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 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
def enclose_polyhedron(number_planes, planes, volume=0.0):
''' uses multiple planes to enclose a polyhedron, and calculates the
polyhedron's geometric parameters.
number_planes:
number of planes of each subset. [list of integers]
planes:
planes of all subsets. Its length equals the sum of 'number_planes'.
[list of Plane3D]
volume:
a given volume to scale the calculated volume to this value.
If it is zero, the unscaled volume is used.
returns: [q, fractional_area, vertices, scale].
Note:
1. This function handles one volume at a time. For multiple volumes at
constant height-ratios, eg. for plotting q-d curves, use
enclose_polyhedron_multivol(), which is faster.
'''
planes_c = [p.as_list() for p in planes]
pr = enclosure(planes_c) # call enclosure() which is implemented in 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 of each plane family: sum of areas of surfaces of a plane family
area_ps = []
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
area_ps = np.array(area_ps) # convert a list to a numpy.ndarray
# total surface area
area_sum = np.sum(area_ps)
# weight of each surface family
f_ps = area_ps / area_sum # array operation: all elements are devided.
# surface-area-to-volume ratio
q = area_sum / volume_calc
# scale the surface areas, point coordinates according to volume
if volume!=0.0:
r = np.power(volume / volume_calc, 1.0/3)
# correct q, f_ps, points_p, (optionally, areal_ps, area_sum)
q = q / r
# f_ps remains the same
for p in points_p:
# p is a list of points on one plane
for xyz in p:
xyz[0] = xyz[0]*r
xyz[1] = xyz[1]*r
xyz[2] = xyz[2]*r
# area_ps = area_ps * (r*r) # array operation: all elements are scaled.
# area_sum = area_sum * (r*r)
return (q, f_ps, points_p, volume)
else:
# r=1.0 # volume is the natural volume_calc.
return (q, f_ps, points_p, volume_calc)