def test_is_group(self):
for grp in groups:
print(grp)
ops = crystallography.symmetry_rotations(grp)
self.assertTrue(self.includes_identity(ops))
self.assertTrue(self.closed(ops))
self.assertTrue(self.has_inverse(ops))
def project_ipf(q, lattice, direction,
sample_symmetry = crystallography.symmetry_rotations("222"),
x = [1,0,0], y = [0,1,0]):
"""
Project a single sample direction onto a crystal
Parameters:
q: lattice orientation
lattice: lattice object describing the crystal system
direction: sample direction
Keyword Args:
sample_symmetry: sample symmetry operators
x: x direction (crystallographic) of the projection
y: y direction (crystallographic) of the projection
"""
xv = lattice.miller2cart_direction(x).normalize()
yv = lattice.miller2cart_direction(y).normalize()
if not np.isclose(xv.dot(yv),0.0):
raise ValueError("Lattice directions are not orthogonal!")
zv = xv.cross(yv)
trans = rotations.Orientation(np.vstack((xv.data,yv.data,zv.data)))
d = tensors.Vector(direction).normalize()
pts = []
for srot in sample_symmetry:
# Sample directions
spt = srot.apply(d)
# Crystal coordinates
cpt = q.apply(spt)
# Lattice symmetry
for op in lattice.symmetry.ops:
cppt = op.apply(cpt)
# Into the right coordinates
fpt = trans.apply(cppt)
pts.append(fpt.data)
# By convention just keep the points in the upper hemisphere
pts = np.array(pts)
pts = pts[pts[:,2]>0]
return pts
def test_definition(self):
for grp in groups:
print(grp)
self.compare(ktw_rotational_groups(grp),
crystallography.symmetry_rotations(grp))
def pole_figure_discrete(orientations, pole, lattice,
projection = "stereographic",
sample_symmetry = crystallography.symmetry_rotations("222"),
x = tensors.Vector([1.0,0,0]), y = tensors.Vector([0,1.0,0]),
axis_labels = ["X", "Y"]):
"""
Plot a standard pole figure given a collection of discrete points.
Parameters:
orientations: list of orientations
pole: pole as a integer list
lattice: crystal lattice class, including crystal symmetry
Keyword Args:
projection: which projection to use
sample_symmetry: what sample symmetry to apply to the pole figure,
defaults to orthorhombic
x: x direction for plot, defaults to [1,0,0]
y: y direction for plot, defaults to [0,1,0]
axis_labels: axis labels to include on the figure
"""
# Get the rotation from the standard coordinates to the given x and y
srot = rotations.Orientation(x,y)
# Get all equivalent poles
p = lattice.miller2cart_direction(pole)
eq_poles = lattice.equivalent_vectors(p)
eq_poles = [pp.normalize() for pp in eq_poles]
# Apply sample symmetric
eq_poles = [op.apply(p) for p in eq_poles for op in sample_symmetry]
# Get the points on the sphere
pts = [srot.apply(o.inverse().apply(pp)) for pp in eq_poles for o in orientations]
# Get rid of those that are in the lower hemisphere
pts = [p for p in pts if p[2] > 0.0]
# Project
if projection == "stereographic":
pop = project_stereographic
lim = limit_stereographic
elif projection == "lambert":
pop = project_lambert_equal_area
lim = limit_lambert_equal_area
else:
raise ValueError("Unknown projection %s" % projection)
cart = np.array([pop(v) for v in pts])
# Convert to polar
polar = np.array([cart2pol(cp) for cp in cart])
# Plot
ax = plt.subplot(111, projection='polar')
ax.scatter(polar[:,0], polar[:,1], c='k', s=10.0)
# Make the graph nice
plt.ylim([0,lim])
ax.grid(False)
ax.get_yaxis().set_visible(False)
if len(axis_labels) == 2:
plt.xticks([0,np.pi/2], axis_labels)
else:
ax.get_xaxis().set_visible(False)
ax.xaxis.set_minor_locator(plt.NullLocator())
def inverse_pole_figure_discrete(orientations, direction, lattice,
reduce_figure = False, color = False,
sample_symmetry = crystallography.symmetry_rotations("222"),
x = [1,0,0], y = [0,1,0], axis_labels = None, nline = 100):
"""
Plot an inverse pole figure given a collection of discrete points.
Parameters:
orientations: list of orientations
direction: sample direction
lattice: crystal lattice class, including crystal symmetry
Keyword Args:
reduce_figure: reduce to some fundamental region.
Options include
False -- don't do it
"cubic" -- cubic convention
[v1,v2,v3] -- list of crystallographic points defining the triangle
color: color points based on the provided triangle
sample_symmetry: what sample symmetry to apply to the pole figure,
defaults to orthorhombic
x: crystallographic x direction for plot, defaults to [1,0,0]
y: crystallographic y direction for plot, defaults to [0,1,0]
axis_labels: axis labels to include on the figure
nline: number of discrete points to use in plotting lines on the triangle
"""
pts = np.vstack(tuple(project_ipf(q, lattice, direction,
sample_symmetry = sample_symmetry, x = x, y = y) for q in orientations))
if reduce_figure:
if reduce_figure == "cubic":
vs = (np.array([0,0,1.0]), np.array([1.0,0,1]), np.array([1.0,1,1]))
elif len(reduce_figure) == 3:
vs = reduce_figure
else:
raise ValueError("Unknown reduction type %s!" % reduce_figure)
pts = reduce_points_triangle(pts, v0 = vs[0], v1=vs[1], v2=vs[2])
pop = project_stereographic
lim = limit_stereographic
cpoints = np.array([pop(v) for v in pts])
# Make the graph nice
if reduce_figure:
ax = plt.subplot(111)
if color:
rgb = ipf_color(pts, v0 = vs[0], v1 = vs[1], v2=vs[2])
ax.scatter(cpoints[:,0], cpoints[:,1], c=rgb, s = 10.0)
else:
ax.scatter(cpoints[:,0], cpoints[:,1], c='k', s = 10.0)
ax.axis('off')
if axis_labels:
plt.text(0.1,0.11,axis_labels[0], transform = plt.gcf().transFigure)
plt.text(0.86,0.11,axis_labels[1], transform = plt.gcf().transFigure)
plt.text(0.74,0.88,axis_labels[2], transform = plt.gcf().transFigure)
for i,j in ((0,1),(1,2),(2,0)):
v1 = vs[i]
v2 = vs[j]
fs = np.linspace(0,1,nline)
pts = np.array([pop((f*v1+(1-f)*v2)/la.norm(f*v1+(1-f)*v2)) for f in fs])
plt.plot(pts[:,0], pts[:,1], color = 'k')
else:
polar = np.array([cart2pol(v) for v in cpoints])
ax = plt.subplot(111, projection='polar')
ax.scatter(polar[:,0], polar[:,1], c='k', s=10.0)
plt.ylim([0,lim])
ax.grid(False)
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
ax.xaxis.set_minor_locator(plt.NullLocator())