def plot_network(vertices, poly, L, file):
plt.cla()
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
# for x,y in vertices:
# ax.scatter(x, y, c="m", marker=".", s=100)
for poly in poly:
indices = poly.indices
for i, index in enumerate(indices):
x1, y1 = vertices[index]
if i == len(indices) - 1:
x2, y2 = vertices[indices[0]]
else:
x2, y2 = vertices[indices[i + 1]]
v1 = np.array((x1, y1))
v2 = np.array((x2, y2))
v2 = v1 + periodic_diff(v2, v1, L)
x2, y2 = v2
ax.plot([x1, x2], [y1, y2], c="c")
v2 = np.array((x2, y2))
v1 = v2 + periodic_diff(v1, v2, L)
x1, y1 = v1
ax.plot([x1, x2], [y1, y2], c="c")
# # plot centers
x, y = poly.get_center(vertices, L)
if x <= 0:
x = x + L[0]
if x >= L[0]:
x = x - L[0]
if y <= 0:
y = y + L[1]
if y >= L[1]:
y = y - L[1]
plt.scatter(x, y, color="c", marker=".")
# remove axis ticks
ax.axes.get_xaxis().set_ticks([])
ax.axes.get_yaxis().set_ticks([])
ax.axis([0, L[0], 0, L[1]])
plt.savefig(file)
plt.close(fig)
return
def T1_transition(vertices, polys, edges, parameters):
lx = parameters['lx']
ly = parameters['ly']
L = np.array([lx, ly])
lmin = parameters['lmin']
reverse = []
for edge in edges:
i1 = edge[0]
i2 = edge[1]
v1 = vertices[i1]
vertex2 = vertices[i2]
v2 = v1 + periodic_diff(vertex2, v1, L)
dist = euclidean_distance(v1[0], v1[1], v2[0], v2[1])
if dist < lmin and (i1, i2) not in reverse:
print "T1", i1, i2, dist
poly_ids = get_4_polys(polys, i1, i2)
if -1 in poly_ids:
pass
else:
# find minimum configuration
reverse.append((i2, i1))
# 6 indices for vertices involved in transition
indices = get_6_indices(polys, i1, i2, poly_ids)
# original configuration
polys_0, edges_0 = T1_0(polys, i1, i2, poly_ids, indices)
E0 = get_energy(vertices, polys_0, edges_0, parameters)
# left T1 transition
polys_l, edges_l = T1_left(polys, i1, i2, poly_ids, indices)
E_left = get_energy(vertices, polys_l, edges_l, parameters)
# # right T1 transition
polys_r, edges_r = T1_right(polys, i1, i2, poly_ids, indices)
E_right = get_energy(vertices, polys_r, edges_r, parameters)
# get minimum
min_energy = np.min((E0, E_left, E_right))
min_i = np.argmin((E0, E_left, E_right))
print min_i
# # do nothing - same configuration
if min_i == 0:
pass
if min_i == 1:
set_T1_left(polys, polys_l, poly_ids, edges, indices)
if min_i == 2:
set_T1_right(polys, polys_r, poly_ids, edges, indices)
return polys, edges
def T1_transition(vertices, polys, edges, parameters): lx = parameters['lx'] ly = parameters['ly'] L = np.array([lx,ly]) lmin = parameters['lmin'] for edge in edges: i1 = edge[0] i2 = edge[1] v1 = vertices[i1] vertex2 = vertices[i2] v2 = v1 + periodic_diff(vertex2, v1, L) dist = euclidean_distance(v1[0], v1[1], v2[0], v2[1]) if dist < lmin: # print "T1", i1, i2, dist poly_ids = get_4_polys(polys, i1, i2) if -1 in poly_ids: pass else: # find minimum configuration # 6 indices for vertices involved in transition indices = get_6_indices(polys, i1, i2, poly_ids) # original configuration polys_0, edges_0 = T1_0(polys, i1, i2, poly_ids, indices) E0 = get_energy(vertices, polys_0, edges_0, parameters) # left T1 transition polys_l, edges_l = T1_left(polys, i1, i2, poly_ids, indices) E_left = get_energy(vertices, polys_l, edges_l, parameters) # # right T1 transition polys_r, edges_r = T1_right(polys, i1, i2, poly_ids, indices) E_right = get_energy(vertices, polys_r, edges_r, parameters) # get minimum min_energy = np.min((E0, E_left, E_right)) min_i = np.argmin((E0, E_left, E_right)) # # do nothing - same configuration if min_i == 0: pass if min_i == 1: set_T1_left(polys, polys_l, poly_ids, edges, indices) if min_i == 2: set_T1_right(polys, polys_r, poly_ids, edges, indices) return polys, edges
def E_adhesion(vertices, edges, Lambda, L):
e = 0.
for edge in edges:
i1 = edge[0]
i2 = edge[1]
v1 = vertices[i1]
vertex2 = vertices[i2]
v2 = v1 + periodic_diff(vertex2, v1, L)
dist = euclidean_distance(v1[0], v1[1], v2[0], v2[1])
e += Lambda * dist
return e
def E_adhesion(vertices, edges, Lambda , L): e = 0. for edge in edges: i1 = edge[0] i2 = edge[1] v1 = vertices[i1] vertex2 = vertices[i2] v2 = v1 + periodic_diff(vertex2, v1, L) dist = euclidean_distance(v1[0], v1[1], v2[0], v2[1]) e += Lambda * dist return e
def plot_network(vertices, polys, L, file):
plt.cla()
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
for x, y in vertices:
ax.scatter(x, y, c="m", marker=".", s=50)
for poly in polys:
indices = poly.indices
for i, index in enumerate(indices):
x1, y1 = vertices[index]
if i == len(indices) - 1:
x2, y2 = vertices[indices[0]]
else:
x2, y2 = vertices[indices[i + 1]]
v1 = np.array((x1, y1))
v2 = np.array((x2, y2))
v2 = v1 + periodic_diff(v2, v1, L)
x2, y2 = v2
ax.plot([x1, x2], [y1, y2], c="c")
v2 = np.array((x2, y2))
v1 = v2 + periodic_diff(v1, v2, L)
x1, y1 = v1
ax.plot([x1, x2], [y1, y2], c="c")
# # plot centers
# x,y = poly.get_center(vertices, L)
# plt.scatter(x,y,color="m", marker="*")
# remove axis ticks
ax.axes.get_xaxis().set_ticks([])
ax.axes.get_yaxis().set_ticks([])
ax.axis([0, L[0], 0, L[1]])
plt.savefig(file)
plt.close(fig)
return
def plot_edges(vertices, edges, L):
plt.cla()
for vertex in vertices:
x = vertex[0]
y = vertex[1]
plt.scatter(x, y, c="c")
for edge in edges:
i1 = edge[0]
i2 = edge[1]
x1, y1 = vertices[i1]
x2, y2 = vertices[i2]
v1 = np.array((x1, y1))
v2 = np.array((x2, y2))
v2 = v1 + periodic_diff(v2, v1, L)
x2, y2 = v2
plt.plot([x1, x2], [y1, y2], c="k")
plt.axis([0, L[0], 0, L[1]])
plt.show()
return
def plot_edges(vertices, edges, L):
plt.cla()
for vertex in vertices:
x = vertex[0]
y = vertex[1]
plt.scatter(x, y, c="c")
for edge in edges:
i1 = edge[0]
i2 = edge[1]
x1, y1 = vertices[i1]
x2, y2 = vertices[i2]
v1 = np.array((x1, y1))
v2 = np.array((x2, y2))
v2 = v1 + periodic_diff(v2, v1, L)
x2, y2 = v2
plt.plot([x1, x2], [y1, y2], c="k")
plt.axis([0, L[0], 0, L[1]])
plt.show()
return
