def surface_areas(d):
'''
input:
origin-to-planes distances.
volume_calc: the natural or unscaled volume of the polyhedron.
area_p: areas of all the planes.
points_p: interception points on the planes, grouped by plane.
return:
area_ps: the area of each plane family (sum of areas of surfaces of a plane family).
'''
global Gamma_ratio
ps_setd_mingled(number_planes, planes, d)
planes_c = [p.as_list() for p in planes]
pr = enclosure(planes_c)
volume_calc = pr[0] # the natural or unscaled volume of the polyhedron.
area_p = pr[1] # areas of all the planes.
points_p = pr[2] # interception points on the planes, grouped by plane.
area_ps = [
] # area of each plane family: sum of areas of surfaces of a plane family.
index_start = 0
for subset_n in number_planes:
index_end = index_start + subset_n
area_ps.append(np.sum(area_p[index_start:index_end]))
index_start = index_end
global volume
diameter = 20.0
volume = 4.0 / 3.0 * np.pi * (
diameter *
0.5)**3 # this volume was used to scale the calculated volume.
area_ps = np.array(area_ps) * np.power(volume / volume_calc, 2.0 / 3)
return area_ps
def intersection_point(number_planes, planes, d):
'''
Calculate the intersection points of surfaces of a plane family.
'''
ps_setd_mingled(number_planes, planes, d)
planes_c = [p.as_list() for p in planes]
pr = enclosure(planes_c)
points_p = pr[2]
return points_p
def main():
print ''
print '1. Format of surface families should be [[a1, b1, c1], [a2, b2, c2],...,[an, bn, cn]], n >= 1.'
print '2. Distance between the center of the polyhedron and the surface should be positive.'
print '3. Color (r, g, b) is represented by the number from 0 to 1.'
print ''
hkl = surface_index() # surface family
print ''
surf_dist = surface_distance(hkl) # distance
print ''
surf_color = surface_color(hkl) # surface color
print 'surface_color', surf_color
print ''
planes, number_planes = crystal_plane(hkl)
ps_setd_mingled(number_planes, planes, surf_dist)
diameter = 20.0
volume = 4.0 / 3.0 * np.pi * (diameter * 0.5)**3
qfp = enclose_polyhedron(number_planes, planes, volume)
p1 = tvtk.PolyData()
n_planes = len(qfp[2])
for i in np.arange(len(number_planes)):
for surf_index in np.arange(sum(number_planes[0:i]),
sum(number_planes[0:i + 1])):
print 'surf_index', surf_index
p1.points = qfp[2][
surf_index] # the coordinates of the intersection of each plane.
faces = crystal_surface(qfp[2][surf_index])
cells = tvtk.CellArray(
) # create a new CellArray object to assign the polys property.
cells.set_cells(
1, faces
) # the first parameter is the number of faces (here is 1),
p1.polys = cells # and the second parameter is an array describing the composition of each face.
p1.point_data.scalars = np.linspace(0.0, 1.0, len(p1.points))
mlab.figure(number_planes, fgcolor=(0, 0, 0), bgcolor=(1, 1, 1))
mlab.pipeline.surface(p1,
representation='surface',
opacity=1.0,
color=surf_color[i])
axe = tvtk.AxesActor(total_length=(3, 3, 3))
mlab.show()
def surface_areas(d):
'''
input:
origin-to-planes distances.
volume_calc: the natural or unscaled volume of the polyhedron.
area_p: areas of all the planes.
points_p: interception points on the planes, grouped by plane.
return:
area_ps: the area of each plane family (sum of areas of surfaces of a plane family).
'''
ps_setd_mingled(number_planes, planes, d)
planes_c = [p.as_list() for p in planes]
pr = enclosure(planes_c)
volume_calc = pr[0] # the natural or unscaled volume of the polyhedron.
area_p = pr[1] # areas of all the planes.
points_p = pr[2] # interception points on the planes, grouped by plane.
# print points_p
area_ps = [
] # area of each plane family: sum of areas of surfaces of a plane family.
index_start = 0
for subset_n in number_planes:
index_end = index_start + subset_n
area_ps.append(np.sum(area_p[index_start:index_end]))
index_start = index_end
# diameter = 1.0e-9
# volume = 4.0/3.0*np.pi* (diameter*0.5)**3 # this volume was used to scale the calculated volume.
area_ps = np.array(area_ps) * np.power(volume / volume_calc, 2.0 / 3)
Vn, En, vl = vertices_number(number_planes, planes, d)
edge_sort = edge_length_sort(number_planes, planes, d, vl)
edge_length_f, edge_length_o = edge_length_fraction(
edge_sort, volume, volume_calc)
return area_ps, edge_length_f, edge_length_o
if len(hkl) == 2:
planes, number_planes = crystal_plane(hkl)
area_target = [0.8, 0.2] # the sum of the area fractions is 1.
Iter_max = 5000
re_xtol = 1e-12
abs_ftol = 1e-12
d0 = [1, 1]
dx = 0.0001
res = optimal_distance_local(Iter_max, re_xtol, abs_ftol, d0, dx)
areas = surface_areas(res[0])
areas_fraction = [
areas[0] / (areas[0] + areas[1]), areas[1] / (areas[0] + areas[1])
]
print 'The optimal distance d is', res[0], ', area is ', areas, '.'
print 'The area fraction is ', areas_fraction, ', target area fraction is', area_target, '.'
ps_setd_mingled(number_planes, planes,
res[0]) # set distances of planes.
if len(hkl) == 1:
planes, number_planes = crystal_plane(hkl)
ps_setd_mingled(number_planes, planes, [2]) # set distances of planes.
qfp = enclose_polyhedron(number_planes, planes, volume)
n_qfp2, qfp2_list = array_to_list(qfp[2])
point_for_plane = open('point_for_plane.txt', 'w+') # open the file
point_for_plane.truncate() # empty the file
np.savetxt('point_for_plane.txt', qfp2_list)
number_of_plane = open('number_of_plane.txt', 'w+')
number_of_plane.truncate()
np.savetxt('number_of_plane.txt', n_qfp2)