def new_center(S, I, Is, c=0.1, N=3, n=100, L=10, L2=1, L3=1, xs=1):
# L += c
# L2 += c
# L3 += c
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
X = x.copy()
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
# N = 3
M = 1000
# n = N
# x = np.linspace(-L, L, N)
# x = spectral.chebNodes(N, -L, L)
x = xs
f1x = spectral.chebEval(cf1x, x, a=-L, b=L) - c
f2x = spectral.chebEval(cf2x, x, a=-L, b=L) + c
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L) - c
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L) + c
f1x[-1] -= 10 * c
f1x[0] -= 1 * c
x[-1] += c / 2
x[0] -= c / 2
f1x *= L2
f2x *= L2
f1x2 *= L3
f2x2 *= L3
surfs = []
s1, a1 = points1(x, f1x, f1x2, S)
s2, a2 = points1(x, f2x, f1x2, s1, s=1, e=1)
s3, a3 = points1(x, f1x, f2x2, s2)
s4, a4 = points1(x, f2x, f2x2, s3, s=1, e=1)
#
ix1 = line1(a1, (1 + I) * M)
ix2 = line1(a2, (2 + I) * M)
#
ix3 = line1(a3, (3 + I) * M)
ix4 = line1(a4, (4 + I) * M)
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # #
ix5.append(line1([a1[0], a3[0]], (I + 5) * M))
ix7.append(line1([a1[0], a2[0]], (I + 7) * M))
ix8.append(line1([a3[0], a4[0]], (I + 8) * M))
for i in range(len(a1) - 1):
if i < (len(a1) - 2):
ix5.append(line1([a1[i + 1], a3[i + 1]], (I + 5) * M + i + 1))
ix6.append(line1([a2[i], a4[i]], (I + 6) * M + i))
ix7.append(line1([a1[i + 1], a2[i]], (I + 7) * M + i + 1))
ix8.append(line1([a3[i + 1], a4[i]], (I + 8) * M + i + 1))
else:
ix5.append(line1([a1[i + 1], a3[i + 1]], (I + 5) * M + i + 1))
ix7.append(line1([a1[i + 1], a2[i - 1]], (I + 7) * M + i + 1))
ix8.append(line1([a3[i + 1], a4[i - 1]], (I + 8) * M + i + 1))
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
for i in range(len(a1)):
if i < len(a1) - 2 and i > 0:
# upper
surfs.append(
surface1([ix1[i - 1], ix5[i], -ix3[i - 1], -ix5[i - 1]],
(1 + Is) * M + i))
# lower
surfs.append(
surface1([ix2[i - 1], ix6[i], -ix4[i - 1], -ix6[i - 1]],
(2 + Is) * M + i))
# left
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i - 1], -ix7[i]],
(3 + Is) * M + i))
# right
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i - 1], -ix8[i]],
(4 + Is) * M + i))
elif i == len(a1) - 2:
surfs.append(
surface1([ix1[i - 1], ix5[i], -ix3[i - 1], -ix5[i - 1]],
(1 + Is) * M + i))
surfs.append(
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]],
(1 + Is) * M + i + 1))
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix7[i]], (3 + Is) * M + i))
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix8[i]], (4 + Is) * M + i))
surfs.append(
surface1([ix5[i + 1], ix8[i + 1], -ix6[i - 1], -ix7[i + 1]],
(2 + Is) * M + i))
elif i == 0:
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix7[i]], (3 + Is) * M + i))
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix8[i]], (4 + Is) * M + i))
surfs.append(
surface1([ix5[i], ix8[i], -ix6[i], -ix7[i]], (2 + Is) * M + i))
return s8, [a1, a2, a3, a4], [[ix7[0], ix8[0]], [ix7[-1], ix8[-1]]], surfs
def left(S, I, Is, xs, As, Bs, b=-0.7, N=3, n=100, L=10, L2=1, L3=1):
b *= L
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
M = 1000
x = np.linspace(x[0], b, N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
f1x *= L2
f2x *= L2
f1x2 *= L3
f2x2 *= L3
s1, a1 = points1(x, f1x, f1x2, S, e=1)
s2, a2 = points1(x, f2x, f1x2, s1, e=1, s=1)
s3, a3 = points1(x, f1x, f2x2, s2, e=1)
s4, a4 = points1(x, f2x, f2x2, s3, e=1, s=1)
#
ix1 = line1(a1 + [As[0][0]], (I + 1) * M)
ix2 = line1([a1[0]] + a2 + [As[1][0]], (I + 2) * M)
#
ix3 = line1(a3 + [As[2][0]], (I + 3) * M)
ix4 = line1([a3[0]] + a4 + [As[3][0]], (I + 4) * M)
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # #
ix5.append(line1([a1[0], a3[0]], (I + 5) * M))
for i in range(len(a1)):
if i < len(a1) - 1:
ix5.append(line1([a1[i + 1], a3[i + 1]], (I + 5) * M + i + 1))
ix6.append(line1([a2[i], a4[i]], (I + 6) * M + i))
ix7.append(line1([a1[i + 1], a2[i]], (I + 7) * M + i))
ix8.append(line1([a3[i + 1], a4[i]], (I + 8) * M + i))
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
surfs = []
for i in range(len(a1)):
if i == 0:
surfs.append(
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]],
(1 + Is) * M + i))
surfs.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix5[i]], (2 + Is) * M + i))
#
surfs.append(surface1([ix1[i], ix7[i], -ix2[i]], (3 + Is) * M + i))
surfs.append(surface1([ix3[i], ix8[i], -ix4[i]], (4 + Is) * M + i))
elif i == len(a1) - 1:
arr1 = np.atleast_1d(np.squeeze([ix1[i], *xs[1], -ix3[i],
-ix5[i]]))
arr2 = np.atleast_1d(
np.squeeze([ix2[i], *xs[0], -ix4[i], -ix6[i - 1]]))
surfs.append(surface1(arr1, (Is + 1) * M + i))
surfs.append(surface1(arr2, (Is + 2) * M + i))
surfs.append(
surface1([ix1[i], Bs[0], -ix2[i], -ix7[i - 1]],
(3 + Is) * M + i))
surfs.append(
surface1([ix3[i], Bs[1], -ix4[i], -ix8[i - 1]],
(4 + Is) * M + i))
else:
# upper
surfs.append(
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]],
(1 + Is) * M + i))
# lower
surfs.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]],
(2 + Is) * M + i))
# left
surfs.append(
surface1([ix1[i], ix7[i], -ix2[i], -ix7[i - 1]],
(3 + Is) * M + i))
# right
surfs.append(
surface1([ix3[i], ix8[i], -ix4[i], -ix8[i - 1]],
(4 + Is) * M + i))
return s4, surfs, x
def center(b=-0.7,
c=0.7,
N=3,
LN=7,
RN=7,
n=100,
L=10,
L2=1,
L3=1,
coeff=0.007,
mu=13):
b *= L
c *= L
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
# N = 3
M = 1000
x = np.linspace(b, c, N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
f1x *= L2
f2x *= L2
f1x2 *= L3
f2x2 *= L3
surfs = []
bsurfs = []
s1, a1 = points1(x, f1x, f1x2, 1)
s2, a2 = points1(x, f2x, f1x2, s1)
s3, a3 = points1(x, f1x, f2x2, s2)
s4, a4 = points1(x, f2x, f2x2, s3)
#
ix1 = line1(a1, 1 * M)
ix2 = line1(a2, 2 * M)
#
ix3 = line1(a3, 3 * M)
ix4 = line1(a4, 4 * M)
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # #
for i in range(len(a1)):
if i < len(a1) - 1 and i != 0:
ix5.append(line1([a1[i], a3[i]], 5 * M + i))
ix6.append(line1([a2[i], a4[i]], 6 * M + i))
ix7.append(line1([a1[i], a2[i]], 7 * M + i))
ix8.append(line1([a3[i], a4[i]], 8 * M + i))
else:
ix7.append(line1([a1[i], a2[i]], 7 * M + i))
ix8.append(line1([a3[i], a4[i]], 8 * M + i))
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
for i in range(len(a1) - 1):
if i < len(a1) - 2 and i > 0:
# upper
surfs.append(
surface1([ix1[i], ix5[i], -ix3[i], -ix5[i - 1]], 1 * M + i))
# lower
surfs.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]], 2 * M + i))
# left
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i], -ix7[i]], 3 * M + i))
# right
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i], -ix8[i]], 4 * M + i))
elif i == len(a1) - 2:
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i], -ix7[i]], 3 * M + i))
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i], -ix8[i]], 4 * M + i))
elif i == 0:
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i], -ix7[i]], 3 * M + i))
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i], -ix8[i]], 4 * M + i))
bsurfsl = []
bsurfsr = []
def right_b(coeff=0.25, mu=7):
xs = np.linspace(f1x2[-1], f2x2[-1], mu)
f3x = np.sin(np.linspace(0, np.pi * (mu - 1), mu) + np.pi / 2)
xr = np.linspace(c, L, RN)
fxr1 = spectral.chebEval(cf1x * L2, xr, a=-L, b=L)
fxr2 = spectral.chebEval(cf2x * L2, xr, a=-L, b=L)
x131 = np.hstack((x[:-1], xr))
st1 = np.hstack((f2x[:-1], fxr2))
st2 = np.hstack((f1x[:-1], fxr1))
meh1 = sp_int.interp1d(x131, st1, kind='linear')
meh2 = sp_int.interp1d(x131, st2, kind='linear')
s5, a5 = points1((c + f3x * coeff)[1:-1],
meh1(c + f3x * coeff)[1:-1], xs[1:-1], s4)
s6, a6 = points1((c + f3x * coeff)[1:-1],
meh2(c + f3x * coeff)[1:-1], xs[1:-1], s5)
ix9 = line1(np.squeeze([[a2[-1]] + a5 + [a4[-1]]]), 9 * M)
ix10 = line1(np.squeeze([[a1[-1]] + a6 + [a3[-1]]]), 10 * M)
ix11 = []
for i in range(mu - 2):
ix11.append(line1([a5[i], a6[i]], 11 * M + i))
ix11 = np.atleast_1d(np.squeeze(ix11))
bsurfsr.append(surface1([ix10[0], -ix11[0], -ix9[0], -ix7[-1]], 5 * M))
for i in range(1, mu - 2):
bsurfsr.append(
surface1([ix10[i], -ix11[i], -ix9[i], ix11[i - 1]], 5 * M + i))
bsurfsr.append(
surface1([ix10[-1], ix8[-1], -ix9[-1], ix11[-1]], 5 * M + i + 1))
arr1 = np.atleast_1d(np.squeeze([ix6[-1], ix4[-1], *-ix9, -ix2[-1]]))
arr2 = np.atleast_1d(np.squeeze([ix5[-1], ix3[-1], *-ix10, -ix1[-1]]))
bsurfsr.append(surface1(arr1, 7 * M))
bsurfsr.append(surface1(arr2, 7 * M + 1))
return s5, s6, [ix9, ix10]
def left_b(s5, s6, coeff=0.25, mu=7):
# mu = 7
xs = np.linspace(f1x2[-1], f2x2[-1], mu)
f3x = np.sin(np.linspace(0, np.pi * (mu - 1), mu) + np.pi / 2)
xl = np.linspace(-L, b, LN)
fxl1 = spectral.chebEval(cf1x * L2, xl, a=-L, b=L)
fxl2 = spectral.chebEval(cf2x * L2, xl, a=-L, b=L)
# print(np.hstack((xl, x[1:])).size)
x131 = np.hstack((xl, x[1:]))
st1 = np.hstack((fxl2, f2x[1:]))
st2 = np.hstack((fxl1, f1x[1:]))
# print(x131)
meh1 = sp_int.interp1d(x131, st1, kind='linear')
meh2 = sp_int.interp1d(x131, st2, kind='linear')
s7, a7 = points1((b + f3x * coeff)[1:-1],
meh1(b + f3x * coeff)[1:-1], xs[1:-1], s6)
s8, a8 = points1((b + f3x * coeff)[1:-1],
meh2(b + f3x * coeff)[1:-1], xs[1:-1], s7)
ix12 = line1(np.squeeze([[a2[0]] + a7 + [a4[0]]]), 12 * M)
ix13 = line1(np.squeeze([[a1[0]] + a8 + [a3[0]]]), 13 * M)
ix14 = []
for i in range(mu - 2):
ix14.append(line1([a7[i], a8[i]], 14 * M + i))
ix14 = np.atleast_1d(np.squeeze(ix14))
bsurfsl.append(surface1([ix13[0], -ix14[0], -ix12[0], -ix7[0]], 6 * M))
for i in range(1, mu - 2):
bsurfsl.append(
surface1([ix13[i], -ix14[i], -ix12[i], ix14[i - 1]],
6 * M + i))
bsurfsl.append(
surface1([ix13[-1], ix8[0], -ix12[-1], ix14[-1]], 6 * M + i + 1))
arr1 = np.atleast_1d(np.squeeze([ix6[0], -ix4[0], *-ix12, ix2[0]]))
arr2 = np.atleast_1d(np.squeeze([ix5[0], -ix3[0], *-ix13, ix1[0]]))
bsurfsl.append(surface1(arr1, 8 * M))
bsurfsl.append(surface1(arr2, 8 * M + 1))
return s8, [ix12, ix13]
s5, s6, rxs = right_b(coeff, mu)
s8, lxs = left_b(s6, s6, coeff, mu)
return s8, lxs, rxs, [a1, a2, a3,
a4], [[ix7[0], ix8[0]],
[ix7[-1], ix8[-1]]], surfs, bsurfsl, bsurfsr, x
def right(S, I, Is, xs, As, Bs, c=0.7, N=3, n=100, L=10, L2=1, L3=1):
c *= L
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
M = 1000
x = np.linspace(c, x[-1], N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
f1x *= L2
f2x *= L2
f1x2 *= L3
f2x2 *= L3
s1, a1 = points1(x, f1x, f1x2, S, s=1)
s2, a2 = points1(x, f2x, f1x2, s1, s=1, e=1)
s3, a3 = points1(x, f1x, f2x2, s2, s=1)
s4, a4 = points1(x, f2x, f2x2, s3, s=1, e=1)
# #
ix1 = line1([As[0][-1]] + a1, (I + 1) * M)
ix2 = line1([As[1][-1]] + a2 + [a1[-1]], (I + 2) * M)
# #
ix3 = line1([As[2][-1]] + a3, (I + 3) * M)
ix4 = line1([As[3][-1]] + a4 + [a3[-1]], (I + 4) * M)
#
ix5 = []
ix6 = []
ix8 = []
ix7 = []
for i in range(len(a1)):
if i < len(a1) - 1:
ix5.append(line1([a1[i], a3[i]], (I + 5) * M + i))
ix6.append(line1([a2[i], a4[i]], (I + 6) * M + i))
ix7.append(line1([a1[i], a2[i]], (I + 7) * M + i))
ix8.append(line1([a3[i], a4[i]], (I + 8) * M + i))
else:
# if i == len(a1) - 2:
ix5.append(line1([a1[i], a3[i]], (I + 5) * M + i))
# ix5.append(line1([a1[i], a3[i]], (I + 6) * M + i))
# ix7.append(line1([a1[i], a2[i]], (I + 7) * M + i))
# ix8.append(line1([a3[i], a4[i]], (I + 8) * M + i))
#
#
#
# #
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
meh = []
for i in range(len(a1)):
if i == 0:
arr1 = np.atleast_1d(
np.squeeze([ix1[i], *(-xs[1]), -ix3[i], ix5[i]]))
arr2 = np.atleast_1d(
np.squeeze([ix2[i], *(-xs[0]), -ix4[i], ix6[i]]))
meh.append(surface1(arr1, (Is + 1) * M + i))
meh.append(surface1(arr2, (Is + 2) * M + i))
meh.append(
surface1([ix1[i], ix7[i], -ix2[i], -Bs[0]], (Is + 3) * M + i))
meh.append(
surface1([ix3[i], ix8[i], -ix4[i], -Bs[1]], (Is + 4) * M + i))
elif i == len(a1) - 1:
meh.append(
surface1([ix1[i], ix5[i], -ix3[i], -ix5[i - 1]],
(Is + 1) * M + i))
meh.append(
surface1([ix2[i], ix5[i], -ix4[i], -ix6[i - 1]],
(Is + 2) * M + i))
# #
meh.append(
surface1([ix1[i], -ix2[i], -ix7[i - 1]], (Is + 3) * M + i))
meh.append(
surface1([ix3[i], -ix4[i], -ix8[i - 1]], (Is + 4) * M + i))
else:
# upper
meh.append(
surface1([ix1[i], ix5[i], -ix3[i], -ix5[i - 1]],
(Is + 1) * M + i))
# lower
meh.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]],
(Is + 2) * M + i))
# #left
meh.append(
surface1([ix1[i], ix7[i], -ix2[i], -ix7[i - 1]],
(Is + 3) * M + i))
# right
meh.append(
surface1([ix3[i], ix8[i], -ix4[i], -ix8[i - 1]],
(Is + 4) * M + i))
return s4, meh, x
def left(S, I, Is, xs, As, Bs, b=-0.7, N=3, n=100):
# n = 100
L = 10
b *= L
lxs = xs[0]
uxs = xs[1]
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
# N = 7
M = 1000
n = N
x = np.linspace(x[0], b, N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
# plt.plot(x, f1x)
# plt.show()
L2 = 1
f1x *= L2
f2x *= L2
def points1(fx, z, I, s=0, e=0):
ind = []
for i in range(s, fx.size - e):
file.write('Point(' + str(I + i) + ') = {' +
", ".join(map(str, (list([x[i], z[i], fx[i], 1])))) +
'};')
file.write('\n')
file.write('//+' + '\n')
ind.append(I + i)
return fx.size + I, ind
def line1(ind, I):
ind1 = []
for i in range(len(ind) - 1):
file.write('Line(' + str(I + i) + ') = {' + str(ind[i]) + ',' +
str(ind[i + 1]) + '};')
file.write('\n')
file.write('//+' + '\n')
ind1.append(I + i)
return np.array(ind1)
def surface1(ix, I):
file.write('Curve Loop(' + str(I) + ') = {' + ', '.join(map(str, ix)) +
'};')
file.write('\n')
file.write('//+' + '\n')
file.write('Plane Surface(' + str(I) + ') = {' + str(I) + '};')
file.write('\n')
file.write('//+' + '\n')
return str(I)
s1, a1 = points1(f1x, f1x2, S, e=1)
s2, a2 = points1(f2x, f1x2, s1, e=1, s=1)
s3, a3 = points1(f1x, f2x2, s2, e=1)
s4, a4 = points1(f2x, f2x2, s3, e=1, s=1)
#
ix1 = line1(a1 + [As[0][0]], (I + 1) * M)
ix2 = line1([a1[0]] + a2 + [As[1][0]], (I + 2) * M)
#
ix3 = line1(a3 + [As[2][0]], (I + 3) * M)
ix4 = line1([a3[0]] + a4 + [As[3][0]], (I + 4) * M)
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # #
ix5.append(line1([a1[0], a3[0]], (I + 5) * M))
for i in range(len(a1)):
if i < len(a1) - 1:
ix5.append(line1([a1[i + 1], a3[i + 1]], (I + 5) * M + i + 1))
ix6.append(line1([a2[i], a4[i]], (I + 6) * M + i))
ix7.append(line1([a1[i + 1], a2[i]], (I + 7) * M + i))
ix8.append(line1([a3[i + 1], a4[i]], (I + 8) * M + i))
# if i == len(a1) - 2:
# ix5.append(line1([a1[i], a3[i]], (I + 5) * M + i))
# ix5.append(line1([a1[i + 1], a3[i + 1]], (I + 6) * M + i + 1))
# ix7.append(line1([a1[i], a2[i - 1]], (I + 7) * M + i))
# ix8.append(line1([a3[i], a4[i - 1]], (I + 8) * M + i))
#
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
#
# print(ix1)
# print(ix5)
# print(ix3)
surfs = []
for i in range(len(a1)):
if i == 0:
surfs.append(
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]],
(1 + Is) * M + i))
surfs.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix5[i]], (2 + Is) * M + i))
#
surfs.append(surface1([ix1[i], ix7[i], -ix2[i]], (3 + Is) * M + i))
surfs.append(surface1([ix3[i], ix8[i], -ix4[i]], (4 + Is) * M + i))
elif i == len(a1) - 1:
arr1 = np.atleast_1d(np.squeeze([ix1[i], *xs[1], -ix3[i],
-ix5[i]]))
arr2 = np.atleast_1d(
np.squeeze([ix2[i], *xs[0], -ix4[i], -ix6[i - 1]]))
surfs.append(surface1(arr1, (Is + 1) * M + i))
surfs.append(surface1(arr2, (Is + 2) * M + i))
surfs.append(
surface1([ix1[i], Bs[0], -ix2[i], -ix7[i - 1]],
(3 + Is) * M + i))
surfs.append(
surface1([ix3[i], Bs[1], -ix4[i], -ix8[i - 1]],
(4 + Is) * M + i))
else:
#upper
surfs.append(
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]],
(1 + Is) * M + i))
#lower
surfs.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]],
(2 + Is) * M + i))
#left
surfs.append(
surface1([ix1[i], ix7[i], -ix2[i], -ix7[i - 1]],
(3 + Is) * M + i))
#right
surfs.append(
surface1([ix3[i], ix8[i], -ix4[i], -ix8[i - 1]],
(4 + Is) * M + i))
return surfs
def right(S, I, Is, xs, As, Bs, c=0.7, N=3, n=100):
surfs = []
# n = 100
L = 10
c *= L
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
# N = 3
M = 1000
n = N
x = np.linspace(c, x[-1], N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
# plt.plot(x, f1x)
# plt.show()
L2 = 1
f1x *= L2
f2x *= L2
def points1(fx, z, I, s=0, e=0):
ind = []
for i in range(s, fx.size - e):
file.write('Point(' + str(I + i) + ') = {' +
", ".join(map(str, (list([x[i], z[i], fx[i], 1])))) +
'};')
file.write('\n')
file.write('//+' + '\n')
ind.append(I + i)
return fx.size + I, ind
def line1(ind, I):
ind1 = []
for i in range(len(ind) - 1):
file.write('Line(' + str(I + i) + ') = {' + str(ind[i]) + ',' +
str(ind[i + 1]) + '};')
file.write('\n')
file.write('//+' + '\n')
ind1.append(I + i)
return np.array(ind1)
def surface1(ix, I):
file.write('Curve Loop(' + str(I) + ') = {' + ', '.join(map(str, ix)) +
'};')
file.write('\n')
file.write('//+' + '\n')
file.write('Plane Surface(' + str(I) + ') = {' + str(I) + '};')
file.write('\n')
file.write('//+' + '\n')
return str(I)
def volume(planes, I):
file.write('Surface Loop(' + str(I) + ') = {' +
', '.join(map(str, planes)) + '};')
file.write('\n')
file.write('//+' + '\n')
file.write('Volume(' + str(I) + ') = {' + str(I) + '};')
file.write('\n')
file.write('//+' + '\n')
s1, a1 = points1(f1x, f1x2, S, s=1)
s2, a2 = points1(f2x, f1x2, s1, s=1, e=1)
s3, a3 = points1(f1x, f2x2, s2, s=1)
s4, a4 = points1(f2x, f2x2, s3, s=1, e=1)
# #
ix1 = line1([As[0][-1]] + a1, (I + 1) * M)
ix2 = line1([As[1][-1]] + a2 + [a1[-1]], (I + 2) * M)
# #
ix3 = line1([As[2][-1]] + a3, (I + 3) * M)
ix4 = line1([As[3][-1]] + a4 + [a3[-1]], (I + 4) * M)
#
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # # #
for i in range(len(a1)):
if i < len(a1) - 1:
ix5.append(line1([a1[i], a3[i]], (I + 5) * M + i))
ix6.append(line1([a2[i], a4[i]], (I + 6) * M + i))
ix7.append(line1([a1[i], a2[i]], (I + 7) * M + i))
ix8.append(line1([a3[i], a4[i]], (I + 8) * M + i))
else:
# if i == len(a1) - 2:
ix5.append(line1([a1[i], a3[i]], (I + 5) * M + i))
# ix5.append(line1([a1[i], a3[i]], (I + 6) * M + i))
# ix7.append(line1([a1[i], a2[i]], (I + 7) * M + i))
# ix8.append(line1([a3[i], a4[i]], (I + 8) * M + i))
#
#
#
# #
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
meh = []
for i in range(len(a1)):
if i == 0:
arr1 = np.atleast_1d(
np.squeeze([ix1[i], *(-xs[1]), -ix3[i], ix5[i]]))
arr2 = np.atleast_1d(
np.squeeze([ix2[i], *(-xs[0]), -ix4[i], ix6[i]]))
meh.append(surface1(arr1, (Is + 1) * M + i))
meh.append(surface1(arr2, (Is + 2) * M + i))
meh.append(
surface1([ix1[i], ix7[i], -ix2[i], -Bs[0]], (Is + 3) * M + i))
meh.append(
surface1([ix3[i], ix8[i], -ix4[i], -Bs[1]], (Is + 4) * M + i))
elif i == len(a1) - 1:
meh.append(
surface1([ix1[i], ix5[i], -ix3[i], -ix5[i - 1]],
(Is + 1) * M + i))
meh.append(
surface1([ix2[i], ix5[i], -ix4[i], -ix6[i - 1]],
(Is + 2) * M + i))
# #
meh.append(
surface1([ix1[i], -ix2[i], -ix7[i - 1]], (Is + 3) * M + i))
meh.append(
surface1([ix3[i], -ix4[i], -ix8[i - 1]], (Is + 4) * M + i))
else:
#upper
meh.append(
surface1([ix1[i], ix5[i], -ix3[i], -ix5[i - 1]],
(Is + 1) * M + i))
#lower
meh.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]],
(Is + 2) * M + i))
# #left
meh.append(
surface1([ix1[i], ix7[i], -ix2[i], -ix7[i - 1]],
(Is + 3) * M + i))
#right
meh.append(
surface1([ix3[i], ix8[i], -ix4[i], -ix8[i - 1]],
(Is + 4) * M + i))
# volume(meh, 1)
return s4, meh
def main():
n = 20
L = 10
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
N = 15
M = 1000
n = N
x = np.linspace(x[0], x[-1], N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
# plt.plot(x, f1x)
# plt.show()
L2 = 1
f1x *= L2
f2x *= L2
def points1(fx, z, I, s=0, e=0):
ind = []
for i in range(s, fx.size - e):
file.write('Point(' + str(I + i) + ') = {' +
", ".join(map(str, (list([x[i], z[i], fx[i], 1])))) +
'};')
file.write('\n')
file.write('//+' + '\n')
ind.append(I + i)
return fx.size + I, ind
def line1(ind, I):
ind1 = []
for i in range(len(ind) - 1):
file.write('Line(' + str(I + i) + ') = {' + str(ind[i]) + ',' +
str(ind[i + 1]) + '};')
file.write('\n')
file.write('//+' + '\n')
ind1.append(I + i)
return np.array(ind1)
def surface1(ix, I):
file.write('Curve Loop(' + str(I) + ') = {' + ', '.join(map(str, ix)) +
'};')
file.write('\n')
file.write('//+' + '\n')
file.write('Plane Surface(' + str(I) + ') = {' + str(I) + '};')
file.write('\n')
file.write('//+' + '\n')
s1, a1 = points1(f1x, f1x2, 1)
a = 1
s2, a2 = points1(f2x, f1x2, s1, s=1, e=1)
s3, a3 = points1(f1x, f2x2, s2)
s4, a4 = points1(f2x, f2x2, s3, s=1, e=1)
#
ix1 = line1(a1, 1 * M)
ix2 = line1([a1[0]] + a2 + [a1[-1]], 2 * M)
#
ix3 = line1(a3, 3 * M)
ix4 = line1([a3[0]] + a4 + [a3[-1]], 4 * M)
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # #
for i in range(len(a1) - 1):
if i < len(a1) - 2:
ix5.append(line1([a1[i], a3[i]], 5 * M + i))
ix6.append(line1([a2[i], a4[i]], 6 * M + i))
if i != 0:
ix7.append(line1([a1[i], a2[i - 1]], 7 * M + i))
ix8.append(line1([a3[i], a4[i - 1]], 8 * M + i))
if i == len(a1) - 2:
ix5.append(line1([a1[i], a3[i]], 5 * M + i))
ix5.append(line1([a1[i + 1], a3[i + 1]], 5 * M + i + 1))
ix7.append(line1([a1[i], a2[i - 1]], 7 * M + i))
ix8.append(line1([a3[i], a4[i - 1]], 8 * M + i))
#
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
for i in range(len(a1) - 1):
if i == 0:
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]], 1 * M + i)
surface1([ix2[i], ix6[i], -ix4[i], -ix5[i]], 2 * M + i)
surface1([ix1[i], ix7[i], -ix2[i]], 3 * M + i)
surface1([ix3[i], ix8[i], -ix4[i]], 4 * M + i)
elif i == len(a1) - 2:
# print('hey')
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]], 1 * M + i)
surface1([ix2[i], ix5[i + 1], -ix4[i], -ix6[i - 1]], 2 * M + i)
#
surface1([ix1[i], -ix2[i], -ix7[i - 1]], 3 * M + i)
surface1([ix3[i], -ix4[i], -ix8[i - 1]], 4 * M + i)
else:
#upper
surface1([ix1[i], ix5[i + 1], -ix3[i], -ix5[i]], 1 * M + i)
#lower
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]], 2 * M + i)
#left
surface1([ix1[i], ix7[i], -ix2[i], -ix7[i - 1]], 3 * M + i)
#right
surface1([ix3[i], ix8[i], -ix4[i], -ix8[i - 1]], 4 * M + i)
def center(b=-0.7, c=0.7, N=3, LN=7, RN=7, n=100):
# n = 100
L = 10
b *= L
c *= L
x2, f1x2, f2x2 = img.imr('img2.png', n)
x, f1x, f2x = img.imr('img.png', n)
x *= L
x2 *= L
X = x.copy()
cf1x = spectral.chebTransform(f1x)
cf2x = spectral.chebTransform(f2x)
cf1x2 = spectral.chebTransform(f1x2)
cf2x2 = spectral.chebTransform(f2x2)
# N = 3
M = 1000
n = N
x = np.linspace(b, c, N)
f1x = spectral.chebEval(cf1x, x, a=-L, b=L)
f2x = spectral.chebEval(cf2x, x, a=-L, b=L)
f1x2 = spectral.chebEval(cf1x2, x, a=-L, b=L)
f2x2 = spectral.chebEval(cf2x2, x, a=-L, b=L)
L2 = 1
f1x *= L2
f2x *= L2
surfs = []
bsurfs = []
def points1(x, fx, z, I, s=0, e=0):
ind = []
for i in range(s, fx.size - e):
file.write('Point(' + str(I + i) + ') = {' +
", ".join(map(str, (list([x[i], z[i], fx[i], 1])))) +
'};')
file.write('\n')
file.write('//+' + '\n')
ind.append(I + i)
return fx.size + I, ind
def line1(ind, I):
ind1 = []
for i in range(len(ind) - 1):
file.write('Line(' + str(I + i) + ') = {' + str(ind[i]) + ',' +
str(ind[i + 1]) + '};')
file.write('\n')
file.write('//+' + '\n')
ind1.append(I + i)
return np.array(ind1)
def surface1(ix, I):
file.write('Curve Loop(' + str(I) + ') = {' + ', '.join(map(str, ix)) +
'};')
file.write('\n')
file.write('//+' + '\n')
file.write('Plane Surface(' + str(I) + ') = {' + str(I) + '};')
file.write('\n')
file.write('//+' + '\n')
return str(I)
s1, a1 = points1(x, f1x, f1x2, 1)
s2, a2 = points1(x, f2x, f1x2, s1)
s3, a3 = points1(x, f1x, f2x2, s2)
s4, a4 = points1(x, f2x, f2x2, s3)
#
ix1 = line1(a1, 1 * M)
ix2 = line1(a2, 2 * M)
#
ix3 = line1(a3, 3 * M)
ix4 = line1(a4, 4 * M)
ix5 = []
ix6 = []
ix8 = []
ix7 = []
# # #
for i in range(len(a1)):
if i < len(a1) - 1 and i != 0:
ix5.append(line1([a1[i], a3[i]], 5 * M + i))
ix6.append(line1([a2[i], a4[i]], 6 * M + i))
ix7.append(line1([a1[i], a2[i]], 7 * M + i))
ix8.append(line1([a3[i], a4[i]], 8 * M + i))
else:
ix7.append(line1([a1[i], a2[i]], 7 * M + i))
ix8.append(line1([a3[i], a4[i]], 8 * M + i))
# elif i == 0:
# ix5.append(line1([a1[i], a3[i]], 5 * M + i))
# ix6.append(line1([a2[i], a4[i]], 6 * M + i))
ix5 = np.atleast_1d(np.squeeze(np.array(ix5)))
ix6 = np.atleast_1d(np.squeeze(np.array(ix6)))
ix7 = np.atleast_1d(np.squeeze(np.array(ix7)))
ix8 = np.atleast_1d(np.squeeze(np.array(ix8)))
# print(ix1)
# print(ix5)
# print(ix3)
# print(ix5)
for i in range(len(a1) - 1):
if i < len(a1) - 2 and i > 0:
# upper
surfs.append(
surface1([ix1[i], ix5[i], -ix3[i], -ix5[i - 1]], 1 * M + i))
# lower
surfs.append(
surface1([ix2[i], ix6[i], -ix4[i], -ix6[i - 1]], 2 * M + i))
#left
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i], -ix7[i]], 3 * M + i))
#right
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i], -ix8[i]], 4 * M + i))
elif i == len(a1) - 2:
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i], -ix7[i]], 3 * M + i))
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i], -ix8[i]], 4 * M + i))
elif i == 0:
surfs.append(
surface1([ix1[i], ix7[i + 1], -ix2[i], -ix7[i]], 3 * M + i))
surfs.append(
surface1([ix3[i], ix8[i + 1], -ix4[i], -ix8[i]], 4 * M + i))
bsurfsl = []
bsurfsr = []
def right_b(coeff=0.25, mu=7):
xs = np.linspace(f1x2[-1], f2x2[-1], mu)
f3x = np.sin(np.linspace(0, np.pi * (mu - 1), mu) + np.pi / 2)
xr = np.linspace(c, L, RN)
fxr1 = spectral.chebEval(cf1x, xr, a=-L, b=L)
fxr2 = spectral.chebEval(cf2x, xr, a=-L, b=L)
# print(np.hstack((xl, x[1:])).size)
x131 = np.hstack((x[:-1], xr))
st1 = np.hstack((f2x[:-1], fxr2))
st2 = np.hstack((f1x[:-1], fxr1))
# print(x131)
meh1 = sp_int.interp1d(x131, st1, kind='linear')
meh2 = sp_int.interp1d(x131, st2, kind='linear')
s5, a5 = points1((c + f3x * coeff)[1:-1],
meh1(c + f3x * coeff)[1:-1], xs[1:-1], s4)
s6, a6 = points1((c + f3x * coeff)[1:-1],
meh2(c + f3x * coeff)[1:-1], xs[1:-1], s5)
ix9 = line1(np.squeeze([[a2[-1]] + a5 + [a4[-1]]]), 9 * M)
ix10 = line1(np.squeeze([[a1[-1]] + a6 + [a3[-1]]]), 10 * M)
ix11 = []
for i in range(mu - 2):
ix11.append(line1([a5[i], a6[i]], 11 * M + i))
ix11 = np.atleast_1d(np.squeeze(ix11))
bsurfsr.append(surface1([ix10[0], -ix11[0], -ix9[0], -ix7[-1]], 5 * M))
for i in range(1, mu - 2):
bsurfsr.append(
surface1([ix10[i], -ix11[i], -ix9[i], ix11[i - 1]], 5 * M + i))
bsurfsr.append(
surface1([ix10[-1], ix8[-1], -ix9[-1], ix11[-1]], 5 * M + i + 1))
arr1 = np.atleast_1d(np.squeeze([ix6[-1], ix4[-1], *-ix9, -ix2[-1]]))
arr2 = np.atleast_1d(np.squeeze([ix5[-1], ix3[-1], *-ix10, -ix1[-1]]))
bsurfsr.append(surface1(arr1, 7 * M))
bsurfsr.append(surface1(arr2, 7 * M + 1))
return s5, s6, [ix9, ix10]
def left_b(s5, s6, coeff=0.25, mu=7):
# mu = 7
xs = np.linspace(f1x2[-1], f2x2[-1], mu)
f3x = np.sin(np.linspace(0, np.pi * (mu - 1), mu) + np.pi / 2)
xl = np.linspace(-L, b, LN)
fxl1 = spectral.chebEval(cf1x, xl, a=-L, b=L)
fxl2 = spectral.chebEval(cf2x, xl, a=-L, b=L)
# print(np.hstack((xl, x[1:])).size)
x131 = np.hstack((xl, x[1:]))
st1 = np.hstack((fxl2, f2x[1:]))
st2 = np.hstack((fxl1, f1x[1:]))
# print(x131)
meh1 = sp_int.interp1d(x131, st1, kind='linear')
meh2 = sp_int.interp1d(x131, st2, kind='linear')
s7, a7 = points1((b + f3x * coeff)[1:-1],
meh1(b + f3x * coeff)[1:-1], xs[1:-1], s6)
s8, a8 = points1((b + f3x * coeff)[1:-1],
meh2(b + f3x * coeff)[1:-1], xs[1:-1], s7)
ix12 = line1(np.squeeze([[a2[0]] + a7 + [a4[0]]]), 12 * M)
ix13 = line1(np.squeeze([[a1[0]] + a8 + [a3[0]]]), 13 * M)
ix14 = []
for i in range(mu - 2):
ix14.append(line1([a7[i], a8[i]], 14 * M + i))
ix14 = np.atleast_1d(np.squeeze(ix14))
bsurfsl.append(surface1([ix13[0], -ix14[0], -ix12[0], -ix7[0]], 6 * M))
for i in range(1, mu - 2):
bsurfsl.append(
surface1([ix13[i], -ix14[i], -ix12[i], ix14[i - 1]],
6 * M + i))
bsurfsl.append(
surface1([ix13[-1], ix8[0], -ix12[-1], ix14[-1]], 6 * M + i + 1))
arr1 = np.atleast_1d(np.squeeze([ix6[0], -ix4[0], *-ix12, ix2[0]]))
arr2 = np.atleast_1d(np.squeeze([ix5[0], -ix3[0], *-ix13, ix1[0]]))
bsurfsl.append(surface1(arr1, 8 * M))
bsurfsl.append(surface1(arr2, 8 * M + 1))
return s8, [ix12, ix13]
s5, s6, rxs = right_b(.07, 13)
s8, lxs = left_b(s6, s6, 0.07, 13)
return s8, lxs, rxs, [a1, a2, a3, a4], [[ix7[0], ix8[0]],
[ix7[-1],
ix8[-1]]], surfs, bsurfsl, bsurfsr