min_level
if not field_max_level:
self.field_max_level = self.field.max()
else:
self.field_max_level = field_max_level
def plot_pole_figures(self, plot_sst=True, display=True, save_as='pdf'):
"""Plot and save a picture with both direct and inverse pole figures.
:param bool plot_sst: controls wether to plot the full inverse pole
figure or only the standard stereographic triangle (True by default).
:param bool display: display the plot if True, else save a picture of
the pole figures (True by default)
:param str save_as: File format used to save the image such as pdf
or png ('pdf' by default)
::
micro = Microstructure(name = 'AlLi_sam8')
micro.grains.append(Grain(11, Orientation.from_euler(np.array([262.364, 16.836, 104.691]))))
Al_fcc = Lattice.face_centered_cubic(0.405) # not really necessary since default lattice is cubic
pf = PoleFigure(microstructure=micro, proj='stereo', lattice=Al_fcc, hkl='111')
pf.mksize = 12
pf.set_map_field('grain_id')
pf.pflegend = True # this works well for a few grains
pf.plot_pole_figures()
.. figure:: _static/AlLi_sam8_pole_figure.png
:width: 750 px
:height: 375 px
:alt: AlLi_sam8_pole_figure
:align: center
A 111 pole figure plotted for a single crystal orientation.
"""
fig = plt.figure(figsize=(10, 5))
# direct PF
ax1 = fig.add_subplot(121, aspect='equal')
self.plot_pf(ax=ax1, mk='o', ann=False)
# inverse PF
ax2 = fig.add_subplot(122, aspect='equal')
if plot_sst:
self.plot_sst(ax=ax2)
else:
self.plot_ipf(ax=ax2)
if display:
plt.show()
else:
plt.savefig('%s_pole_figure.%s' %
(self.microstructure.get_sample_name(), save_as),
format=save_as)
def plot_crystal_dir(self, c_dir, **kwargs):
"""Function to plot a crystal direction on a pole figure.
:param c_dir: A vector describing the crystal direction.
:param dict kwargs: a dictionnary of keyword/values to control the
plot, it should at least contain a reference to a pyplot axes
to draw the pole using keyword 'ax'.
:raise ValueError: if the projection type is not supported
"""
if c_dir[2] < 0:
c_dir *= -1 # make unit vector have z>0
if self.proj == 'flat':
cp = c_dir
elif self.proj == 'stereo':
c = c_dir + self.z
c /= c[2] # SP'/SP = r/z with r=1
cp = c
# cp = np.cross(c, self.z)
else:
raise ValueError('Error, unsupported projection type', self.proj)
ax = kwargs.get('ax')
mk = kwargs.get('mk', 'o')
edge_col = kwargs.get('markeredgecolor', 'k')
ann = kwargs.get('ann', None)
lab = kwargs.get('lab', '')
col = kwargs.get('col', 'k')
col = col.reshape(1, -1)
#ax.plot(cp[0], cp[1], linewidth=0, markerfacecolor=col, marker=mk,
# markeredgecolor=edge_col, markersize=self.mksize, label=lab)
mksize = kwargs.get('mksize', self.mksize)
ax.scatter(cp[0],
cp[1],
linewidth=0,
c=col,
marker=mk,
edgecolors=edge_col,
s=mksize,
label=lab)
# Next 3 lines are necessary in case c_dir[2]=0, as for Euler angles [45, 45, 0]
if c_dir[2] < 0.000001:
ax.scatter(-cp[0],
-cp[1],
linewidth=0,
c=col,
marker=mk,
s=mksize,
label=lab)
if ann:
ax.annotate(c_dir.view(), (cp[0], cp[1] - 0.1),
xycoords='data',
fontsize=8,
horizontalalignment='center',
verticalalignment='center')
def plot_line_between_crystal_dir(self,
c1,
c2,
ax=None,
steps=11,
col='k'):
"""Plot a curve between two crystal directions.
The curve is actually composed of several straight lines segments to
draw from direction 1 to direction 2.
:param c1: vector describing crystal direction 1
:param c2: vector describing crystal direction 2
:param ax: a reference to a pyplot ax to draw the line
:param int steps: number of straight lines composing the curve
(11 by default)
:param col: line color (black by default)
"""
path = np.zeros((steps, 2), dtype=float)
for j, i in enumerate(np.linspace(0., 1., steps)):
ci = i * c1 + (1 - i) * c2
ci /= np.linalg.norm(ci)
if self.proj == 'stereo':
ci += self.z
ci /= ci[2]
path[j, 0] = ci[0]
path[j, 1] = ci[1]
ax.plot(path[:, 0],
path[:, 1],
color=col,
markersize=self.mksize,
linewidth=2)
def plot_pf_background(self, ax, labels=True):
"""Function to plot the background of the pole figure.
:param ax: a reference to a pyplot ax to draw the backgroud.
:param bool labels: add lables to axes (True by default).
"""
an = np.linspace(0, 2 * np.pi, 100)
ax.plot(np.cos(an), np.sin(an), 'k-')
ax.plot([-1, 1], [0, 0], 'k-')
ax.plot([0, 0], [-1, 1], 'k-')
axe_labels = ['X', 'Y', 'Z']
if self.axis == 'Z':
(h, v, u) = (0, 1, 2)
elif self.axis == 'Y':
(h, v, u) = (0, 2, 1)
else:
(h, v, u) = (1, 2, 0)
if labels:
ax.annotate(axe_labels[h], (1.01, 0.0),
xycoords='data',
fontsize=16,
horizontalalignment='left',
verticalalignment='center')
ax.annotate(axe_labels[v], (0.0, 1.01),
xycoords='data',
fontsize=16,
horizontalalignment='center',
verticalalignment='bottom')
def plot_pf_dir(self, c_dir, **kwargs):
"""Plot a crystal direction in a direct pole figure.
:param c_dir: a vector describing the crystal direction.
:param dict kwargs: a dictionnary of keyword/values to control the
plot, it should at least contain a reference to a pyplot axes
to draw the pole using keyword 'ax'.
"""
if self.axis == 'Z':
(h, v, u) = (0, 1, 2)
elif self.axis == 'Y':
(h, v, u) = (0, 2, 1)
else:
(h, v, u) = (1, 2, 0)
# the direction to plot is given by c_dir[h,v,u]
if self.verbose:
print('corrected for pf axis:', c_dir[[h, v, u]])
self.plot_crystal_dir(c_dir[[h, v, u]], **kwargs)
def plot_pf(self, ax=None, mk='o', ann=False):
"""Create the direct pole figure.
:param ax: a reference to a pyplot ax to draw the poles.
:param mk: marker used to plot the poles (disc by default).
:param bool ann: Annotate the pole with the coordinates of the vector
if True (False by default).
"""
self.plot_pf_background(ax)
kwargs = {'ax': ax, 'mk': mk, 'ann': ann}
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'])
gt = g.transpose()
if self.resize_markers:
kwargs['mksize'] = 0.15 * np.sqrt(
grain['volume'] / volume_max) * 1000
label = ''
if self.map_field == 'grain_id':
label = 'grain ' + str(grain['idnumber'])
kwargs['lab'] = label
for i, hkl_plane in enumerate(self.poles):
if i > 0:
kwargs['lab'] = ''
c = hkl_plane.normal()
c_rot = gt.dot(c)
if self.verbose:
h, k, l = hkl_plane.miller_indices()
print('plotting (%d%d%d) with normal %s in sample CS '
'(corrected for pf axis): %s' % (h, k, l, c, c_rot))
col = self.get_color_from_field(grain)
kwargs['col'] = col
self.plot_pf_dir(c_rot, **kwargs)
ax.axis([-1.1, 1.1, -1.1, 1.1])
if self.pflegend and self.map_field == 'grain_id':
ax.legend(bbox_to_anchor=(0.05, 1),
loc=1,
numpoints=1,
prop={'size': 10})
ax.axis('off')
ax.set_title('{%s} direct %s projection' % (self.family, self.proj))
def create_pf_contour(self, ax=None, ang_step=10):
"""Compute the distribution of orientation and plot it using contouring.
This plot the distribution of orientation in the microstructure
associated with this PoleFigure instance, as a continuous
distribution using angular bining with the specified step.
the distribution is constructed at runtime by discretizing the
angular space and counting the number of poles in each bin.
Then the plot_pf_contour method is called to actually plot the data.
.. warning::
This function has not been tested properly, use at your own risk.
:param ax: a reference to a pyplot ax to draw the contours.
:param int ang_step: angular step in degrees to use for constructing
the orientation distribution data (10 degrees by default)
"""
# discretise the angular space (azimuth and altitude)
ang_step *= np.pi / 180 # change to radians
n_phi = int(1 + 2 * np.pi / ang_step)
n_psi = int(1 + 0.5 * np.pi / ang_step)
phis = np.linspace(0, 2 * np.pi, n_phi)
psis = np.linspace(0, np.pi / 2, n_psi)
xv, yv = np.meshgrid(phis, psis)
values = np.zeros((n_psi, n_phi), dtype=int)
for grain in self.microstructure.grains:
g = Orientation.Rodrigues2OrientationMatrix(grain['orientation'])
gt = g.transpose()
for hkl_plane in self.poles:
c = hkl_plane.normal()
c_rot = gt.dot(c)
# handle poles pointing down
if c_rot[2] < 0:
c_rot *= -1 # make unit vector have z>0
if c_rot[1] >= 0:
phi = np.arccos(c_rot[0] /
np.sqrt(c_rot[0]**2 + c_rot[1]**2))
else:
phi = 2 * np.pi - np.arccos(
c_rot[0] / np.sqrt(c_rot[0]**2 + c_rot[1]**2))
psi = np.arccos(c_rot[2]) # since c_rot is normed
i_phi = int((phi + 0.5 * ang_step) / ang_step) % n_phi
j_psi = int((psi + 0.5 * ang_step) / ang_step) % n_psi
values[j_psi, i_phi] += 1
if self.proj == 'stereo': # double check which one is flat/stereo
x = (2 * yv / np.pi) * np.cos(xv)
y = (2 * yv / np.pi) * np.sin(xv)
else:
x = np.sin(yv) * np.cos(xv)
y = np.sin(yv) * np.sin(xv)
# close the pole figure by duplicating azimuth=0
values[:, -1] = values[:, 0]
self.plot_pf_contour(ax, x, y, values)
def plot_pf_contour(self, ax, x, y, values):
"""Plot the direct pole figure using contours.
.. warning::
This function has not been tested properly, use at your own risk.
"""
self.plot_pf_background(ax)
ax.contourf(x, y, values)
# ax.plot(x, y, 'ko')
ax.axis([-1.1, 1.1, -1.1, 1.1])
ax.axis('off')
ax.set_title('{%s} direct %s projection' % (self.family, self.proj))
def sst_symmetry(self, v):
"""Transform a given vector according to the lattice symmetry associated
with the pole figure.
This function transform a vector so that it lies in the smallest
symmetry equivalent zone.
:param v: the vector to transform.
:return: the transformed vector.
"""
# get the symmetry from the lattice associated with the pole figure
symmetry = self.lattice._symmetry
if symmetry is Symmetry.cubic:
return PoleFigure.sst_symmetry_cubic(v)
elif symmetry is Symmetry.hexagonal:
syms = symmetry.symmetry_operators()
for i in range(syms.shape[0]):
sym = syms[i]
v_sym = np.dot(sym, v)
# look at vectors pointing up
if v_sym[2] < 0:
v_sym *= -1
# now evaluate if projection is in the sst
if v_sym[1] < 0 or v_sym[0] < 0:
continue
elif v_sym[1] / v_sym[0] > np.tan(np.pi / 6):
continue
else:
break
return v_sym
else:
print('unsupported symmetry: %s' % symmetry)
return None
@staticmethod
def sst_symmetry_cubic(z_rot):
"""Transform a given vector according to the cubic symmetry.
This function transform a vector so that it lies in the unit SST triangle.
:param z_rot: vector to transform.
:return: the transformed vector.
"""
if z_rot[0] < 0:
z_rot[0] = -z_rot[0]
if z_rot[1] < 0:
z_rot[1] = -z_rot[1]
if z_rot[2] < 0:
z_rot[2] = -z_rot[2]
if z_rot[2] > z_rot[1]:
z_rot[1], z_rot[2] = z_rot[2], z_rot[1]
if z_rot[1] > z_rot[0]:
z_rot[0], z_rot[1] = z_rot[1], z_rot[0]
if z_rot[2] > z_rot[1]:
z_rot[1], z_rot[2] = z_rot[2], z_rot[1]
return np.array([z_rot[1], z_rot[2], z_rot[0]])
def get_color_from_field(self, grain):
"""Get the color of the given grain according to the chosen field.
This function will return the color associated with the given grain.
Depending on how the pole figure has been configured (see the
`set_map_field` function), it will be obtained from:
* the grain id, according to the `Microstructure.rand_cmap` function
* ipf the colour will reflect the orientation according to the IPF
coloring scheme
* the field value mapped on a pyplot color map if the lut field of
the PoleFigure instance is a string.
* a color directly read from the lut field; in this case the field
value must reflect the category of the given grain.
:param grain: the `Grain` instance.
:return: the color as a 3 element numpy array representing the rgb values.
"""
if self.map_field:
if self.map_field == 'grain_id':
col = Microstructure.rand_cmap().colors[grain['idnumber']]
elif self.map_field == 'ipf':
if self.axis == 'X':
axis = np.array([1., 0., 0.])
elif self.axis == 'Y':
axis = np.array([0., 1., 0.])
else:
axis = np.array([0., 0., 1.])
col = Orientation.from_rodrigues(
grain['orientation']).get_ipf_colour(axis=axis)
else:
# retrieve the position of the grain in the list
rank = self.microstructure.get_grain_ids().tolist().index(
grain['idnumber'])
if type(self.lut) is str:
# get the color map from pyplot
color_map = cm.get_cmap(self.lut, 256)
# use the field value for this grain and the field range bounds
color = int(255 * max(
min((self.field[rank] - self.field_min_level) /
float(self.field_max_level - self.field_min_level),
1.0), 0.0))
col = color_map(np.arange(256))[color]
else:
col = self.lut[
self.field[rank]] # directly access the color
return col
else:
return np.array([0., 0., 0.])
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 plot_ipf(self, **kwargs):
""" Create the inverse pole figure for direction Z.
: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).
"""
ax = kwargs.get('ax')
self.plot_pf_background(ax, labels=False)
# now plot the sample axis
for grain in self.microstructure.grains:
g = Orientation.Rodrigues2OrientationMatrix(grain['orientation'])
if self.axis == 'Z':
axis = self.z
elif self.axis == 'Y':
axis = self.y
else:
axis = self.x
axis_rot = g.dot(axis)
kwargs['col'] = self.get_color_from_field(grain)
self.plot_crystal_dir(axis_rot, **kwargs)
if self.verbose:
print('plotting ', self.axis, ' in crystal CS:', axis_rot)
ax.axis([-1.1, 1.1, -1.1, 1.1])
ax.axis('off')
ax.set_title('%s-axis inverse %s projection' % (self.axis, self.proj))
@staticmethod
def plot(orientations, **kwargs):
"""Plot a pole figure (both direct and inverse) for a list of crystal
orientations.
:param orientations: the list of crystalline
:py:class:`~pymicro.crystal.microstructure.Orientation` to
plot.
"""
micro = Microstructure(autodelete=True)
if isinstance(orientations, list):
for i in range(len(orientations)):
micro.add_grains([o.euler for o in orientations])
elif isinstance(orientations, Orientation):
micro.add_grains([orientations.euler])
else:
print('Unrecognized argument: %s' % orientations.__repr__)
pf = PoleFigure(microstructure=micro, **kwargs)
pf.plot_pole_figures(display=True)
@staticmethod
def plot_euler(phi1, Phi, phi2, **kwargs):
"""Directly plot a pole figure for a single orientation given its
three Euler angles.
::
PoleFigure.plot_euler(10, 20, 30)
:param float phi1: first Euler angle (in degree).
:param float Phi: second Euler angle (in degree).
:param float phi2: third Euler angle (in degree).
"""
PoleFigure.plot(Orientation.from_euler(np.array([phi1, Phi, phi2])),
**kwargs)