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1
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1334
1327
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
-
8708
I
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9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
1
3
2
7
-
1334
1328
g
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o
u
t
h
o
les;
(
b
)
C
o
n
ce
p
tio
n
d
o
m
ain
w
ith
a
h
o
le
T
h
u
s
,
t
h
e
a
u
to
m
a
tic
g
e
n
er
atio
n
o
f
a
r
etic
u
lated
s
tr
u
c
tu
r
e
b
e
g
in
s
b
y
li
n
k
i
n
g
t
h
e
p
o
in
t
s
d
is
c
r
etizin
g
t
h
e
b
o
u
n
d
ar
y
o
f
t
h
e
d
esi
g
n
d
o
m
ai
n
as
s
h
o
w
i
n
g
in
Fi
g
u
r
e
1
.
T
h
en
,
t
h
e
b
ar
s
t
h
at
ar
e
n
o
t
e
n
tire
l
y
co
n
tain
ed
in
th
e
d
esig
n
ar
ea
w
i
ll
b
e
e
li
m
in
a
ted
.
An
d
f
i
n
all
y
,
t
h
e
b
ar
s
r
etain
e
d
w
i
ll
b
e
r
ed
is
tr
ib
u
ted
to
i
n
cr
ea
s
e
t
h
e
r
i
g
id
it
y
o
f
th
e
s
tr
u
ctu
r
e.
Ho
w
e
v
er
f
i
n
d
in
g
a
b
ar
r
em
o
v
al
cr
iter
io
n
i
s
n
o
t
s
o
o
b
v
io
u
s
.
I
n
th
i
s
p
ap
er
,
w
e
s
u
g
g
e
s
t
an
a
lg
o
r
ith
m
to
g
e
n
er
ate
a
r
eticu
la
ted
s
tr
u
ctu
r
e
a
u
to
m
at
icall
y
w
h
atev
er
th
e
t
y
p
e
o
f
t
h
e
d
esi
g
n
d
o
m
ai
n
.
Ou
r
n
e
w
alg
o
r
it
h
m
i
s
d
e
f
in
ed
in
t
w
o
m
ai
n
p
h
ase
s
.
I
t
s
tar
ts
b
y
c
o
n
n
ec
ti
n
g
all
i
n
itia
l
n
o
d
es
o
f
t
h
e
s
tr
u
ct
u
r
e.
T
h
e
n
,
it
p
r
o
p
o
s
es
an
eli
m
in
at
io
n
c
r
iter
io
n
to
r
ej
ec
t
s
eg
m
e
n
ts
th
at
ar
e
n
o
t
in
cl
u
d
ed
en
tire
l
y
in
t
h
e
co
n
ce
p
tio
n
d
o
m
ain
.
T
h
is
eli
m
in
a
tio
n
is
b
ased
o
n
a
m
et
h
o
d
o
f
co
m
p
u
tatio
n
al
g
eo
m
etr
y
.
T
h
e
p
ap
er
is
d
iv
id
ed
in
to
f
i
v
e
s
ec
tio
n
s
.
Sect
io
n
2
s
it
u
ate
t
h
e
p
r
o
b
lem
b
y
i
n
tr
o
d
u
cin
g
th
e
b
asics
o
n
th
e
g
e
n
er
atio
n
o
f
r
etic
u
lated
s
tr
u
ctu
r
e
s
,
an
d
g
i
v
es
a
b
r
ief
o
v
er
v
ie
w
o
f
p
r
ev
io
u
s
w
o
r
k
s
d
o
n
e
o
n
th
is
s
u
b
j
ec
t.
T
h
e
n
e
w
al
g
o
r
ith
m
is
ex
p
lai
n
e
d
in
Sectio
n
3
.
I
n
Sectio
n
4
,
a
n
o
v
er
v
ie
w
o
f
t
h
e
s
tr
u
ctu
r
e
’
s
d
ef
o
r
m
atio
n
e
n
er
g
y
is
g
i
v
en
to
in
tr
o
d
u
ce
t
h
e
o
p
tim
izatio
n
w
o
r
k
o
f
th
e
g
e
n
er
ate
d
s
tr
u
ctu
r
e
.
Fi
n
all
y
,
i
n
Sectio
n
5
,
co
n
clu
s
io
n
s
ar
e
d
r
a
w
n
.
2.
P
RO
B
L
E
M
SI
T
UA
T
I
O
N
2
.
1
.
G
ener
a
t
ing
a
re
t
icula
t
ed
s
t
ruct
ure
T
h
e
alg
o
r
ith
m
s
f
o
r
g
e
n
er
ati
n
g
r
eticu
lated
s
tr
u
ct
u
r
es
d
if
f
e
r
ac
co
r
d
in
g
to
th
e
t
y
p
e
o
f
t
h
e
d
esig
n
d
o
m
ai
n
.
I
n
a
co
n
v
e
x
d
o
m
ai
n
Ω
,
t
w
o
p
o
in
ts
A
an
d
B
ar
e
co
n
n
ec
ted
b
y
a
s
eg
m
e
n
t
co
n
tai
n
e
d
en
tire
l
y
in
Ω
.
T
h
is
p
r
o
p
er
ty
h
as
b
ee
n
e
x
p
lo
ited
b
y
C
h
i
h
eb
&
P
an
ase
n
k
o
[
1
]
to
g
en
er
ate
au
to
m
atica
ll
y
r
eticu
lat
ed
s
tr
u
ctu
r
es
f
r
o
m
a
co
n
v
e
x
d
esig
n
d
o
m
ai
n
.
T
h
eir
tech
n
iq
u
e,
n
a
m
ed
A
G
R
S,
b
eg
in
s
w
it
h
a
d
is
cr
etiza
tio
n
o
f
t
h
e
b
o
u
n
d
ar
y
o
f
th
e
d
esig
n
d
o
m
ain
i
n
to
a
f
in
i
te
n
u
m
b
er
o
f
p
o
in
ts
.
T
h
en
,
t
h
ese
p
o
in
ts
ar
e
li
n
k
ed
in
p
air
s
to
r
ep
r
e
s
en
t t
h
e
r
etic
u
lated
s
tr
u
ct
u
r
e
w
h
ic
h
is
t
h
e
n
s
u
b
j
ec
ted
to
an
o
p
tim
iza
tio
n
tr
ea
t
m
en
t
en
ab
li
n
g
to
o
b
tain
a
m
o
s
t
o
p
ti
m
al
s
tr
u
ct
u
r
e.
Fig
u
r
e
2
p
r
esen
ts
a
n
ex
a
m
p
le
o
f
th
e
r
etic
u
lated
s
tr
u
c
tu
r
e
g
e
n
er
atio
n
u
s
i
n
g
A
G
R
S.
(
a)
(
b
)
Fig
u
r
e
2
.
Gen
er
atin
g
a
r
eticu
la
ted
s
tr
u
ctu
r
e
i
n
a
co
n
v
ex
d
o
m
ain
(
a)
C
o
n
v
ex
co
n
ce
p
tio
n
d
o
m
ai
n
;
(
b
)
C
o
r
r
esp
o
n
d
in
g
r
eticu
lated
s
tr
u
ct
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Hyb
r
id
meth
o
d
fo
r
a
u
t
o
ma
tin
g
g
en
era
tio
n
o
f reticu
la
ted
s
tr
u
ctu
r
es (
la
tt
ice
s
tr
u
ctu
r
e
s)
…
(
Z
in
eb
B
ia
lla
ten
)
1329
T
h
er
ef
o
r
e,
a
co
n
v
ex
d
esig
n
d
o
m
a
in
is
a
s
p
ec
ial
ca
s
e
o
f
d
esig
n
d
o
m
ain
s
,
an
d
all
d
o
m
ai
n
s
ar
e
n
o
t
co
n
v
e
x
.
B
y
s
t
u
d
y
i
n
g
n
o
n
-
co
n
v
ex
d
esi
g
n
d
o
m
ai
n
s
,
w
e
n
o
ticed
th
at
th
er
e
ar
e
n
o
n
-
co
n
v
e
x
d
o
m
a
in
s
th
a
t
m
a
y
b
e
d
ec
o
m
p
o
s
ed
i
n
to
a
f
i
n
ite
n
u
m
b
er
o
f
co
n
v
ex
s
u
b
-
d
o
m
a
in
s
.
So
,
w
e
r
ec
e
n
tl
y
p
r
o
p
o
s
ed
an
al
g
o
r
ith
m
[
2
]
to
g
en
er
ate
a
n
d
o
p
ti
m
ize
a
r
etic
u
lated
s
tr
u
ct
u
r
e
f
r
o
m
a
d
esi
g
n
d
o
m
ai
n
o
f
t
h
is
ca
teg
o
r
y
.
T
h
e
p
r
o
p
o
s
ed
a
lg
o
r
ith
m
u
s
e
s
a
co
n
v
ex
d
ec
o
m
p
o
s
itio
n
tech
n
iq
u
e
to
o
b
tain
a
f
in
ite
n
u
m
b
er
o
f
co
n
v
e
x
s
u
b
-
d
o
m
ai
n
s
.
E
ac
h
o
f
th
ese
s
u
b
-
d
o
m
ai
n
s
is
co
n
s
id
er
ed
to
b
e
an
in
p
u
t
o
f
t
h
e
Au
to
m
atic
Gen
er
atio
n
o
f
R
etic
u
lated
St
r
u
ctu
r
es
al
g
o
r
ith
m
(
A
G
R
S)
[
1
]
.
T
h
er
ef
o
r
e,
a
r
eticu
lated
s
tr
u
ct
u
r
e
is
g
e
n
er
ated
b
y
a
co
n
v
e
x
s
u
b
-
d
o
m
ai
n
.
S
u
b
s
e
q
u
en
tl
y
,
t
h
e
p
ar
tial
s
o
lu
tio
n
s
ar
e
m
er
g
ed
to
o
b
tain
th
e
o
v
er
all
r
eticu
lated
s
tr
u
ct
u
r
e.
A
ll t
h
ese
s
tep
s
w
er
e
p
r
esen
t
ed
in
Fig
u
r
e
3
.
Fig
u
r
e
3
.
Dec
o
m
p
o
s
i
n
g
a
n
o
n
-
co
n
v
e
x
d
o
m
ain
a
n
d
Gen
er
ati
n
g
a
r
eticu
lated
s
tr
u
ct
u
r
e
A
s
ec
o
n
d
ca
te
g
o
r
y
o
f
n
o
n
-
co
n
v
e
x
d
esi
g
n
d
o
m
ai
n
s
is
th
o
s
e
th
at
ca
n
n
o
t
b
e
d
ec
o
m
p
o
s
ed
i
n
to
ex
ac
tl
y
co
n
v
e
x
s
u
b
-
d
o
m
ai
n
s
.
T
h
e
co
m
p
lex
i
t
y
o
f
th
e
s
e
ar
ea
s
in
cr
ea
s
es
i
f
th
e
y
co
n
tai
n
h
o
les.
W
e
ar
e
in
ter
ested
in
th
is
t
y
p
e
o
f
n
o
n
-
co
n
v
e
x
d
o
m
ai
n
s
.
3.
P
RO
P
O
SE
D
SO
L
UT
I
O
N
T
h
e
au
to
m
at
ic
g
en
er
atio
n
o
f
a
r
eticu
lated
s
tr
u
ctu
r
e
b
eg
i
n
s
w
it
h
a
d
is
cr
etiza
tio
n
o
f
th
e
c
o
n
to
u
r
in
to
a
f
i
n
ite
n
u
m
b
er
o
f
p
o
in
t
s
.
E
ac
h
p
o
in
t
o
f
d
is
cr
etiza
t
io
n
is
a
n
o
d
e
o
f
t
h
e
s
tr
u
ctu
r
e.
T
h
en
,
th
e
n
o
d
es
ar
e
lin
k
ed
i
n
p
air
s
to
cr
ea
te
t
h
e
s
eg
m
e
n
t
s
o
f
t
h
e
r
etic
u
lated
s
tr
u
ctu
r
e.
T
h
e
s
et
o
f
cr
ea
ted
s
e
g
m
e
n
t
s
i
s
ca
lled
E
.
No
w
a
s
e
g
m
en
t i
s
eli
m
i
n
ated
if
it is
n
o
t c
o
m
p
letel
y
co
n
tai
n
e
d
in
th
e
d
esi
g
n
d
o
m
a
in
,
i
n
o
th
er
w
o
r
d
s
:
L
et
Ω
b
e
th
e
n
o
n
-
co
n
v
ex
d
esi
g
n
d
o
m
ai
n
,
t
h
e
s
e
g
m
e
n
t S
m
u
s
t b
e
eli
m
in
a
ted
if
:
̂
̇
(1
)
T
h
e
s
et
o
f
s
eg
m
e
n
ts
to
b
e
eli
m
in
ated
is
d
ef
i
n
ed
as
f
o
llo
w
s
:
E
SA
E
=
{
S
/
̂
̇
}
(
2
)
T
h
e
p
r
o
ce
s
s
o
f
au
to
m
atic
g
e
n
er
atio
n
is
ill
u
s
tr
ated
in
Fi
g
u
r
e
4
.
A
cc
o
r
d
in
g
to
(
5
)
,
a
s
eg
m
en
t
S
is
eli
m
i
n
ated
if
t
h
er
e
is
a
p
o
in
t o
f
its
i
n
ter
io
r
w
h
ic
h
d
o
es n
o
t b
elo
n
g
to
Ω
.
I
n
Fi
g
u
r
e
5
,
th
e
t
w
o
s
eg
m
e
n
ts
an
d
ar
e
to
b
e
elim
i
n
ated
.
Fo
r
,
all
p
o
in
ts
o
f
it
s
in
ter
io
r
d
o
n
o
t
b
elo
n
g
to
t
h
e
d
esi
g
n
d
o
m
ain
.
So
a
s
i
n
g
le
test
is
e
n
o
u
g
h
to
eli
m
in
ate
th
is
t
y
p
e
o
f
s
e
g
m
en
t.
Ho
w
ev
er
,
t
h
e
s
eg
m
e
n
t
is
p
ar
tiall
y
co
n
tain
ed
in
Ω
s
o
f
in
d
i
n
g
a
p
o
in
t
th
at
d
o
es
n
o
t
b
elo
n
g
to
Ω
ca
n
b
e
ex
p
en
s
i
v
e
s
i
n
ce
it
m
a
y
r
eq
u
ir
e
a
lar
g
e
n
u
m
b
er
o
f
test
s
.
L
et
b
e
a
s
eg
m
e
n
t o
f
t
h
e
s
tr
u
ct
u
r
e,
an
d
M
(
)
a
p
o
in
t o
f
:
if
M
d
o
es n
o
t b
elo
n
g
to
Ω
t
h
e
n
is
eli
m
i
n
ated
au
to
m
atica
ll
y
.
(
3
)
First,
it
w
as
i
m
p
o
r
tan
t
to
s
et
u
p
a
tech
n
iq
u
e
to
c
h
o
o
s
e
t
h
e
p
o
in
ts
o
f
th
e
s
e
g
m
en
t
f
o
r
w
h
ic
h
t
h
e
r
elatio
n
(
6
)
m
u
s
t
b
e
v
er
i
f
ied
.
Sin
ce
a
s
e
g
m
en
t
i
s
in
f
i
n
it
y
o
f
p
o
in
ts
,
w
e
w
er
e
i
n
s
p
ir
ed
b
y
a
b
r
ac
k
etin
g
m
et
h
o
d
to
r
ep
r
esen
t
t
h
e
s
e
g
m
e
n
t
w
it
h
a
s
et
o
f
p
o
in
t
s
(
)
.
T
h
e
b
r
ac
k
etin
g
i
s
a
m
et
h
o
d
u
s
ed
to
d
ec
id
e
o
n
t
h
e
ex
is
te
n
ce
o
f
ze
r
o
s
o
f
a
g
i
v
e
n
f
u
n
ctio
n
i
n
an
i
n
ter
v
al.
T
h
is
m
et
h
o
d
p
r
o
p
o
s
es
to
s
u
b
d
iv
id
e
an
in
ter
v
al
in
to
a
f
i
n
ite
n
u
m
b
er
o
f
s
u
b
-
i
n
ter
v
al
s
w
i
th
t
h
e
s
a
m
e
s
ize,
an
d
th
en
th
e
r
esear
ch
p
r
o
ce
s
s
is
ap
p
lied
to
ea
ch
s
u
b
-
in
ter
v
a
l.
B
u
t,
d
eter
m
in
i
n
g
w
h
eth
er
a
p
o
in
t
b
elo
n
g
s
to
a
d
o
m
a
in
i
s
n
o
t
a
s
i
m
p
le
p
r
o
b
lem
a
tic.
T
h
er
ef
o
r
e,
w
e
p
r
o
p
o
s
e
to
u
s
e
a
g
eo
m
etr
y
al
g
o
r
ith
m
to
s
o
lv
e
t
h
is
p
r
o
b
lem
.
I
t’
s
an
al
g
o
r
ith
m
th
at
i
s
a
b
le
to
d
eter
m
in
e
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
1
3
2
7
-
1334
1330
p
o
s
itio
n
o
f
a
p
o
in
t
w
it
h
r
e
s
p
ec
t
to
a
p
o
l
y
g
o
n
:
i
n
s
id
e,
o
u
ts
id
e
o
r
o
n
th
e
ed
g
e
s
o
f
t
h
e
p
o
l
y
g
o
n
.
Fo
r
o
u
r
ca
s
e,
th
e
p
o
ly
g
o
n
is
t
h
e
ap
p
r
o
x
i
m
atio
n
o
f
t
h
e
i
n
itial
d
esi
g
n
d
o
m
ain
cr
ea
ted
b
y
l
in
k
i
n
g
t
h
e
d
is
cr
eti
za
tio
n
n
o
d
es
o
f
t
h
e
b
o
u
n
d
ar
ies o
f
t
h
e
d
esig
n
d
o
m
a
in
(
in
cl
u
d
i
n
g
t
h
e
b
o
u
n
d
ar
ies o
f
th
e
h
o
les).
Fig
u
r
e
4
.
Gen
er
atin
g
a
r
eticu
la
ted
s
tr
u
ctu
r
e
s
tep
s
(
a)
No
n
-
co
n
v
e
x
co
n
ce
p
tio
n
d
o
m
ain
; (
b
)
Dis
cr
et
izatio
n
;
(
c)
C
r
ea
ti
n
g
s
e
g
m
e
n
t
s
;
(
d
)
E
lim
i
n
ati
n
g
i
m
p
r
o
p
er
s
eg
m
en
ts
Fig
u
r
e
4
.
Seg
m
en
t
s
to
eli
m
in
a
te
3
.
1
.
P
o
int
in po
ly
g
o
n:
r
e
v
iew
T
h
e
p
o
in
t
in
p
o
ly
g
o
n
is
a
v
er
y
n
atu
r
al
p
r
o
b
le
m
in
t
h
e
f
ield
o
f
co
m
p
u
tatio
n
al
g
eo
m
e
tr
y
w
h
ic
h
d
ec
id
e
w
h
et
h
er
a
p
o
in
t
is
in
s
id
e
o
r
o
u
ts
id
e
a
p
o
ly
g
o
n
.
So
,
w
e
w
an
t
to
u
s
e
th
i
s
tech
n
iq
u
e
to
ch
ec
k
ea
c
h
p
o
in
t
o
f
a
s
tu
d
ied
s
eg
m
e
n
t a
n
d
d
ec
id
e
w
h
et
h
er
it is
i
n
s
id
e
t
h
e
s
t
u
d
ied
co
n
ce
p
tio
n
d
o
m
a
in
.
Ma
n
y
al
g
o
r
ith
m
s
ar
e
u
s
ed
in
liter
atu
r
e
to
lo
ca
te
a
p
o
in
t
r
elativ
e
to
a
p
o
ly
g
o
n
.
T
w
o
ex
a
m
p
les
ar
e
s
h
o
w
n
o
n
Fi
g
u
r
e
6
.
O
n
e
o
f
th
e
f
ir
s
t
p
o
i
n
t
-
in
-
p
o
l
y
g
o
n
a
lg
o
r
ith
m
s
is
C
r
o
s
s
in
g
N
u
m
b
er
alg
o
r
ith
m
(
C
N
A)
[3
]
-
[
5
]
.
Giv
en
a
p
o
l
y
g
o
n
P
a
n
d
a
p
o
in
t
M,
C
A
N
co
u
n
ts
th
e
n
u
m
b
er
o
f
ti
m
e
s
a
r
a
y
s
tar
ti
n
g
f
r
o
m
th
e
p
o
in
t
M
cr
o
s
s
es
t
h
e
p
o
l
y
g
o
n
b
o
u
n
d
ar
y
ed
g
es.
T
h
e
p
o
i
n
t
i
s
o
u
ts
id
e
w
h
e
n
t
h
is
"
cr
o
s
s
in
g
n
u
m
b
er
"
is
e
v
en
;
o
th
er
w
i
s
e,
w
h
e
n
it
is
o
d
d
,
th
e
p
o
in
t
is
i
n
s
id
e.
T
h
is
m
eth
o
d
is
e
f
f
icie
n
t
f
o
r
all
t
y
p
es
o
f
p
o
l
y
g
o
n
s
an
d
it
w
o
r
k
s
i
n
ti
m
e
(
n
is
t
h
e
n
u
m
b
er
o
f
t
h
e
p
o
l
y
g
o
n
ed
g
es)
[
6
]
.
Fig
u
r
e
5
.
(
a)
C
r
o
s
s
in
g
n
u
m
b
er
m
eth
o
d
; (
b
)
W
in
d
in
g
n
u
m
b
er
m
et
h
o
d
Fo
r
th
e
w
i
n
d
in
g
n
u
m
b
er
alg
o
r
ith
m
(
W
NA
)
[
5
]
,
it
co
u
n
ts
t
h
e
n
u
m
b
er
o
f
ti
m
es
t
h
e
p
o
l
y
g
o
n
w
i
n
d
s
ar
o
u
n
d
th
e
p
o
in
t
M.
T
h
e
p
o
in
t
is
o
u
ts
id
e
o
n
l
y
w
h
e
n
t
h
is
"
w
i
n
d
i
n
g
n
u
m
b
er
"
is
ze
r
o
;
o
th
er
w
i
s
e,
th
e
p
o
i
n
t
i
s
in
s
id
e.
T
h
is
al
g
o
r
ith
m
is
n
o
t
d
esira
b
le
f
o
r
p
o
ly
g
o
n
s
w
i
th
a
lar
g
e
n
u
m
b
er
o
f
s
e
ts
.
Ho
w
e
v
er
,
an
i
m
p
r
o
v
ed
i
m
p
le
m
en
ta
tio
n
o
f
th
e
w
i
n
d
in
g
n
u
m
b
er
w
a
s
p
r
o
p
o
s
ed
b
y
Ho
r
m
a
n
n
&
Ag
at
h
o
s
[
7
]
f
o
r
s
elf
-
i
n
ter
s
ec
ti
n
g
p
o
ly
g
o
n
s
.
W
NA
&
C
A
N
ar
e
al
g
o
r
ith
m
s
b
ased
o
n
co
m
p
u
ti
n
g
a
p
ar
a
m
eter
.
T
h
ey
ar
e
s
i
m
p
le
to
i
m
p
l
e
m
en
t
b
u
t
b
o
th
o
f
th
e
m
ar
e
s
lo
w
e
s
p
ec
i
all
y
i
f
th
e
n
u
m
b
er
o
f
p
o
l
y
g
o
n
’
s
v
er
tice
s
is
lar
g
e.
So
,
o
th
er
alg
o
r
ith
m
s
w
er
e
p
r
o
p
o
s
ed
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
s
o
lu
tio
n
s
.
T
h
ese
alg
o
r
ith
m
s
ad
o
p
t
th
e
p
r
in
cip
le
o
f
“
d
iv
id
e
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Hyb
r
id
meth
o
d
fo
r
a
u
t
o
ma
tin
g
g
en
era
tio
n
o
f reticu
la
ted
s
tr
u
ctu
r
es (
la
tt
ice
s
tr
u
ctu
r
e
s)
…
(
Z
in
eb
B
ia
lla
ten
)
1331
co
n
q
u
er
”.
So
,
th
e
y
p
r
o
p
o
s
e
a
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
d
iv
id
in
g
t
h
e
p
o
l
y
g
o
n
i
n
to
a
s
et
o
f
s
i
m
p
l
er
p
o
ly
g
o
n
s
(
co
n
v
e
x
p
o
ly
g
o
n
s
[
8
]
,
tr
ian
g
les
[
9
]
,
an
d
tr
ap
ez
o
id
s
[
1
0
]
)
.
A
f
ter
d
ec
o
m
p
o
s
itio
n
ea
c
h
al
g
o
r
ith
m
u
s
e
s
o
n
e
o
f
t
h
e
b
asic
alg
o
r
ith
m
s
to
d
eter
m
in
e
t
h
e
p
o
s
itio
n
o
f
t
h
e
p
o
in
t i
n
q
u
e
s
tio
n
.
3
.
2
.
Ne
w
a
l
g
o
rit
h
m
s
t
ep
s
T
h
e
s
o
lu
tio
n
th
at
w
e
p
r
o
p
o
s
e
in
th
i
s
w
o
r
k
i
s
a
h
y
b
r
id
alg
o
r
ith
m
u
s
i
n
g
th
e
p
r
in
cip
le
s
o
f
th
e
A
GR
S
alg
o
r
ith
m
[
1
]
to
g
en
er
ate
a
r
eticu
lated
s
tr
u
ctu
r
e
i
n
an
ar
b
itra
r
y
co
n
ce
p
tio
n
d
o
m
ai
n
.
T
h
e
s
tep
s
o
f
th
is
n
e
w
alg
o
r
ith
m
ar
e
as f
o
llo
w
s
:
Step
1
:
T
h
e
d
esig
n
er
g
iv
e
s
th
e
d
es
ig
n
d
o
m
ai
n
.
I
t
is
e
n
o
u
g
h
t
h
at
h
e
d
ef
i
n
es
t
h
e
o
u
ter
b
o
r
d
er
o
f
th
is
d
o
m
ai
n
an
d
p
o
s
s
ib
l
y
t
h
e
b
o
r
d
er
s
o
f
th
e
h
o
les (
if
t
h
e
y
e
x
i
s
t)
.
Step
2
:
B
o
r
d
e
r
s
ar
e
d
is
cr
etize
d
w
it
h
a
s
u
f
f
icie
n
t n
u
m
b
er
o
f
p
o
in
ts
.
T
h
ese
p
o
in
t
s
ar
e
th
e
i
n
it
ial
n
o
d
e
s
o
f
t
h
e
f
u
tu
r
e
s
tr
u
ct
u
r
e.
Step
3
:
A
ll
p
o
in
ts
ar
e
lin
k
ed
i
n
p
ai
r
s
.
E
ac
h
li
n
k
r
ep
r
esen
ts
a
c
an
d
id
ate
s
e
g
m
e
n
t
o
f
t
h
e
r
eti
cu
lated
s
tr
u
ct
u
r
e.
So
m
e
s
e
g
m
e
n
t
s
ar
e
n
o
t
c
o
m
p
letel
y
co
n
tai
n
ed
in
th
e
co
n
ce
p
tio
n
d
o
m
ai
n
.
So
,
t
h
e
y
ar
e
eli
m
i
n
ated
in
s
tep
4
.
Step
4
:
Fo
r
ea
ch
s
eg
m
e
n
t
(
(
)
&
(
)
ar
e
tw
o
p
o
in
ts
o
f
s
tep
2
)
,
w
e
ap
p
l
y
a
p
o
in
t
-
in
-
p
o
l
y
g
o
n
alg
o
r
ith
m
to
m
ai
n
tai
n
o
r
eli
m
i
n
ate
th
is
s
e
g
m
en
t.
Ho
w
e
v
er
,
ap
p
ly
i
n
g
th
i
s
t
y
p
e
o
f
al
g
o
r
ith
m
s
o
n
th
e
d
esig
n
d
o
m
ai
n
ass
u
m
es
t
h
at
i
t
is
a
clo
s
ed
p
o
l
y
g
o
n
.
So
,
th
e
b
o
u
n
d
ar
y
n
ea
r
th
e
s
e
g
m
en
t
m
u
s
t
b
e
ap
p
r
o
x
im
a
ted
to
a
clo
s
ed
p
o
ly
g
o
n
.
is
d
is
cr
etize
d
i
n
to
a
s
et
o
f
p
o
in
ts
(
)
.
So
,
ch
ec
k
i
n
g
t
h
e
eli
m
i
n
atio
n
cr
iter
io
n
f
o
r
t
h
e
s
eg
m
e
n
t is to
ch
ec
k
i
f
ea
ch
(
)
is
in
s
id
e
o
r
o
u
ts
id
e
t
h
e
“
p
o
l
y
g
o
n
”:
Fo
r
ea
ch
(
)
,
C
all
an
al
g
o
r
ith
m
P
o
in
t
-
In
-
P
o
lyg
o
n
,
Step
5
:
Af
ter
eli
m
i
n
ati
n
g
i
n
ap
p
r
o
p
r
ia
te
s
eg
m
e
n
ts
,
w
e
d
eter
m
i
n
e
t
h
e
p
o
in
ts
o
f
i
n
ter
s
ec
tio
n
b
et
w
ee
n
th
e
v
alid
ated
s
eg
m
e
n
ts
.
T
h
en
,
w
e
ca
lcu
late
t
h
e
co
n
n
ec
ti
v
it
y
m
at
r
ix
o
f
th
e
g
e
n
er
ated
s
tr
u
ct
u
r
e.
Fig
u
r
e
7
s
h
o
w
s
a
n
ex
a
m
p
le
of
i
m
p
le
m
en
ta
tio
n
o
f
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
Fig
u
r
e
6
.
Au
to
m
at
ic
g
e
n
er
atio
n
o
f
a
r
eticu
la
ted
s
tr
u
ct
u
r
e
in
a
n
ar
b
itra
r
y
n
o
n
-
co
n
v
ex
co
n
ce
p
tio
n
d
o
m
ai
n
T
h
e
s
o
lu
tio
n
w
e
p
r
o
p
o
s
e
is
h
y
b
r
id
izatio
n
b
et
w
ee
n
t
w
o
s
o
lu
tio
n
s
.
First
w
e
tak
e
ad
v
a
n
tag
e
o
f
th
e
s
i
m
p
lic
it
y
o
f
t
h
e
p
r
in
cip
le
o
f
g
en
er
ati
n
g
r
eticu
lated
s
tr
u
ct
u
r
es
in
a
co
n
v
e
x
d
o
m
ai
n
.
T
h
en
,
w
e
v
al
id
ate
ea
ch
s
eg
m
e
n
t u
s
in
g
a
r
ed
u
ce
d
co
m
p
lex
it
y
al
g
o
r
it
h
m
.
Mo
r
eo
v
er
,
if
t
h
e
n
u
m
b
er
o
f
d
is
cr
etiza
tio
n
p
o
in
ts
is
lar
g
e
th
en
t
h
e
n
u
m
b
er
o
f
s
e
g
m
en
ts
to
test
i
s
i
m
p
o
r
tan
t.
So
it
w
a
s
i
n
ter
est
in
g
to
d
esi
g
n
o
u
r
s
o
lu
tio
n
a
s
a
p
ar
allel
p
r
o
g
r
a
m
.
P
ar
allelis
m
r
ed
u
ce
s
t
h
e
r
u
n
n
i
n
g
ti
m
e
a
n
d
o
p
ti
m
izes
th
e
u
s
e
o
f
m
ater
ial
r
e
s
o
u
r
ce
s
w
h
ic
h
in
cr
ea
s
e
t
h
e
ef
f
icie
n
c
y
o
f
o
u
r
alg
o
r
ith
m
.
T
h
is
m
ec
h
a
n
i
s
m
co
u
ld
b
e
u
s
ed
in
t
w
o
co
n
te
x
ts
:
a.
T
o
s
elec
t th
e
s
e
g
m
en
t to
b
e
p
r
o
ce
s
s
ed
: Seg
m
e
n
ts
ca
n
b
e
s
h
ar
ed
b
etw
ee
n
m
u
ltip
le
p
r
o
ce
s
s
es
b.
Sh
ar
i
n
g
t
h
e
te
s
ts
o
f
th
e
eli
m
in
atio
n
cr
iter
io
n
b
et
w
ee
n
s
e
v
er
al
p
r
o
ce
s
s
es.
So
e
ac
h
s
e
g
m
en
t
w
o
u
ld
b
e
tr
ea
ted
b
y
m
an
y
p
r
o
ce
s
s
es
Ou
r
m
et
h
o
d
is
b
ased
o
n
d
is
c
r
etizin
g
t
h
e
s
tu
d
ied
s
eg
m
e
n
t.
So
,
it
i
s
s
e
n
s
iti
v
e
to
t
h
e
n
u
m
b
er
o
f
t
h
e
d
is
cr
etiza
tio
n
p
o
in
ts
.
I
n
s
o
m
e
ca
s
es,
th
i
s
n
u
m
b
er
s
h
o
u
ld
b
e
s
u
f
f
icien
t
to
d
etec
t
th
e
p
o
in
ts
th
at
ar
e
o
u
t
o
f
th
e
co
n
ce
p
tio
n
d
o
m
ain
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
1
3
2
7
-
1334
1332
I
n
Fi
g
u
r
e
8
,
t
h
e
co
n
ce
p
tio
n
d
o
m
a
in
h
a
s
a
r
ef
le
x
v
er
te
x
w
it
h
an
an
g
le
t
h
at
ten
d
s
to
2
π
.
As
s
h
o
w
n
o
n
th
e
f
i
g
u
r
e,
t
h
e
d
is
cr
etiza
tio
n
o
f
t
h
e
s
e
g
m
en
t
m
u
s
t
cr
ea
te
a
s
u
f
f
icie
n
t
n
u
m
b
er
o
f
p
o
in
ts
o
n
th
e
d
ia
m
eter
o
f
t
h
e
cir
cle
to
d
ec
i
d
e
th
at
th
e
s
eg
m
en
t
m
u
s
t
b
e
eli
m
i
n
ated
.
T
h
e
e
x
p
er
i
m
e
n
ts
h
a
v
e
s
h
o
w
n
t
h
at
if
th
e
b
r
id
g
e
cr
ea
ted
b
y
s
u
c
h
an
an
g
le
is
o
f
th
e
o
r
d
er
o
f
,
a
n
u
m
b
er
o
f
2
0
0
p
o
i
n
ts
i
s
s
u
f
f
icie
n
t
to
eli
m
i
n
ate
t
h
e
s
eg
m
e
n
t
s
ee
Fig
u
r
e
9
.
Fig
u
r
e
7
.
Sp
ec
ial
ca
s
e
Fig
u
r
e
8
.
B
r
id
g
e
o
f
o
r
d
er
o
f
Un
til
n
o
w
,
t
h
e
d
esi
g
n
er
h
as
to
ch
o
o
s
e
th
e
s
tep
o
f
d
is
cr
et
izatio
n
.
B
u
t,
it
w
o
u
ld
b
e
in
t
er
esti
n
g
to
au
to
m
ate
t
h
is
s
tep
ac
co
r
d
in
g
t
o
th
e
n
at
u
r
e
o
f
t
h
e
co
n
ce
p
tio
n
d
o
m
ain
.
I
n
t
h
e
o
t
h
er
h
a
n
d
,
th
e
m
et
h
o
d
w
e
u
s
e
to
v
alid
ate
a
s
e
g
m
en
t
h
a
s
f
o
r
i
n
p
u
ts
a
p
o
in
t
an
d
a
p
o
l
y
g
o
n
.
B
u
t
o
u
r
d
esig
n
d
o
m
ai
n
s
ar
e
n
o
t
n
ec
ess
ar
il
y
p
o
l
y
g
o
n
s
b
u
t
ar
b
itra
r
y
cu
r
v
es.
T
h
en
,
it
w
a
s
n
ec
es
s
ar
y
to
ap
p
r
o
x
i
m
ate
th
e
co
n
to
u
r
s
o
f
t
h
e
d
esi
g
n
d
o
m
ai
n
to
a
p
o
ly
g
o
n
su
c
h
th
a
t
its
s
id
es
ar
e
th
e
s
eg
m
en
ts
li
n
k
in
g
t
w
o
p
o
in
t
s
.
T
h
is
ap
p
r
o
x
i
m
atio
n
s
h
o
u
ld
b
e
co
n
cise
to
g
u
ar
a
n
tee
t
h
at
it
w
o
u
ld
n
o
t
i
m
p
ac
t
t
h
e
r
es
u
lt
s
.
So
,
w
e
c
h
o
o
s
e
a
d
is
cr
etiza
tio
n
f
in
e
en
o
u
g
h
to
ap
p
r
o
ac
h
th
e
co
n
tin
u
it
y
o
f
t
h
e
d
esi
g
n
d
o
m
ai
n
.
4.
NO
DA
L
DI
SPLA
CE
M
E
NT
A
r
etic
u
lated
s
tr
u
ct
u
r
e
is
d
esig
n
ed
to
b
e
r
ig
id
an
d
b
ala
n
ce
d
.
Mo
r
eo
v
er
it
ca
n
b
e
s
u
b
j
ec
ted
to
m
ec
h
a
n
ical
o
r
th
er
m
al
f
o
r
ce
s
o
f
d
ef
o
r
m
at
io
n
i
n
f
lu
e
n
ci
n
g
its
s
ti
f
f
n
es
s
.
T
h
ese
f
o
r
ce
s
ar
e
ap
p
lied
o
n
th
e
n
o
d
es
o
f
th
e
s
tr
u
ct
u
r
e
w
h
at
p
r
o
d
u
ce
s
a
d
is
p
lace
m
en
t o
f
th
e
s
e
n
o
d
es
.
Op
ti
m
izi
n
g
a
r
etic
u
lated
s
tr
u
c
tu
r
e
m
ea
n
s
m
i
n
i
m
izi
n
g
its
d
e
f
o
r
m
at
io
n
e
n
er
g
y
.
T
h
is
e
n
er
g
y
is
d
ef
i
n
ed
u
s
i
n
g
th
e
n
o
d
al
d
is
p
lace
m
e
n
t
m
atr
i
x
:
(
4
)
U:
n
o
d
al
d
is
p
lace
m
e
n
t v
ec
to
r
F: v
ec
to
r
o
f
n
o
d
al
f
o
r
ce
s
So
,
af
ter
g
e
n
er
ati
n
g
th
e
s
tr
u
ctu
r
e
w
e
n
ee
d
to
ca
lc
u
late
th
e
d
ef
o
r
m
atio
n
e
n
er
g
y
.
W
e
s
tar
t
b
y
ca
lcu
lati
n
g
t
h
e
n
o
d
al
d
is
p
lace
m
en
ts
.
Fo
r
th
is
,
w
e
u
s
e
an
eq
u
atio
n
d
e
f
in
in
g
a
r
elatio
n
b
et
w
e
en
s
ti
f
f
n
es
s
m
atr
i
x
,
v
ec
to
r
o
f
n
o
d
al
d
is
p
lace
m
e
n
ts
an
d
v
ec
to
r
o
f
n
o
d
al
f
o
r
ce
s
:
(5
)
s
u
c
h
t
h
at:
K
is
a
s
q
u
ar
e
m
atr
ix
o
f
s
ize
2
×
n
(
n
i
s
t
h
e
n
u
m
b
er
o
f
th
e
s
tr
u
ct
u
r
e
n
o
d
es);
U
an
d
F
ar
e
v
ec
to
r
s
o
f
s
ize
2
×n
.
W
e
s
u
g
g
es
t
in
o
u
r
to
o
l
a
f
ea
t
u
r
e
to
ca
lcu
late
t
h
e
d
ef
o
r
m
a
ti
o
n
en
er
g
y
o
f
t
h
e
g
en
er
ated
s
t
r
u
ctu
r
e
i
n
o
r
d
er
to
in
tr
o
d
u
ce
th
e
o
p
ti
m
iz
atio
n
w
o
r
k
s
.
So
,
th
r
ee
i
n
p
u
t
s
a
r
e
to
b
e
d
ef
in
ed
:
C
o
n
n
ec
tiv
i
t
y
m
atr
i
x
,
n
o
d
es
w
it
h
ze
r
o
d
is
p
lace
m
e
n
t a
n
d
t
h
e
v
ec
to
r
o
f
n
o
d
al
f
o
r
ce
s
.
T
h
e
g
en
er
atio
n
o
p
er
atio
n
,
p
r
esen
ted
i
n
t
h
i
s
p
ap
er
,
p
r
o
d
u
ce
s
a
r
eticu
lated
s
tr
u
ct
u
r
e
r
ep
r
es
en
ted
b
y
a
co
n
n
ec
ti
v
it
y
m
atr
i
x
.
A
co
n
n
ec
tiv
it
y
m
a
tr
ix
is
p
r
o
d
u
ce
d
to
b
e
u
s
ed
f
o
r
d
escr
ib
in
g
th
e
eq
u
i
lib
r
iu
m
eq
u
at
io
n
o
f
th
is
s
tr
u
ctu
r
e.
I
t
i
s
a
s
q
u
ar
e
b
in
ar
y
m
atr
i
x
t
h
at
d
escr
ib
es
co
n
n
ec
tio
n
s
b
et
w
ee
n
t
h
e
n
o
d
es
o
f
t
h
e
s
tr
u
ct
u
r
e.
A
co
n
n
ec
tio
n
b
et
w
ee
n
t
w
o
p
o
i
n
ts
i
s
eq
u
i
v
al
e
n
t to
a
s
e
g
m
en
t.
A
l
s
o
,
f
o
r
an
y
s
tr
u
ct
u
r
e,
w
e
h
a
v
e
n
o
d
es
w
i
th
ze
r
o
d
is
p
lace
m
e
n
t
a
n
d
n
o
d
es
t
h
at
ar
e
u
n
d
er
lo
ad
.
T
h
o
s
e
th
at
ar
e
ze
r
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I
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1333
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t
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i
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t
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late
t
h
e
b
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av
io
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th
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s
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r
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to
s
t
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d
y
it
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s
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ilit
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d
it
s
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ig
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y
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B
u
t
t
h
is
s
i
m
u
lat
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is
n
o
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en
o
u
g
h
a
n
d
w
e
m
u
s
t
also
m
a
k
e
s
u
r
e
to
d
esig
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it
in
t
h
e
b
est
m
o
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el.
Fo
r
o
u
r
p
r
o
j
ec
t,
w
e
d
ef
in
ed
m
o
r
e
t
h
an
a
le
v
el
o
f
o
p
ti
m
izatio
n
a
n
d
w
e
ai
m
to
u
s
e
a
m
etah
e
u
r
s
t
ic
al
g
o
r
ith
m
to
r
ea
ch
o
u
r
g
o
al.
A
m
eta
h
eu
r
i
s
tic
al
g
o
r
ith
m
s
o
lv
es
h
ar
d
p
r
o
b
lem
s
f
o
r
w
h
ic
h
w
e
ca
n
n
o
t
h
a
v
e
ex
ac
t
s
o
lu
t
io
n
s
w
it
h
clas
s
ical
m
et
h
o
d
s
.
I
n
liter
atu
r
e,
s
ev
er
al
alg
o
r
ith
m
s
w
er
e
p
r
o
p
o
s
ed
to
d
ef
in
e
an
o
p
ti
m
a
l
s
tr
u
ct
u
r
e
[
1
2
]
,
[
13
]
an
d
a
s
et
o
f
alg
o
r
ith
m
s
w
a
s
d
esti
n
ed
to
o
p
t
i
m
ize
latt
ice
s
tr
u
ct
u
r
es
[
1
4
]
-
[
1
6
]
.
So
th
is
to
p
ic
o
f
o
p
tim
izat
io
n
w
ill
b
e
d
etailled
in
f
u
t
u
r
e
w
o
r
k
.
Fig
u
r
e
9
.
Var
iatio
n
o
f
th
e
d
e
f
o
r
m
atio
n
e
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er
g
y
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ep
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t
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e
tr
an
s
v
er
s
e
s
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ctio
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o
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t
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ar
s
Fig
u
r
e
10
.
I
m
p
ac
t o
f
t
h
e
m
a
n
u
f
ac
t
u
r
in
g
m
a
ter
ial
o
f
th
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b
ar
s
o
n
th
e
e
n
er
g
y
o
f
d
ef
o
r
m
atio
n
5.
CO
NCLU
SI
O
N
T
h
is
w
o
r
k
ai
m
s
to
cr
ea
te
a
to
o
l
h
elp
in
g
in
d
u
s
tr
ial
en
g
i
n
ee
r
s
to
d
esi
g
n
r
etic
u
lated
s
tr
u
ctu
r
e
s
i
n
ef
f
icien
t
w
a
y
.
T
h
e
d
esig
n
er
o
n
l
y
g
i
v
es
t
h
e
en
v
elo
p
e
o
f
t
h
e
s
tr
u
ct
u
r
e
an
d
o
u
r
to
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l
tak
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r
e
o
f
th
e
g
e
n
er
atio
n
o
f
t
h
e
s
tr
u
ct
u
r
e
w
i
th
a
n
o
p
ti
m
u
m
f
o
r
m
.
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n
t
h
is
p
ap
er
,
w
e
d
ev
elo
p
ed
an
alg
o
r
it
h
m
to
g
en
er
ate
r
eticu
lated
s
tr
u
ct
u
r
es
i
n
ar
b
itra
r
y
co
n
ce
p
tio
n
d
o
m
ain
.
T
h
e
al
g
o
r
ith
m
i
s
a
g
en
er
aliza
t
io
n
o
f
al
g
o
r
ith
m
s
g
e
n
er
ati
n
g
r
eticu
lated
s
tr
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ctu
r
e
s
f
o
r
s
p
ec
ial
ca
s
es
o
f
co
n
ce
p
tio
n
d
o
m
a
in
s
.
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h
is
s
o
l
u
tio
n
i
s
wo
r
k
in
g
o
n
co
m
p
le
x
co
n
ce
p
tio
n
d
o
m
ain
s
ev
e
n
t
h
o
s
e
w
it
h
h
o
le
s
.
A
to
o
l
f
o
r
in
d
u
s
tr
ial
d
esi
g
n
m
u
s
t
s
t
u
d
y
t
h
e
b
eh
av
io
r
o
f
th
e
s
tr
u
ctu
r
e
to
b
e
d
esig
n
ed
.
T
h
e
s
tu
d
y
o
f
th
i
s
b
eh
av
io
r
w
o
u
ld
lead
u
s
to
c
h
o
o
s
e
th
e
s
elec
tio
n
o
f
th
e
b
ar
s
co
n
s
ti
tu
t
in
g
t
h
e
o
p
ti
m
al
f
o
r
m
o
f
t
h
e
s
tr
u
ct
u
r
e.
No
w
,
o
p
ti
m
izi
n
g
th
e
s
tr
u
c
tu
r
e
a
m
o
u
n
t
s
to
p
r
o
p
o
s
e
th
e
f
o
r
m
t
h
at
m
i
n
i
m
izes
its
d
e
f
o
r
m
a
tio
n
en
er
g
y
.
So
,
w
e
p
r
esen
t
h
er
e
an
ex
a
m
p
le
o
f
g
en
er
ated
s
tr
u
ct
u
r
e
an
d
th
e
ca
lcu
latio
n
s
ch
e
m
e
o
f
t
h
is
en
er
g
y
,
s
tar
ti
n
g
w
it
h
a
ca
lcu
latio
n
o
f
t
h
e
n
o
d
al
d
is
p
lace
m
en
ts
o
f
t
h
e
s
tr
u
ct
u
r
e.
RE
F
E
R
E
NC
E
S
[1
]
Ch
ih
e
b
,
R.
a
n
d
P
a
n
a
se
n
k
o
,
G
.
,
"
A
No
v
e
l
A
lg
o
rit
h
m
f
o
r
th
e
Co
n
c
e
p
ti
o
n
a
n
d
Op
ti
m
iza
ti
o
n
o
f
Re
ti
c
u
late
S
tru
c
t
u
re
s
A
p
p
li
c
a
b
le A
n
a
l
y
sis,
"
v
o
l.
9
1
(
5
),
p
p
.
1
0
1
9
-
1
0
2
7
,
2
0
1
2
.
[2
]
Biallate
n
,
Z.
,
C
h
ih
e
b
,
R.
,
El
A
f
ia,
A
.
,
a
n
d
F
a
izi,
R.
,
"
No
v
e
l
M
e
th
o
d
to
G
e
n
e
ra
te an
d
Op
ti
m
ize
Re
ti
c
u
late
d
S
tru
c
tu
re
s
of
a
No
n
-
Co
n
v
e
x
Co
n
c
e
p
ti
o
n
Do
m
a
in
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
S
o
ft
w
a
re
En
g
in
e
e
rin
g
a
n
d
I
ts
Ap
p
l
ica
ti
o
n
s
,
v
o
l.
1
1
(2
),
p
p
1
7
-
26
,
2
0
1
7
.
[3
]
G
a
l
e
tzk
a
,
M
.
,
a
n
d
G
lau
n
e
r,
P
.
,
"
A
S
i
m
p
le
a
n
d
C
o
rre
c
t
Ev
e
n
-
Od
d
A
lg
o
rit
h
m
f
o
r
th
e
P
o
in
t
-
in
-
P
o
ly
g
o
n
P
r
o
b
lem
f
o
r
Co
m
p
lex
P
o
ly
g
o
n
s,
"
In
Pro
c
e
e
d
in
g
s
o
f
t
h
e
1
2
t
h
In
ter
n
a
ti
o
n
a
l
J
o
i
n
t
Co
n
fer
e
n
c
e
o
n
Co
mp
u
ter
Vi
sio
n
,
Ima
g
i
n
g
a
n
d
Co
mp
u
ter
Gr
a
p
h
ics
T
h
e
o
ry
a
n
d
Ap
p
li
c
a
ti
o
n
s (
VIS
IGRAP
P
2
0
1
7
),
v
o
l.
1
:
G
R
A
P
P
,
2
0
1
7
.
[4
]
Ha
in
e
s,
E.
,
"
P
o
i
n
t
i
n
P
o
ly
g
o
n
S
trate
g
ies
,
"
G
ra
p
h
ics
g
e
ms
IV
,
v
o
l.
9
9
4
,
pp
24
-
26
,
1
9
9
4
.
[5
]
J.
D.
F
o
le
y
,
A
.
v
a
n
D
a
m
,
S
.
K.
F
e
in
e
r,
J.
F
.
Hu
g
h
e
s
,
"
Co
m
p
u
ter
G
r
a
p
h
ics
-
P
rin
c
i
p
les
a
n
d
P
ra
c
ti
c
e
2
n
d
e
d
,
"
Ad
d
iso
n
-
W
e
sle
y
,
Rea
d
in
g
,
M
A
,
1
9
9
0
.
[6
]
Žalik
,
B.
a
n
d
Ko
li
n
g
e
ro
v
a
,
I.
,
"
A
C
e
ll
-
b
a
se
d
P
o
i
n
t
-
in
-
p
o
ly
g
o
n
A
l
g
o
rit
h
m
S
u
it
a
b
le
f
o
r
L
a
rg
e
S
e
ts
o
f
P
o
in
ts,
"
Co
mp
u
ter
s
&
G
e
o
sc
ien
c
e
s
,
v
o
l.
2
7
(1
0
),
pp.
1
1
3
5
-
1
1
4
5
,
2
0
0
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
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g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
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3
2
7
-
1334
1334
[7
]
Ho
rm
a
n
n
,
K.,
&
Ag
a
th
o
s,
A
.
,
"
T
h
e
P
o
in
t
in
P
o
ly
g
o
n
P
r
o
b
lem
f
o
r
A
rb
it
ra
ry
P
o
ly
g
o
n
s
,
"
Co
mp
u
t
a
ti
o
n
a
l
Ge
o
me
try
,
v
o
l.
2
0
(
3
),
pp.
1
3
1
-
1
4
4
,
2
0
0
1
.
[8
]
L
i,
J.,
W
a
n
g
,
W
.
C.
,
W
u
,
E.
H.
,
"
P
o
in
t
-
in
-
p
o
ly
g
o
n
T
e
sts
b
y
Co
n
v
e
x
De
c
o
m
p
o
siti
o
n
,
"
Co
mp
u
ter
s
&
G
ra
p
h
ics
,
v
o
l.
31
(4
),
pp.
6
3
6
–
6
4
8
,
2
0
0
7
.
[9
]
F
e
it
o
,
F
.
,
T
o
rre
s,
J.C.
,
Ure
n
a
,
A
.
,
"
Orie
n
tatio
n
,
S
im
p
li
c
it
y
,
a
n
d
In
c
lu
sio
n
T
e
st
f
o
r
P
lan
a
r
P
o
ly
g
o
n
s
,
"
Co
mp
u
ter
s
&
Gr
a
p
h
ics
,
v
o
l
.
19
(4
),
p
p
.
5
9
5
–
6
0
0
,
1
9
9
5
.
[1
0
]
Zalik
,
B.
,
Clap
w
o
rth
y
,
G
.
J.,
"
A
U
n
iv
e
rsa
l
T
ra
p
e
z
o
id
a
ti
o
n
A
lg
o
rit
h
m
f
o
r
P
lan
a
r
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4
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r.
c
h
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b
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m
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s.n
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t.
m
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Dr
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),
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Em
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