def cp04(L_x = 4, L_y = 4, n_x = 2, n_y = 4, n_steps = 100):
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
show_iter = False,
MAX_ITER = 500)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
z_nodes = n_h[(0, -1), :].flatten()
z_cnstr = [[(n, 2, 1.0)] for n in z_nodes]
y_links = []
for n_arr in n_h.T:
for n in n_arr[1:]:
y_links.append([(n_arr[0], 1, 1.0), (n, 1, -1.0)])
x_cnstr = [[(n_h[0, 0], 0, 1.0)]]
y_cnstr = [[(n_h[0, -1], 1, 1.0)],
[(n_h[0, 0], 1, 1.0)]]
cp.cnstr_lhs = z_cnstr + y_links + x_cnstr + y_cnstr
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype = float)
cp.cnstr_rhs[-1] = 3.9
return cp
def create_cp_fc_inclined(L_x=4, L_y=4, n_x=2, n_y=4, n_steps=100):
"""Create scalable rhombus crease pattern with face constraints
"""
cp = RhombusCreasePattern(n_steps=n_steps, L_x=L_x, L_y=L_y, n_x=n_x, n_y=n_y, show_iter=False, MAX_ITER=50)
n_h = cp.n_h
n_v = cp.n_v
n_i = cp.n_i
y_links = []
# n_h0 = n_h[(0, -1), :-1]
# n_h1 = n_h[(0, -1), 1:]
# for nv, nh0, nh1 in zip(n_v.T, n_h0.T, n_h1.T):
# for v, h0, h1 in zip(nv, nh0, nh1):
# print 'constraining', h0, h1
# y_links.append([(h0, 1, 1.0), (h1, 1, -1.0)])
n_h0 = n_h[(0, -1), :-1]
n_h1 = n_h[(0, -1), 1:]
for nv in n_v.T:
print "adding constraint", nv
y_links.append([(nv[0], 0, 1.0), (nv[1], 0, 1.0)])
# here was a conflict @todo - resolve with Jan
# for nv, nh0, nh1 in zip(n_v.T, n_h0.T, n_h1.T):
# for v, h0, h1 in zip(nv, nh0, nh1):
# y_links.append([(v, 1, 1.0), (h1, 1, -0.5)])
cp.cnstr_lhs = y_links
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype=float)
print "cnstr_lhs", cp.cnstr_lhs
print "cnstr_rhs", cp.cnstr_rhs
# A = L_x * 0.2
A = 0.2
# face_z_t = FF(Rf = z_ - 4 * A * t_ / L_x * x_ * (1 - x_ / L_x))
face_z_t = FF(Rf=z_ - 4 * A * t_ * x_ * (1 - x_ / L_x))
face_x_L2 = FF(Rf=x_ - L_x / 2)
face_y_L2 = FF(Rf=y_ - L_y / 2)
# face_y_Ly = FF(Rf = y_ - L_y)
# old
n_h_idx = n_x / 2
z_nodes = n_h[:, :].flatten()
# y_nodes = n_i[:, 0] # + list(n_v[:, :].flatten())
y_nodes = n_i[0, 0] # + list(n_v[:, :].flatten())
cp.cnstr_lst = [
(face_y_L2, [n_i[0, 0]]),
(face_z_t, z_nodes),
## (face_x_L2, n_h[2, (0, -1)].flatten()),
# (face_x_L2, n_h[n_h_idx, (0, -1)].flatten()),
(face_x_L2, n_h[n_h_idx, :].flatten()),
]
return cp
def cp01(L_x = 4, L_y = 2, n_x = 2, n_y = 2, n_steps = 80):
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
z0_ratio = 0.01,
show_iter = False,
MAX_ITER = 500)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
cp.cnstr_lhs = [[(n_h[0, 0], 2, 1.0)], # 0
[(n_h[0, -1], 2, 1.0)], # 1
[(n_h[-1, 0], 2, 1.0)], # 2
[(n_h[-1, -1], 2, 1.0)], # 3
[(n_h[1, 0], 2, 1.0)], # 4
[(n_h[0, 0], 1, 1.0), (n_h[1, 0], 1, -1.0)], # 5
[(n_h[0, 0], 1, 1.0), (n_h[-1, 0], 1, -1.0)], # 6
[(n_h[0, -1], 1, 1.0), (n_h[1, -1], 1, -1.0)], # 7
[(n_h[0, -1], 1, 1.0), (n_h[-1, -1], 1, -1.0)], # 8
[(n_h[1, 0], 0, 1.0)], # 9
[(n_h[0, -1], 1, 1.0)], # 10
]
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((14,), dtype = float)
cp.cnstr_rhs[4] = 1.999999999
return cp
def create_cp_fc(L_x = 4, L_y = 4, n_x = 1, n_y = 2,
n_steps = 100):
'''Create scalable rhombus crease pattern with face constraints
'''
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
show_iter = False,
MAX_ITER = 500)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
n_h_idx = n_y / 4
x_links = []
y_links = []
z_links = []
# for n_arr in n_h[:, (-1,)].T:
# for idx, n in enumerate(n_arr[1:]):
# y_links.append([(n_arr[0], 1, 1.0), (n, 1, -1.0)])
for n in n_v[-1, 1:]:
x_links.append([(n_v[-1, 0], 0, 1.0), (n, 0, -1.0)])
for n0, n1 in zip(n_v[0, :], n_v[-1, :]):
z_links.append([(n0, 2, 1.0), (n1, 2, -1.0)])
#cntrl = [[(n_h[-1, -1], 1, 1.0)]]
#cntrl = [[(n_h[-1, 1], 0, 1.0)]]
cp.cnstr_lhs = x_links + y_links + z_links # + cntrl
#cp.cnstr_lhs = z_cnstr
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype = float)
#cp.cnstr_rhs[-1] = -L_x * 0.34
face_z_0 = FF(Rf = z_ - 0)
face_x_0 = FF(Rf = x_ - 0)
face_x_L = FF(Rf = x_ - L_x * (1 - 0.2 * t_))
face_y_0 = FF(Rf = y_ - 0)
face_y_L = FF(Rf = y_ - L_y * (1 - 0.1 * t_))#* x_ / L_x))
cp.cnstr_lst = [(face_x_0, n_h[0, :]), # [n_h[0, 0], n_h[0, -1]]),
(face_z_0, n_h[0, :]), # [n_h[0, 0], n_h[0, -1]]),
(face_y_0, n_h[:, 0]),
# (face_x_L, []),
(face_y_L, n_h[:, -1])]
# cp.cnstr_rhs[-1] = -L_y * 0.9999
return cp
def create_cp_fc_02(L_x=4, L_y=4, n_x=2, n_y=2, z0_ratio=0.1, n_steps=100):
"""Create scalable rhombus crease pattern with face constraints
One basic element with general formulation (extension in y-direction variabel)
(extension in x-direction has to be adepted manually)
"""
cp = RhombusCreasePattern(
n_steps=n_steps, L_x=L_x, L_y=L_y, n_x=n_x, n_y=n_y, show_iter=False, z0_ratio=z0_ratio, MAX_ITER=50
)
n_h = cp.n_h
n_v = cp.n_v
n_i = cp.n_i
n_h_idx = n_x / 2
n_h_idx = n_x / 2
y_links = []
for n_arr in n_h[0:3, :].T:
for idx, n in enumerate(n_arr[1:]):
n_x = len(n_arr)
y_links.append([(n_arr[0], 1, 1.0), (n, 1, -1.0)])
"""
Extension in x-direction
"""
# y_links.append([(n_h[0,0], 1, 1.0), (n_h[-1,0], 1, -1.0)])
# y_links.append([(n_h[0,0], 1, 1.0), (n_h[-2,0], 1, -1.0)])
y_links.append([(n_h[0, -1], 1, 1.0)])
y_links.append([(n_h[1, 0], 0, 1.0)])
cp.cnstr_lhs = y_links
print "n_h[1, 0]", n_h[1, 0]
print "n_h[-1,-1]", n_h[-1, 0]
print "n_h[1, -1]", n_h[1, -1]
print "n_h[-1,-1]", n_h[-1, -1]
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype=float)
print "cnstr_lhs", cp.cnstr_lhs
print "cnstr_rhs", cp.cnstr_rhs
A = 0.2
face_z_t = FF(Rf=z_ - 4 * A * t_ * x_ * (1 - x_ / L_x))
cp.cnstr_lst = [(face_z_t, n_h[1:-1, 0]), (face_z_t, n_h[0, :]), (face_z_t, n_h[-1, :])]
print "edge1", n_h[0, :]
print "edge2", n_h[-1, :]
print "center", n_h[1:-1, 0]
return cp
def cp05(L_x = 4, L_y = 4, n_x = 2, n_y = 4,
n_steps = 100, skew_coeff = 0.0):
'''Exploit symmetric constraints
'''
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
show_iter = False,
MAX_ITER = 500)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
z_nodes = n_h[(0, -1), :].flatten()
z_cnstr = [[(n, 2, 1.0)] for n in z_nodes]
y_links = []
for n_arr in n_h[:, (0, -1)].T:
for idx, n in enumerate(n_arr[1:]):
n_x = len(n_arr)
coeff = skew_coeff * float(idx + 1) / float(n_x)
y_links.append([(n_arr[0], 1, 1.0 - coeff), (n, 1, -1.0)])
for n_arr in n_h[:, 1:-1].T:
y_links.append([(n_arr[0], 1, 1.0), (n_arr[-1], 1, -1.0)])
x_links = []
z_links = []
# for n0, n1 in zip(n_h[1:-1, 0], n_h[1:-1, -1]):
# x_links.append([(n0, 0, 1.0), (n1, 0, 1.0)])
# z_links.append([(n0, 2, 1.0), (n1, 2, -1.0)])
for n in n_v[0, 1:]:
z_links.append([(n_v[0, 0], 2, 1.0), (n, 2, -1.0)])
n_h_idx = n_y / 4
x_cnstr = [[(n_h[0, n_h_idx], 0, 1.0)]]
y_cnstr = [[(n_h[0, n_h_idx], 1, 1.0)]]
cntrl = [[(n_h[-1, n_h_idx], 0, 1.0)]]
#cntrl = [[(n_h[-1, 0], 1, 1.0)]]
cp.cnstr_lhs = z_cnstr + x_links + y_links + z_links + x_cnstr + y_cnstr + cntrl
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype = float)
cp.cnstr_rhs[-1] = -L_x * 0.1
return cp
def create_cp_fc_03(L_x=4, L_y=4, n_x=2, n_y=2, z0_ratio=0.1, n_steps=100):
"""Create scalable rhombus crease pattern with face constraints
other constraints chosen (more in field in z-direction)
"""
cp = RhombusCreasePattern(
n_steps=n_steps, L_x=L_x, L_y=L_y, n_x=n_x, n_y=n_y, show_iter=False, z0_ratio=z0_ratio, MAX_ITER=50
)
n_h = cp.n_h
n_v = cp.n_v
n_i = cp.n_i
y_links = []
n_h_idx = (n_x + 1) / 2
print "n_h_idx", n_h_idx
for idx, n in enumerate(n_h[1:, 0]):
y_links.append([(n_h[0, 0], 1, 1.0), (n, 1, -1.0)])
for idx, n in enumerate(n_h[1:-1, -1]):
y_links.append([(n_h[0, -1], 1, 1.0), (n, 1, -1.0)])
for idx, n in enumerate(n_h[n_h_idx, 1:]):
y_links.append([(n, 0, 1.0)])
y_links.append([(n_h[0, -1], 1, 1.0)])
cp.cnstr_lhs = y_links
print "n_h[1, 0]", n_h[1, 0]
print "n_h[-1,-1]", n_h[-1, 0]
print "n_h[1, -1]", n_h[1, -1]
print "n_h[-1,-1]", n_h[-1, -1]
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype=float)
print "cnstr_lhs", cp.cnstr_lhs
print "cnstr_rhs", cp.cnstr_rhs
A = 0.2
face_z_t = FF(Rf=z_ - 4 * A * t_ * x_ * (1 - x_ / L_x))
# face_x_L2 = FF(Rf = x_ - L_x / 2)
n_arr = np.hstack([n_h[n_h_idx, :].flatten(), n_h[0, :].flatten(), n_h[-1, :].flatten()])
cp.cnstr_lst = [(face_z_t, n_arr)]
print "edge1", n_h[0, :]
print "edge2", n_h[-1, :]
print "center", n_h[1:-1, :]
return cp
def create_cp_fc_01(L_x=4, L_y=4, n_x=2, n_y=2, z0_ratio=0.1, n_steps=100):
"""Create scalable rhombus crease pattern with face constraints
One basic element with no general formulation
"""
cp = RhombusCreasePattern(
n_steps=n_steps, L_x=L_x, L_y=L_y, n_x=n_x, n_y=n_y, show_iter=False, z0_ratio=z0_ratio, MAX_ITER=50
)
n_h = cp.n_h
n_v = cp.n_v
n_i = cp.n_i
cp.cnstr_lhs = [
[(n_h[0, 0], 1, 1.0), (n_h[1, 0], 1, -1.0)], # 1
[(n_h[0, 0], 1, 1.0), (n_h[-1, 0], 1, -1.0)], # 2
[(n_h[0, -1], 1, 1.0), (n_h[1, -1], 1, -1.0)], # 3
[(n_h[0, -1], 1, 1.0), (n_h[-1, -1], 1, -1.0)], # 4
[(n_h[0, -1], 1, 1.0)],
[(n_h[1, 0], 0, 1.0)],
]
print "n_h[1, 0]", n_h[1, 0]
print "n_h[-1,-1]", n_h[-1, 0]
print "n_h[1, -1]", n_h[1, -1]
print "n_h[-1,-1]", n_h[-1, -1]
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype=float)
print "cnstr_lhs", cp.cnstr_lhs
print "cnstr_rhs", cp.cnstr_rhs
A = 0.2
face_z_t = FF(Rf=z_ - 4 * A * t_ * x_ * (1 - x_ / L_x))
face_x_L2 = FF(Rf=x_ - L_x / 2)
cp.cnstr_lst = [(face_z_t, n_h[0, :]), (face_z_t, n_h[-1, :]), (face_z_t, [n_h[1, 0]])]
print "edge1", n_h[0, :]
print "edge2", n_h[-1, :]
return cp
def cp03(L_x = 4, L_y = 4, n_x = 2, n_y = 4, n_steps = 80):
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
show_iter = False,
MAX_ITER = 500)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
cp.cnstr_lhs = [[(n_h[0, 0], 2, 1.0)], # 0
[(n_h[0, -1], 2, 1.0)], # 1
[(n_h[-1, 0], 2, 1.0)], # 2
[(n_h[-1, -1], 2, 1.0)], # 3
[(n_h[0, 1], 2, 1.0)], # 4
[(n_h[-1, 1], 2, 1.0)], # 5
[(n_h[0, 0], 1, 1.0)], # 6
[(n_h[0, 0], 1, 1.0), (n_h[1, 0], 1, -1.0)], # 7
[(n_h[0, 0], 1, 1.0), (n_h[-1, 0], 1, -1.0)], # 8
[(n_h[0, -1], 1, 1.0), (n_h[1, -1], 1, -1.0)], # 9
[(n_h[0, -1], 1, 1.0), (n_h[-1, -1], 1, -1.0)], # 10
[(n_h[1, 1], 0, 1.0)], # 11
[(n_h[0, -1], 1, 1.0)], # 12
[(n_h[1, 1], 1, 1.0), (n_h[0, 1], 1, -1.0)], # 13
[(n_h[1, 1], 1, 1.0), (n_h[-1, 1], 1, -1.0)], # 14
# [(n_h[1, 1], 2, 1.0), (n_h[1, 0], 2, -1.0)], # 13
# [(n_h[1, 1], 1, 1.0), (n_h[1, -1], 2, -1.0)], # 14
]
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((15,), dtype = float)
cp.cnstr_rhs[6] = 3.95
return cp
def create_cp_dc(L_x = 4, L_y = 4, n_x = 1, n_y = 2,
n_steps = 100):
'''Create scalable rhombus crease pattern with dof_constraints
'''
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
show_iter = False,
MAX_ITER = 500)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
n_h_idx = n_y / 4
x_links = []
y_links = []
z_links = []
z_nodes = n_h[(0, 0, -1, -1), (0, -1, -1, 0)].flatten()
print 'z_nodes', z_nodes
#z_cnstr = [[(n, 2, 1.0)] for n in z_nodes]
x_cnstr = [[(n_h[0, 0], 0, 1.0)]]
y_cnstr = [[(n_h[0, 0], 1, 1.0)]]
z_cnstr = [[(n_h[0, 0], 2, 1.0)]]
for n_arr in n_h[:, (0, -1)].T:
for idx, n in enumerate(n_arr[1:]):
n_x = len(n_arr)
y_links.append([(n_arr[0], 1, 1.0), (n, 1, -1.0)])
for n in n_h[0, 1:]:
z_links.append([(n_h[0, 0], 2, 1.0), (n, 2, -1.0)])
x_links.append([(n_h[0, 0], 0, 1.0), (n, 0, -1.0)])
#x_links.append([(n_h[0, -1], 0, 1.0), (n_h[0, -1], 1, -0.5)])
for n in n_v[-1, 1:]:
x_links.append([(n_v[-1, 0], 0, 1.0), (n, 0, -1.0)])
for n0, n1 in zip(n_v[0, :], n_v[-1, :]):
z_links.append([(n0, 2, 1.0), (n1, 2, -1.0)])
#cntrl = [[(n_h[-1, -1], 1, 1.0)]]
cntrl = [[(n_h[-1, 1], 0, 1.0)]]
print 'x_cnstr', len(x_cnstr)
print 'y_cnstr', len(y_cnstr)
print 'z_cnstr', len(z_cnstr)
print 'x_links', len(x_links)
print 'y_links', len(y_links)
print 'z_links', len(z_links)
cp.cnstr_lhs = z_cnstr + x_links + y_links + z_links + x_cnstr + y_cnstr + cntrl
#cp.cnstr_lhs = z_cnstr
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype = float)
cp.cnstr_rhs[-1] = -L_x * 0.34
# cp.cnstr_rhs[-1] = -L_y * 0.9999
return cp
def create_cp_fc_inclined(L_x = 4, L_y = 4, n_x = 1, n_y = 2,
n_steps = 100):
'''Create scalable rhombus crease pattern with face constraints
'''
cp = RhombusCreasePattern(n_steps = n_steps,
L_x = L_x,
L_y = L_y,
n_x = n_x,
n_y = n_y,
show_iter = False,
MAX_ITER = 2000)
n_h = cp.n_h
n_i = cp.n_i
n_v = cp.n_v
n_h_idx = n_y / 4
x_links = []
y_links = []
z_links = []
# for n_arr in n_h[:, (-1,)].T:
# for idx, n in enumerate(n_arr[1:]):
# y_links.append([(n_arr[0], 1, 1.0), (n, 1, -1.0)])
# for n in n_v[-1, 1:]:
# x_links.append([(n_v[-1, 0], 0, 1.0), (n, 0, -1.0)])
# for n0, n1 in zip(n_v[0, :], n_v[-1, :]):
# z_links.append([(n0, 2, 1.0), (n1, 2, -1.0)])
# y_links.append([(n0, 1, 1.0), (n1, 1, -1.0)])
#cntrl = [[(n_h[-1, -1], 1, 1.0)]]
#cntrl = [[(n_h[-1, 1], 0, 1.0)]]
cp.cnstr_lhs = x_links + y_links + z_links # + cntrl
#cp.cnstr_lhs = z_cnstr
# lift node 0 in z-axes
cp.cnstr_rhs = np.zeros((len(cp.cnstr_lhs),), dtype = float)
#cp.cnstr_rhs[-1] = -L_x * 0.34
# face_z_0 = FF(Rf = z_ - (1 - x_ / L_x) * 0.2 * t_)
face_z_0 = FF(Rf = z_ - 0)
face_x_0 = FF(Rf = x_ - 0)
# face_x_L = FF(Rf = x_ - L_x * (1 - 0.2 * t_))
# face_y_0 = FF(Rf = y_ - 0)
# face_y_L = FF(Rf = y_ - L_y * (1 - 0.1 * t_))
#parallel movement bothsided
face_y_0 = FF(Rf = y_ - L_y * (0.05 * t_))# * x_ / L_x)
face_y_L = FF(Rf = y_ - L_y * (1 - 0.05 * t_))# * x_ / L_x)
#parallel movement: one side inclined
# face_y_0 = FF(Rf = y_ - L_y / 2.0 * (0.1 * t_) * x_ / L_x)
# face_y_L = FF(Rf = y_ - L_y * (1 - 0.05 * t_))# * x_ / L_x)
#one side inclined, other side fixed
# face_y_0 = FF(Rf = y_ - 0)
# face_y_L = FF(Rf = y_ - L_y + L_y * 0.1 * t_* x_ / L_x)
##symmetric inclined along x
# face_y_0 = FF(Rf = y_ - L_y / 2.0 * 0.1 * t_ * x_ / L_x)
# face_y_L = FF(Rf = y_ - L_y + L_y / 2.0 * 0.1 * t_ * x_ / L_x)
#
##symmetric inclined along both x and y
# face_y_0 = FF(Rf = y_ - L_y / 2.0 * 0.05 * t_ * y_ / L_y)
# face_y_L = FF(Rf = y_ - L_y + L_y / 2.0 * 0.05 * t_ * y_ / L_y)
# cp.cnstr_lst = [(face_x_0, n_h[0, :]),
# (face_z_0, n_h[0, :]),
# (face_y_0, n_h[:, 0]),
# (face_y_L, n_h[:, -1])]
z_nodes = n_h[:, :].flatten()
print z_nodes
cp.cnstr_lst = [(face_x_0, [n_h[0, 0]]),
(face_z_0, z_nodes),
(face_y_0, n_h[:, 0]),
(face_y_L, n_h[:, -1])]
return cp