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I
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8708
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d
escr
ib
es
d
if
f
er
en
t
m
et
h
o
d
s
u
s
e
f
u
l
in
t
h
e
d
is
c
o
v
er
y
o
f
th
e
s
u
i
tab
le
au
x
il
iar
y
p
o
in
t.
T
h
e
f
o
u
r
th
s
ec
t
io
n
p
r
esen
ts
t
h
e
i
m
p
le
m
en
ta
tio
n
r
es
u
lts
.
T
h
e
ar
ticle
is
co
n
cl
u
d
ed
in
th
e
e
n
d
o
f
th
e
ar
ticle.
2.
DE
F
I
N
I
T
I
O
N
O
F
T
H
E
P
R
O
B
L
E
M
AND
T
H
E
E
VA
L
U
AT
I
O
N
F
UN
CT
I
O
N
T
h
e
p
r
o
b
lem
o
f
d
is
co
v
er
i
n
g
t
h
e
r
i
g
h
t
w
a
y
to
m
o
v
e
a
UAV
is
an
is
s
u
e
w
i
th
a
lo
t
o
f
in
p
u
t
p
ar
am
eter
s
an
d
th
e
an
s
w
er
is
n
o
t
u
n
iq
u
e.
T
h
er
ef
o
r
e,
th
is
p
r
o
b
lem
m
u
s
t
b
e
s
o
lv
ed
u
s
in
g
m
at
h
e
m
atic
al
m
o
d
elin
g
o
f
t
h
e
ef
f
ec
tiv
e
p
ar
a
m
e
ter
s
to
ch
o
o
s
e
th
e
p
ath
.
I
n
t
h
is
p
r
o
b
le
m
,
s
in
ce
it
is
i
m
p
o
s
s
ib
le
to
p
as
s
th
e
n
at
u
r
al
an
d
s
y
n
t
h
etic
o
b
s
tacle
s
,
v
er
y
lo
w
o
r
v
er
y
h
ig
h
altit
u
d
e
ar
ea
s
an
d
u
n
a
u
t
h
o
r
ized
ar
ea
s
,
s
o
m
e
d
ec
is
io
n
s
ar
e
co
n
s
id
er
ed
as
co
n
s
tr
ain
s
wh
ile
o
t
h
er
d
ec
is
io
n
p
ar
a
m
et
er
s
ar
e
co
n
s
id
er
ed
as
an
e
v
alu
a
tio
n
f
u
n
ct
io
n
.
P
r
ac
tically
,
t
h
e
p
r
o
b
lem
o
f
d
eter
m
i
n
i
n
g
t
h
e
o
p
ti
m
al
r
o
u
te
b
ec
o
m
e
s
th
e
m
ath
e
m
at
ical
m
ax
i
m
izin
g
o
r
m
i
n
i
m
izi
n
g
o
f
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
w
it
h
r
esp
ec
t
to
t
h
e
p
r
ed
ef
in
ed
co
n
s
tr
ain
s
.
T
h
e
s
ele
cted
r
o
u
te
in
v
o
lv
es
th
e
d
eter
m
in
at
io
n
o
f
t
h
e
p
o
in
ts
(
th
e
len
g
t
h
,
w
id
t
h
a
n
d
h
e
i
g
h
t
o
f
ea
c
h
p
o
in
t)
,
b
eg
i
n
n
i
n
g
f
r
o
m
th
e
p
o
in
t
o
f
o
r
ig
in
a
n
d
en
d
i
n
g
w
it
h
t
h
e
p
o
in
t
o
f
d
esti
n
atio
n
.
I
n
t
h
i
s
p
ap
er
,
th
e
s
p
ee
d
o
f
a
ir
cr
af
t
m
o
v
e
m
en
t
i
s
co
n
s
tan
t
an
d
th
e
p
ath
i
s
d
eter
m
i
n
ed
w
a
s
d
eter
m
in
ed
i
n
d
ep
en
d
en
tl
y
o
f
s
p
ee
d
.
T
h
e
in
ten
d
ed
p
r
o
v
is
io
n
s
o
f
t
h
e
ar
ticle
co
n
tain
ed
h
e
ig
h
t,
le
n
g
t
h
a
n
d
u
n
au
t
h
o
r
ized
ig
h
t r
eg
io
n
s
.
On
e
o
f
t
h
e
s
o
lu
tio
n
s
to
co
v
er
all
t
h
e
d
ef
i
n
ed
co
n
s
tr
ai
n
t
s
i
s
t
h
e
u
s
e
o
f
a
p
h
a
s
e
m
ac
h
i
n
e
to
p
r
o
d
u
ce
an
o
v
er
all
i
n
d
icato
r
.
I
n
t
h
is
m
eth
o
d
,
all
th
e
in
f
o
r
m
at
io
n
o
f
t
h
e
d
ef
i
n
ed
en
v
ir
o
n
m
e
n
t
to
cr
o
s
s
an
d
u
n
au
th
o
r
ized
ar
ea
s
to
fl
y
ar
e
g
i
v
en
to
t
h
e
p
h
ase
m
ac
h
i
n
e.
T
h
is
p
h
ase
c
ar
p
r
o
d
u
ce
s
an
in
d
icato
r
f
o
r
ea
ch
p
o
in
t
o
f
th
e
en
v
ir
o
n
m
e
n
t
w
h
ic
h
i
s
ca
lled
t
h
e
d
esira
b
le
p
ass
i
n
d
icato
r
.
I
t
co
v
er
s
all
t
h
e
d
ef
i
n
ed
co
n
s
tr
ai
n
ts
o
f
t
h
e
p
r
o
b
lem
.
T
h
e
m
o
d
el
o
b
tain
ed
f
r
o
m
t
h
e
f
u
zz
y
m
ac
h
i
n
e
is
ca
lled
a
p
h
ase
m
ap
.
T
h
e
aim
i
s
to
o
b
tain
a
r
o
u
te
th
at
b
etter
s
atis
f
i
es t
h
e
d
esire
d
p
ass
i
n
d
icato
r
.
T
h
e
m
o
d
eli
n
g
o
f
[
1
4
]
is
ad
o
p
ted
in
th
i
s
ar
ticle
i
n
w
h
ic
h
t
h
e
af
o
r
e
m
e
n
tio
n
ed
t
h
r
ee
co
n
s
tr
ain
ts
h
a
v
e
b
ee
n
m
o
d
eled
w
it
h
th
e
p
h
as
e
m
ac
h
i
n
e.
T
h
e
p
r
esen
ted
m
o
d
el
s
p
ec
if
i
e
s
th
e
p
er
f
o
r
m
a
n
ce
f
u
n
ctio
n
o
f
t
h
e
p
r
o
b
l
em
.
T
h
is
f
u
n
ctio
n
is
ab
le
to
r
ec
eiv
e
th
e
p
o
s
itio
n
o
f
an
y
p
o
in
t
in
t
h
e
en
v
ir
o
n
m
en
t
a
n
d
p
r
o
v
id
e
a
ce
r
tain
a
m
o
u
n
t
a
s
e
f
f
icien
c
y
.
A
s
p
ec
if
i
ca
tio
n
o
f
th
e
li
n
e
b
et
w
ee
n
th
e
s
tar
tin
g
a
n
d
d
esti
n
atio
n
p
o
in
t
a
s
t
h
e
p
ass
in
g
r
o
u
te
w
a
s
ai
m
ed
at.
T
h
is
li
n
e
co
n
s
is
ts
o
f
p
o
i
n
ts
.
T
h
e
p
o
s
itio
n
o
f
p
o
in
ts
i
s
p
lace
d
in
t
h
e
p
er
f
o
r
m
a
n
ce
f
u
n
ctio
n
.
T
h
e
to
tal
o
f
o
b
tain
ed
am
o
u
n
t
o
f
th
e
p
er
f
o
r
m
a
n
ce
f
u
n
ctio
n
o
f
p
o
in
ts
o
f
a
lin
e
s
h
o
w
s
t
h
e
p
er
f
o
r
m
an
ce
a
m
o
u
n
t
o
f
th
e
li
n
e.
T
h
e
r
o
u
te
b
et
w
ee
n
th
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
i
s
o
p
ti
m
al
w
h
en
t
h
e
p
er
f
o
r
m
a
n
ce
f
u
n
ctio
n
is
m
u
c
h
less
,
w
h
ich
ad
h
er
es b
etter
to
th
e
co
n
s
tr
ai
n
t
s
.
T
o
s
ea
r
ch
th
e
o
p
ti
m
u
m
p
o
i
n
ts
o
f
th
e
r
o
u
te
d
if
f
er
e
n
t
s
ea
r
c
h
i
n
g
m
et
h
o
d
s
m
i
g
h
tb
e
u
s
ed
.
T
w
o
r
ec
en
t
l
y
p
r
o
p
o
s
ed
m
et
h
o
d
s
,
w
h
ic
h
w
e
w
il
l
co
m
p
ar
e
o
u
r
m
e
th
o
d
w
ith
th
o
s
e,
ar
e
th
e
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
is
u
s
ed
i
n
[
8
]
,
an
d
th
e
G
A
[
1
4
]
.
T
h
is
co
m
p
ar
is
o
n
i
s
o
n
t
h
e
b
a
s
is
o
f
t
h
e
ca
lcu
la
tio
n
ti
m
e
a
n
d
b
etter
d
ir
ec
tio
n
i
n
r
eg
ar
d
to
f
u
zz
y
m
ap
.
3.
T
H
E
O
F
F
E
R
E
D
M
E
T
H
O
D
T
h
is
s
ec
tio
n
p
r
ese
n
ts
a
m
et
h
o
d
to
d
is
co
v
er
an
ap
p
r
o
p
r
iate
r
o
u
te
b
et
w
ee
n
t
h
eso
u
r
ce
an
d
d
esti
n
a
tio
n
.
Fig
u
r
e
1
s
h
o
w
s
a
s
a
m
p
le
f
u
z
z
y
m
ap
o
f
a
n
e
n
v
ir
o
n
m
e
n
t,
i
n
w
h
ic
h
ea
ch
p
o
in
t
o
f
t
h
e
m
ap
b
elo
n
g
s
to
a
f
u
zz
y
f
u
n
ctio
n
.
T
h
e
co
n
s
tr
ai
n
ts
ar
ein
s
er
ted
to
a
f
u
zz
y
f
u
n
cti
o
n
.
Dar
k
b
l
u
e
r
eg
io
n
s
ar
e
p
r
ef
er
r
ed
ar
ea
w
it
h
m
i
n
i
m
u
m
co
s
t
a
n
d
m
a
x
i
m
u
m
p
er
f
o
r
m
a
n
ce
a
n
d
th
e
r
ed
r
eg
io
n
s
b
elo
n
g
to
n
o
n
-
a
u
t
h
o
r
ized
ar
ea
s
w
i
th
m
ax
i
m
u
m
co
s
t
an
d
m
in
i
m
u
m
p
er
f
o
r
m
a
n
ce
.
I
n
Fig
u
r
e
1
p
o
in
t
A
is
co
n
s
id
er
ed
as
th
e
s
o
u
r
ce
an
d
p
o
in
t
B
as
th
e
d
esti
n
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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8
8
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8708
I
J
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C
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Vo
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7
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No
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1
,
Feb
r
u
ar
y
201
7
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3
9
2
–
401
394
Fig
u
r
e
1
.
A
h
y
p
o
th
et
ical
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v
ir
o
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e
n
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n
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icatin
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tate
m
e
n
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e
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r
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m
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,
So
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r
ce
B
an
d
au
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y
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o
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t M
3
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1
.
Dec
is
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n
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M
a
k
ing
Reg
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rding
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Alt
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e
Ro
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I
t
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p
ath
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ai
g
h
t
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A
B
.
T
h
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o
r
e
lin
e
A
B
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th
e
s
h
o
r
test
p
ath
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et
w
ee
n
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an
d
B
.
B
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t
as
s
h
o
w
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i
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ig
u
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e,
lin
e
A
B
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ass
es
t
h
r
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h
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o
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itio
n
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.
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p
ath
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o
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h
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i
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u
ir
ed
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T
h
e
p
o
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t
n
a
m
ed
M
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n
s
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er
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au
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o
in
t.
T
h
e
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e
A
M
a
n
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MB
ar
e
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cted
w
ith
t
h
e
t
wo
p
o
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ts
A
an
d
B
.
T
h
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ir
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n
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er
t
h
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A
B
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t d
o
es n
o
t p
ass
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f
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u
lt a
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I
f
F
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n
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n
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AB
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e
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s
t
o
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B
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ir
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tio
n
,
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f
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>
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AM
+FM
B
T
h
e
n
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h
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p
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t
M
i
s
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o
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ize
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h
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s
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.
B
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i
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T
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M
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t
o
p
ti
m
ize
t
h
e
co
s
t
f
u
n
ctio
n
.
T
h
e
p
er
ce
n
ta
g
e
o
f
co
s
t
f
u
n
ct
io
n
im
p
r
o
v
e
m
en
t b
y
th
e
a
u
x
iliar
y
p
o
in
t is ca
lled
OP
T
an
d
its
r
el
atio
n
is
e
x
p
lain
ed
as
f
o
llo
w
s
:
I
n
th
i
s
r
elatio
n
,
A
,
B
an
d
M
a
r
e
s
o
u
r
ce
,
d
esti
n
atio
n
an
d
a
u
x
iliar
y
p
o
in
t,
r
esp
ec
ti
v
el
y
.
I
f
O
PT
>
0
,
M
is
t
h
e
p
r
o
p
er
au
x
iliar
y
p
o
in
t
a
n
d
if
OP
T
<
0
,
th
e
au
x
iliar
y
p
o
in
t
d
o
es
n
o
t
ac
t
h
elp
f
u
ll
y
a
n
d
o
n
l
y
le
n
g
t
h
en
s
t
h
e
r
o
u
te.
I
f
M
is
in
th
e
li
n
e
A
B
,
OPT
=
0
.
I
t
s
h
o
u
ld
b
e
n
o
ted
t
h
at
v
ar
io
u
s
co
n
s
tr
ain
t
s
ar
e
a
v
a
ilab
le
in
th
e
f
i
tn
e
s
s
f
u
n
ctio
n
,
an
d
d
is
tan
ce
is
j
u
s
t
o
n
e
o
f
th
e
m
.
Fo
r
th
is
r
ea
s
o
n
,
i
n
s
o
m
e
ca
s
e
s
,
b
r
ea
k
in
g
a
lin
e
i
n
to
t
w
o
lin
es
b
y
t
h
e
au
x
i
liar
y
f
u
n
ctio
n
i
n
cr
ea
s
es
t
h
e
d
is
tan
ce
an
d
d
ec
r
ea
s
es
o
th
er
co
n
s
tr
ain
ts
o
f
t
h
e
f
i
t
n
es
s
f
u
n
ct
io
n
.
He
n
ce
,
th
e
a
m
o
u
n
t
o
f
t
h
e
to
tal
f
i
t
n
ess
f
u
n
ctio
n
g
e
n
er
all
y
d
ec
r
ea
s
es
t
h
r
o
u
g
h
t
h
e
a
u
x
iliar
y
p
o
in
t.
T
h
e
b
asic
id
ea
h
er
e
w
a
s
d
er
iv
ed
f
r
o
m
t
h
e
b
eh
a
v
io
r
o
f
a
h
u
m
a
n
w
h
e
n
e
n
co
u
n
ter
in
g
an
o
b
s
tacle
.
A
h
u
m
an
c
h
a
n
g
es
d
ir
ec
tio
n
w
h
e
n
f
ac
i
n
g
a
n
o
b
s
tacle
an
d
tr
ies
to
cr
o
s
s
f
r
o
m
o
n
e
o
f
it
s
s
id
es.
Ou
r
p
r
o
p
o
s
ed
m
et
h
o
d
is
also
th
e
s
a
m
e
i
s
h
u
m
a
n
d
ec
is
io
n
m
ak
i
n
g
.
OP
T
v
alu
e
i
n
d
icate
s
f
e
w
er
co
s
ts
,
u
s
i
n
g
t
h
e
au
x
i
liar
y
p
o
in
t.
I
f
t
h
e
v
al
u
ei
s
less
th
a
n
ze
r
o
,
it
in
d
icate
s
t
h
at
th
e
s
a
m
e
p
r
i
m
a
r
y
s
tr
aig
h
t
li
n
e
b
et
w
ee
n
th
e
t
w
o
p
o
in
ts
is
a
g
o
o
d
w
a
y
a
n
d
th
e
u
s
e
o
f
a
u
x
iliar
y
p
o
in
t d
o
es n
o
t i
m
p
r
o
v
e
th
e
r
o
u
te.
B
y
b
r
ea
k
i
n
g
a
li
n
e
a
n
d
t
u
r
n
i
n
g
it
i
n
to
t
w
o
li
n
e
s
,
an
a
u
x
il
iar
y
li
n
e
w
ill
lead
to
a
b
etter
r
o
u
te.
I
n
t
h
e
s
a
m
e
w
a
y
,
t
h
e
F
u
n
ctio
n
F
f
o
r
th
e
t
w
o
o
b
tain
ed
li
n
es
ca
n
b
e
p
er
f
o
r
m
ed
.
B
y
s
o
d
o
in
g
,
t
h
e
s
t
r
aig
h
t
lin
e
b
et
w
ee
n
th
e
t
w
o
p
o
in
t
s
o
f
s
o
u
r
ce
a
n
d
d
esti
n
atio
n
is
b
r
o
k
en
.
T
h
en
,
t
h
ese
t
w
o
lin
e
s
ar
e
co
n
v
er
ted
i
n
to
t
w
o
o
th
er
li
n
e
s
.
T
h
is
p
r
o
ce
d
u
r
e
is
co
n
tin
u
ed
u
n
til
t
h
e
len
g
t
h
o
f
t
w
o
li
n
es
b
e
co
m
e
s
m
o
r
e
th
a
n
th
e
m
i
n
i
m
u
m
a
m
o
u
n
t.
Fi
g
u
r
e
2
in
d
icate
s
th
e
r
e
s
u
l
t
f
o
r
th
e
t
wo
h
y
p
o
th
e
tical
p
o
in
t
s
.
T
h
e
r
o
u
te
b
et
w
ee
n
t
h
e
t
w
o
p
o
in
t
s
o
f
A
an
d
B
i
s
d
iv
id
ed
in
to
au
x
iliar
y
p
o
in
ts
.
I
n
f
ac
t,
th
ese
li
n
es,
w
i
th
t
h
e
h
elp
o
f
a
s
lig
h
t
d
ev
ia
tio
n
i
n
th
e
r
o
u
te,
en
ab
les
f
o
r
t
h
e
s
atis
f
ac
tio
n
o
f
t
h
e
e
v
al
u
atio
n
f
u
n
ct
io
n
.
C
las
s
ical
ar
tific
ial
in
t
ellig
e
n
ce
m
et
h
o
d
s
[
1
5
]
,
s
o
lv
i
n
g
t
h
e
p
r
o
b
le
m
s
ar
e
ca
teg
o
r
ized
to
b
o
tto
m
to
to
p
o
r
to
p
to
b
o
tto
m
m
eth
o
d
s
.
I
n
th
is
r
esear
c
h
,
o
u
r
ap
p
r
o
ac
h
is
to
p
to
b
o
tto
m
.
T
h
is
i
m
p
lies
t
h
at
t
h
e
f
ir
s
t
i
s
s
u
e
w
as
s
p
lit
in
to
t
w
o
p
ar
ts
,
w
it
h
ea
c
h
p
ar
t
f
u
r
t
h
er
d
iv
id
ed
in
to
s
m
aller
p
ar
ts
.
Fig
u
r
e
3
d
em
o
n
s
tr
ate
s
h
o
w
th
is
s
ea
r
ch
o
cc
u
r
s
.
Fi
n
d
P
ath
f
u
n
ctio
n
ta
k
es
th
e
p
o
in
ts
o
f
s
o
u
r
ce
an
d
d
e
s
tin
a
tio
n
,
a
n
d
f
i
n
d
s
th
e
n
ec
e
s
s
ar
y
a
u
x
iliar
y
p
o
i
n
ts
.
First
b
y
u
s
i
n
g
th
e
f
u
n
ctio
n
Fin
d
A
cillar
y
P
o
in
t,
th
e
a
u
x
i
liar
y
p
o
in
t
b
et
w
ee
n
t
h
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
is
d
eter
m
in
ed
.
T
h
en
T
h
e
OPT
v
alu
e
is
ca
lc
u
l
ated
.
A
lo
w
er
v
al
u
e
o
f
OP
T
is
lo
w
er
t
h
an
th
e
m
i
n
i
m
u
m
a
m
o
u
n
t
in
d
icate
s
t
h
at
b
r
ea
k
in
g
t
h
e
s
tr
ai
g
h
t
li
n
e
b
e
t
w
ee
n
t
h
e
s
o
u
r
ce
a
n
d
d
esti
n
ati
o
n
is
a
s
i
g
n
o
f
litt
le
p
r
o
f
it.
T
h
er
ef
o
r
e,
th
e
s
a
m
e
s
tr
aig
h
t
li
n
e
b
et
w
ee
n
t
h
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
i
s
a
n
n
o
u
n
ce
d
as
a
d
es
ir
ab
le
r
o
u
te.
Ho
w
e
v
er
,
if
t
h
e
a
m
o
u
n
t
i
s
m
o
r
e
th
a
n
t
h
e
m
i
n
i
m
a
l
a
m
o
u
n
t,
t
h
e
d
ir
ec
t
li
n
e
b
et
w
ee
n
t
h
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
in
to
t
w
o
l
in
e
s
is
b
r
o
k
en
w
i
th
th
e
h
elp
o
f
a
u
x
iliar
y
p
o
in
t
s
.
I
f
th
e
len
g
t
h
o
f
ea
ch
o
f
th
e
t
w
o
lin
es
i
s
m
o
r
e
th
a
n
th
e
m
i
n
i
m
al
a
m
o
u
n
t,
t
h
e
a
lg
o
r
ith
m
ca
n
b
e
r
ep
ea
ted
f
o
r
ea
c
h
o
f
t
h
e
t
w
o
b
r
o
k
e
n
l
i
n
e
s
.
I
n
f
a
ct,
th
e
s
tr
ai
g
h
t
li
n
e
b
et
w
ee
n
th
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
ca
n
b
e
d
iv
id
ed
in
to
s
u
ch
p
iece
s
t
h
at
ar
e
v
er
y
s
m
all,
an
d
th
e
b
r
ea
k
i
n
g
o
f
th
e
b
en
e
f
icia
l
p
ar
ts
b
ec
o
m
es
u
n
n
ec
e
s
s
ar
y
.
Fo
r
ex
a
m
p
le,
in
Fig
u
r
e
2
,
p
o
in
ts
A
a
n
d
B
ar
e
s
o
u
r
ce
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
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8708
O
ff
in
e/On
lin
e
Op
timu
m
R
o
u
tin
g
o
f a
UA
V
Usi
n
g
A
u
xilia
r
y
P
o
in
ts
(
A
b
b
a
s
F
a
d
a
vi
)
395
d
esti
n
atio
n
,
r
esp
ec
ti
v
el
y
.
P
o
in
t
M1
is
s
elec
ted
as
a
n
a
u
x
iliar
y
p
o
in
t
b
et
w
ee
n
t
h
ese
t
w
o
p
o
in
ts
.
A
p
o
in
t
b
et
w
ee
n
M1
a
n
d
M4
is
s
ele
cted
as
t
h
e
au
x
il
iar
y
p
o
in
t
b
et
w
ee
n
p
o
in
ts
M1
a
n
d
A
.
H
o
w
e
v
er
,
n
o
p
o
in
t
is
s
elec
ted
b
et
w
ee
n
t
h
e
p
o
in
t
s
A
an
d
M4
b
ec
au
s
e
t
h
e
s
tr
aig
h
t
l
in
e
b
et
w
ee
n
th
e
t
w
o
p
o
in
ts
is
s
u
itab
le
e
n
o
u
g
h
.
I
t
is
p
o
s
s
ib
le
to
o
b
tain
an
a
u
x
ili
ar
y
p
o
in
t
th
a
t
r
ed
u
ce
s
t
h
e
co
m
p
u
tat
io
n
al
co
s
t.
Ho
w
e
v
er
,
th
e
i
m
p
r
o
v
e
m
e
n
t
i
s
s
o
lo
w
t
h
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it
ca
n
b
e
i
g
n
o
r
ed
d
u
e
to
th
e
co
m
p
u
tatio
n
al
co
s
t.
B
et
w
ee
n
p
o
in
t
s
M4
an
d
M1
,
M2
au
x
il
iar
y
p
o
in
t
i
s
s
elec
ted
.
T
h
e
d
is
ta
n
ce
b
et
w
ee
n
t
h
e
t
w
o
p
o
in
ts
,
M4
an
d
M2
,
is
s
m
a
ll.
Fo
r
t
h
i
s
r
ea
s
o
n
,
n
o
au
x
i
liar
y
p
o
in
t
h
a
s
b
ee
n
s
elec
ted
b
et
w
ee
n
p
o
in
t
s
M1
an
d
M2
.
No
w
t
h
e
q
u
es
tio
n
i
s
h
o
w
to
s
elec
t
th
e
a
u
x
i
liar
y
p
o
in
t
i
n
t
h
e
Fin
d
Au
x
i
liar
y
P
o
in
t
f
u
n
cti
o
n
.
As
it
i
s
clea
r
f
r
o
m
p
s
e
u
d
o
co
d
e,
th
e
d
esti
n
a
tio
n
-
s
o
u
r
ce
p
o
s
itio
n
i
s
s
p
ec
if
ied
as
t
h
e
i
n
p
u
t
p
r
o
b
le
m
b
u
t
t
h
e
p
o
s
itio
n
o
f
au
x
i
liar
y
p
o
in
t
s
s
till
r
e
m
ain
s
u
n
clea
r
.
T
h
e
n
ex
t
s
ec
tio
n
ai
m
s
to
an
s
w
er
th
e
q
u
e
s
tio
n
o
f
wh
er
e
is
th
e
o
p
ti
m
al
p
o
s
itio
n
f
o
r
th
e
a
u
x
iliar
y
p
o
in
t
s
.
Fi
g
u
r
e
2.
Dis
p
la
y
i
n
g
th
e
a
u
x
i
li
ar
y
p
o
in
t b
et
w
ee
n
t
h
e
t
w
o
p
o
in
ts
o
f
s
o
u
r
ce
an
d
d
esti
n
atio
n
Fig
u
r
e
3
.
Fin
d
P
ath
f
u
n
ctio
n
ta
k
es t
h
e
p
o
in
ts
o
f
s
o
u
r
ce
an
d
d
esti
n
a
tio
n
,
an
d
f
in
d
s
th
e
n
ec
es
s
ar
y
au
x
iliar
y
p
o
in
ts
3
.
2
.
F
ind
ing
a
Su
it
a
ble A
u
x
il
ia
ry
P
o
int
T
o
s
ea
r
ch
f
o
r
th
e
au
x
iliar
y
p
o
in
t,
th
er
e
is
n
ee
d
to
li
m
it
th
e
s
ea
r
c
h
s
p
ac
e.
E
m
p
ir
ical
l
y
,
it
w
a
s
d
is
co
v
er
ed
th
at
t
h
e
o
p
ti
m
al
a
u
x
iliar
y
p
o
in
t
i
s
lo
ca
ted
b
et
w
ee
n
t
h
eso
u
r
ce
a
n
d
d
esti
n
atio
n
.
I
n
Fi
g
u
r
e
4
,
p
o
in
t
A
is
th
e
s
o
u
r
ce
an
d
B
is
th
e
d
est
in
atio
n
.
I
n
t
h
e
f
ir
s
t
ass
u
m
p
t
io
n
,
th
e
s
q
u
ar
e
R
SP
Q
w
er
e
co
n
s
id
er
ed
an
d
th
e
th
e
au
x
i
liar
y
p
o
in
t
w
as
as
s
u
m
ed
i
n
th
i
s
r
ec
tan
g
le.
T
h
e
le
n
g
t
h
o
f
R
Q
a
n
d
SP
is
h
al
f
o
f
A
B
a
n
d
is
p
er
p
en
d
icu
lar
to
A
B
.
A
s
s
ee
n
i
n
t
h
e
p
r
ev
io
u
s
s
ec
tio
n
,
th
e
d
i
s
co
v
er
y
o
f
th
e
c
o
o
r
d
in
ates
o
f
th
e
a
u
x
iliar
y
p
o
in
t
w
h
ich
ca
n
b
r
ea
k
th
e
d
ir
ec
t
lin
e
i
n
to
t
w
o
n
e
w
l
i
n
es,
an
d
ca
u
s
e
t
h
e
lar
g
e
s
t
d
ec
lin
e
i
n
th
e
v
al
u
e
o
f
t
h
e
co
s
t
f
u
n
ctio
n
w
as
ai
m
ed
at.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
1
,
Feb
r
u
ar
y
201
7
:
3
9
2
–
401
396
T
h
is
s
ec
tio
n
tr
ies
to
d
ea
l
w
it
h
h
o
w
to
s
ea
r
ch
f
o
r
th
e
a
u
x
il
ia
r
y
p
o
in
t
M
i
n
t
h
e
R
SP
Q
r
ec
tan
g
le.
T
o
d
o
th
is
,
v
ar
io
u
s
m
et
h
o
d
s
ar
e
u
s
ed
.
3
.
2
.
1
.
F
ull
Sea
rc
h M
et
ho
d
I
n
t
h
e
Fu
ll
s
ea
r
c
h
m
et
h
o
d
,
all
p
o
s
s
ib
le
ca
s
es
ar
e
ex
a
m
i
n
ed
.
T
o
f
in
d
t
h
e
a
u
x
iliar
y
p
o
in
t,
t
h
e
p
o
in
t
s
in
s
id
e
t
h
e
r
ec
tan
g
le
ar
e
s
ea
r
ch
ed
to
f
in
d
th
e
b
est a
u
x
i
li
ar
y
p
o
in
t.
I
n
th
is
w
a
y
,
th
r
o
u
g
h
ex
a
m
i
n
i
n
g
all
th
e
p
o
in
t
s
in
s
id
e
th
e
r
ec
tan
g
le
an
d
t
h
eir
OP
T
ca
lcu
latio
n
,
t
h
e
p
o
in
t M
is
s
elec
ted
o
n
t
h
e
b
asi
s
o
f
m
a
x
i
m
ized
OP
T
.
T
h
is
w
il
l b
est h
elp
in
t
h
e
d
is
co
v
er
y
o
f
th
e
au
x
iliar
y
p
o
in
t,
b
u
t th
e
co
m
p
u
tatio
n
al
co
s
t is
v
er
y
h
i
g
h
.
3
.
2
.
2
.
Usi
ng
P
SO
T
o
allev
iate
th
is
p
r
o
b
le
m
,
P
SO
[
1
6
]
m
et
h
o
d
ca
n
b
e
u
s
ed
.
T
h
is
m
et
h
o
d
co
n
s
i
s
ts
o
f
a
s
et
o
f
p
ar
ticles,
w
it
h
ea
ch
o
n
e
lo
o
k
i
n
g
f
o
r
an
o
p
tim
a
l
s
o
lu
tio
n
.
I
n
itiall
y
,
ea
ch
o
f
th
e
p
ar
ticles
ch
o
o
s
es
an
an
s
w
er
r
an
d
o
m
l
y
.
T
h
en
,
b
y
c
h
ec
k
i
n
g
t
h
e
a
n
s
w
er
s
an
d
co
n
s
u
lti
n
g
t
h
e
p
ar
ticles,
th
e
y
m
o
v
e
to
th
e
b
etter
a
n
s
wer
.
Usi
n
g
e
v
er
y
b
it
o
f
its
o
w
n
e
x
p
er
ien
ce
a
n
d
th
e
b
est ex
p
er
ien
ce
o
f
all
t
h
e
p
ar
ti
cles,
p
ar
ticles ca
n
m
o
v
e
b
etter
.
Fig
u
r
e
4
.
T
h
e
p
o
in
ts
A
an
d
B
ar
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
p
o
in
ts
.
Sear
c
h
s
p
ac
e
r
ec
tan
g
le
li
m
it
s
th
e
a
u
x
iliar
y
p
o
in
ts
.
T
h
e
len
g
t
h
o
f
r
ec
ta
n
g
le
eq
u
als th
e
d
is
tan
ce
o
f
th
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
a
n
d
th
e
w
i
d
th
o
f
th
e
r
ec
tan
g
le
i
s
h
al
f
o
f
i
t
T
h
e
p
o
s
itio
n
o
f
t
h
e
s
u
g
g
este
d
au
x
iliar
y
p
o
in
t
in
t
h
e
t
w
o
-
d
i
m
en
s
io
n
al
s
p
ac
e
is
co
n
s
id
e
r
ed
as
t
h
e
an
s
w
er
s
p
ec
if
icatio
n
s
o
f
ea
c
h
p
ar
ticle
an
d
t
h
e
p
o
in
ts
in
s
id
e
t
h
e
R
SP
Q
r
ec
ta
n
g
le
as
th
e
s
ea
r
ch
s
p
ac
e.
A
b
etter
p
o
s
itio
n
is
o
n
e
w
h
ic
h
b
etter
s
atis
f
ies
r
o
u
tin
g
co
n
s
tr
ai
n
ts
.
So
m
e
p
o
in
t
s
b
ec
o
m
e
ca
n
d
id
ates
in
t
h
e
s
ea
r
ch
s
p
ac
e
r
an
d
o
m
l
y
.
T
h
e
n
,
t
h
r
o
u
g
h
P
S
O
p
o
s
itio
n
,
t
h
ese
p
o
in
ts
ar
e
o
p
ti
m
ized
to
b
e
ab
le
to
f
i
n
d
th
e
o
p
ti
m
al
a
u
x
iliar
y
p
o
in
t.
I
f
an
au
x
il
iar
y
p
o
in
t c
o
u
ld
n
o
t b
e
f
o
u
n
d
af
ter
s
ev
er
al
r
e
p
etitio
n
s
,
t
h
e
s
ea
r
ch
w
i
ll b
e
s
t
o
p
p
ed
.
3
.
3
.
T
he
Use o
f
P
er
pend
icula
r
E
m
p
ir
icall
y
,
it
w
as
d
is
co
v
er
ed
th
at
th
e
o
p
tim
a
l
au
x
iliar
y
p
o
in
t
is
m
o
s
tl
y
ar
o
u
n
d
o
r
o
n
th
e
p
er
p
en
d
icu
lar
lin
e
co
n
n
ec
ti
n
g
th
e
s
o
u
r
ce
a
n
d
d
esti
n
atio
n
.
T
h
er
ef
o
r
e,
w
e
ass
u
m
ed
t
h
at
t
h
e
a
u
x
i
liar
y
p
o
in
t i
s
o
n
th
e
p
er
p
en
d
ic
u
lar
li
n
e
o
f
A
B
.
T
h
is
a
s
s
u
m
p
tio
n
co
u
ld
o
n
l
y
lo
o
k
o
n
a
p
er
p
en
d
icu
lar
li
n
e
t
o
f
i
n
d
a
n
a
u
x
il
iar
y
p
o
in
t.
T
h
e
len
g
th
o
f
t
h
e
p
er
p
e
n
d
icu
lar
is
li
m
ited
to
h
al
f
o
f
A
B
s
u
c
h
as
R
S
an
d
P
Q.
B
y
s
o
d
o
in
g
,
th
e
ch
ec
k
in
g
p
o
in
ts
ar
e
g
r
ea
tl
y
r
ed
u
ce
d
.
4.
T
H
E
R
E
SU
L
T
S O
F
SI
M
UL
AT
I
O
N
I
n
th
i
s
s
ec
t
io
n
,
t
h
e
r
esu
lts
o
f
p
r
ef
o
r
m
i
n
g
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
p
r
esen
ted
i
n
a
r
ea
l
en
v
ir
o
n
m
en
t.
T
h
e
co
n
s
id
er
ed
en
v
ir
o
n
m
e
n
t
i
n
t
h
e
p
r
o
b
lem
is
t
h
e
r
ea
l
e
n
v
i
r
o
n
m
e
n
t
i
n
E
lb
u
r
z
Mo
u
n
tai
n
s
.
T
h
e
d
im
e
n
s
io
n
o
f
th
e
en
v
ir
o
n
m
e
n
t
i
s
1
8
,
0
0
0
b
y
4
5
,
0
0
0
,
w
it
h
t
h
e
ac
cu
r
ac
y
o
f
9
0
s
q
u
ar
e
m
eter
s
.
A
s
p
r
ese
n
t
ed
in
[
1
4
]
th
e
f
u
zz
y
m
ap
is
a
m
atr
i
x
o
f
2
0
0
b
y
5
0
0
.
E
ac
h
p
o
in
t
i
n
t
h
e
m
a
tr
ix
p
r
es
en
ted
a
d
ef
i
n
ite
p
er
f
o
r
m
an
ce
f
u
n
ct
io
n
s
ac
co
r
d
in
g
to
th
e
th
r
ee
s
p
ec
i
f
ied
co
n
s
tr
ai
n
ts
.
T
h
e
o
f
ier
ed
alg
o
r
ith
m
w
as
i
m
p
le
m
en
ted
o
n
M
A
T
L
A
B
s
o
f
t
w
ar
e.
I
n
ea
ch
ex
p
er
i
m
en
t,
th
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
w
er
e
m
ad
e
clea
r
b
y
th
e
u
s
er
a
n
d
t
h
e
o
f
ier
ed
a
lg
o
r
ith
m
a
n
n
o
u
n
ce
d
t
h
e
te
s
t
r
esu
lt
s
as
a
n
o
u
tp
u
t
ac
co
r
d
in
g
to
th
e
p
er
f
o
r
m
a
n
ce
f
u
n
ctio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
O
ff
in
e/On
lin
e
Op
timu
m
R
o
u
tin
g
o
f a
UA
V
Usi
n
g
A
u
xilia
r
y
P
o
in
ts
(
A
b
b
a
s
F
a
d
a
vi
)
397
4
.
1
.
Det
er
m
i
nin
g
t
he
Ro
ute
by
A
ux
ilia
ry
P
o
ints
Fig
u
r
e
5
an
d
Fig
u
r
e
6
s
h
o
w
,
t
h
e
r
o
u
tes
o
f
a
U
A
V
i
n
t
w
o
d
i
f
ier
en
t
e
n
v
ir
o
n
m
en
t
s
an
d
d
if
ie
r
en
t
f
u
zz
y
m
ap
s
.
T
h
e
r
o
u
tes
h
a
v
e
b
ee
n
i
d
en
tifie
d
b
y
a
u
x
iliar
y
p
o
in
ts
ac
co
r
d
in
g
to
th
e
m
eth
o
d
d
esc
r
ib
ed
in
3
.
2
.
T
h
ese
au
x
i
liar
y
p
o
i
n
ts
w
er
e
d
eter
m
i
n
ed
b
y
t
h
e
F
u
ll
s
ea
r
ch
m
e
th
o
d
.
B
o
th
f
i
g
u
r
es
r
elate
d
to
f
u
zz
y
m
ap
ar
e
m
en
t
io
n
ed
an
d
h
av
e
d
i
f
ier
en
t r
o
u
tes.
As
o
b
s
er
v
ed
f
r
o
m
Fi
g
u
r
e
5
a
n
d
Fi
g
u
r
e
6
,
t
h
e
r
o
u
te
o
f
m
o
v
e
m
e
n
t
w
as
d
eter
m
in
ed
b
y
t
h
e
au
x
iliar
y
p
o
in
t.
T
h
is
i
m
p
lies
t
h
at
t
h
e
s
tr
aig
h
t lin
e
b
et
w
ee
n
t
h
e
s
o
u
r
ce
an
d
d
esti
n
at
io
n
is
b
r
o
k
e
n
b
y
a
u
x
i
liar
y
p
o
in
t
s
.
Fig
u
r
e
5
.
T
h
e
au
x
iliar
y
p
o
in
ts
d
eter
m
in
ed
b
y
t
h
e
F
u
ll se
ar
c
h
m
et
h
o
d
th
e
b
lack
p
o
in
t
s
ar
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
an
d
t
h
e
r
ed
p
o
in
ts
t
h
e
au
x
iliar
y
p
o
in
ts
Fig
u
r
e
6
.
T
h
e
au
x
iliar
y
p
o
in
ts
d
eter
m
in
ed
b
y
t
h
e
F
u
ll sear
c
h
m
et
h
o
d
th
e
b
lack
p
o
in
t
s
ar
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
an
d
t
h
e
r
ed
p
o
in
ts
th
e
au
x
iliar
y
p
o
in
ts
T
o
ex
a
m
i
n
e
th
e
o
p
ti
m
iza
tio
n
a
m
o
u
n
t
b
y
au
x
il
iar
y
p
o
in
ts
,
t
h
e
f
o
llo
w
i
n
g
r
elatio
n
is
ex
p
r
e
s
s
ed
as
th
e
m
o
s
t c
o
m
p
lete
o
n
e:
(
1
)
n
is
th
e
n
u
m
b
er
o
f
s
e
g
m
en
t
s
i
n
to
w
h
ich
th
e
l
in
e
A
B
i
s
d
iv
i
d
ed
.
Fo
r
f
u
r
th
er
e
x
a
m
in
at
io
n
,
1
0
0
p
air
s
o
f
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o
u
r
ce
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d
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esti
n
a
tio
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t
s
w
er
e
c
o
n
s
id
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ed
r
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d
o
m
l
y
an
d
t
h
e
a
m
o
u
n
t
o
f
av
er
a
g
e
OP
T
is
r
ep
o
r
ted
in
th
e
eq
u
atio
n
(
1
)
.
T
h
is
n
u
m
b
er
in
d
icate
d
th
e
p
o
s
itiv
e
ef
f
ec
t o
f
u
s
in
g
t
h
e
au
x
iliar
y
p
o
i
n
ts
i
n
d
eter
m
i
n
i
n
g
t
h
e
s
u
itab
le
r
o
u
te.
4
.
2
.
Det
er
m
i
nin
g
t
he
Au
x
ilia
ry
P
o
ints
by
P
SO
T
h
e
test
f
o
r
th
e
s
a
m
e
s
o
u
r
ce
,
d
esti
n
atio
n
an
d
en
v
ir
o
n
m
e
n
ts
o
f
th
e
p
r
ev
io
u
s
p
ar
t
w
as
r
ep
ea
ted
.
T
h
e
d
if
f
er
e
n
ce
w
a
s
th
e
i
n
th
e
d
et
er
m
in
a
tio
n
o
f
th
e
a
u
x
iliar
y
p
o
in
t
b
y
P
SO.
T
h
e
au
x
iliar
y
p
o
in
t
o
b
tain
ed
f
r
o
m
s
ea
r
ch
i
n
g
all
t
h
e
p
o
in
ts
w
as
t
h
e
b
est
a
v
ailab
le
au
x
iliar
y
p
o
in
t.
Ho
w
e
v
er
,
t
h
e
au
x
il
iar
y
p
o
in
t
o
b
tain
ed
f
r
o
m
P
SO
w
a
s
o
n
e
o
f
t
h
e
b
est
av
a
ilab
le
au
x
iliar
y
p
o
in
t
s
.
Fo
r
t
h
is
r
ea
s
o
n
,
t
h
e
o
b
tain
ed
OP
T
o
f
F
u
ll
s
ea
r
ch
w
a
s
d
if
f
er
e
n
t f
r
o
m
th
e
OP
T
o
b
tain
ed
f
r
o
m
P
SO.
T
h
e
n
u
m
b
er
o
f
p
ar
ticles
w
a
s
s
et
as
1
0
.
T
h
e
ex
p
er
i
m
e
n
t
w
a
s
r
ep
ea
ted
1
0
0
tim
es.
T
h
e
m
ea
n
v
a
lu
e
o
b
tain
ed
b
y
t
h
e
au
x
il
iar
y
p
o
in
t
w
it
h
P
SO
w
as
p
r
esen
ted
in
tab
le
1
.
A
s
it
is
clea
r
,
t
h
is
a
m
o
u
n
t
w
as
le
s
s
t
h
a
n
th
e
F
u
ll sear
c
h
OP
T
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
1
,
Feb
r
u
ar
y
201
7
:
3
9
2
–
401
398
On
e
o
f
t
h
e
m
a
in
f
ac
to
r
s
i
n
th
e
s
ea
r
ch
alg
o
r
it
h
m
is
t
h
e
s
ea
r
ch
ti
m
e.
I
n
o
r
d
er
to
p
er
f
o
r
m
th
e
alg
o
r
ith
m
o
n
lin
e,
t
h
e
s
ea
r
c
h
ti
m
e
s
h
o
u
ld
b
e
r
ed
u
ce
d
as
m
in
i
m
u
m
as
p
o
s
s
ib
le.
I
n
t
h
is
ar
ticle
t
h
e
a
v
er
ag
e
s
ea
r
ch
ti
m
e
f
o
r
f
i
n
d
in
g
t
h
e
r
o
u
tes
ar
e
p
r
esen
t
ed
f
o
r
d
if
f
er
en
t
s
ea
r
ch
in
g
m
e
th
o
d
s
.
Fo
r
b
et
ter
co
m
p
ar
is
o
n
av
er
ag
e
s
ea
r
c
h
i
n
g
ti
m
e
o
f
th
e
t
h
e
a
u
x
i
liar
y
p
o
in
t
m
et
h
o
d
w
it
h
f
u
ll
s
ea
r
ch
in
t
h
e
r
ec
tan
g
le
w
a
s
co
n
s
id
er
ed
as
r
ef
er
en
ce
an
d
o
t
h
er
m
et
h
o
d
ar
e
co
m
p
ar
ed
w
it
h
t
h
i
s
r
ef
er
e
n
ce
.
T
ab
le
1
s
h
o
w
s
t
h
at
s
ea
r
ch
ti
m
e
w
i
th
P
SO
i
n
t
h
e
s
a
m
e
r
ec
ta
n
g
le
is
o
n
l
y
0
.
0
6
o
f
th
e
f
u
ll
s
ea
r
ch
m
e
th
o
d
.
4
.
3
.
Det
er
m
i
nin
g
t
he
Au
x
ilia
ry
P
o
ints
o
n t
he
P
er
pend
icu
la
r
T
h
e
ex
p
er
im
e
n
t
w
a
s
r
ep
ea
ted
f
o
r
th
e
s
a
m
e
s
o
u
r
ce
a
n
d
d
est
in
atio
n
a
n
d
th
e
p
r
ev
io
u
s
e
n
v
i
r
o
n
m
e
n
ts
,
w
it
h
th
e
ex
ce
p
tio
n
t
h
at
t
h
e
a
u
x
i
liar
y
p
o
in
t
o
n
t
h
e
p
er
p
en
d
icu
lar
li
n
e
co
n
n
ec
t
in
g
t
h
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
w
a
s
d
eter
m
in
ed
.
OP
T
v
alu
e
o
b
tain
ed
w
it
h
t
h
e
a
u
x
iliar
y
p
o
in
ts
o
n
t
h
e
p
er
p
en
d
ic
u
lar
li
n
e
i
s
s
h
o
w
n
i
n
tab
le
1
.
As it is cle
ar
,
th
is
v
a
lu
e
w
a
s
le
s
s
t
h
an
F
u
ll
s
ea
r
ch
OP
T
.
Sear
c
h
ti
m
e
d
u
r
atio
n
i
s
s
h
o
w
n
i
n
ta
b
le
1.
4
.
4
.
A
Co
m
pa
ri
s
o
n o
f
t
he
T
hree
M
e
t
ho
ds
o
f
Sea
rc
hin
g
Aux
ili
a
ry
P
o
ints
T
h
r
ee
m
et
h
o
d
s
in
an
e
n
v
ir
o
n
m
en
t
w
it
h
th
e
s
p
ec
i
f
ied
s
o
u
r
c
e
an
d
d
esti
n
atio
n
w
a
s
p
er
f
o
r
m
ed
,
an
d
th
e
r
esu
lt
s
s
h
o
w
n
w
i
th
d
i
f
f
er
en
t
c
o
lo
r
s
in
Fi
g
u
r
e
7
.
A
s
i
t
is
cle
ar
f
r
o
m
Fi
g
u
r
e
7
,
all
th
r
ee
m
eth
o
d
s
r
ea
ch
ed
t
h
e
an
s
w
er
,
b
u
t e
ac
h
w
it
h
d
if
f
er
en
t r
o
u
tes.
Fig
u
r
e
7
.
R
o
u
tes r
u
n
n
i
n
g
t
h
e
F
u
ll sear
c
h
,
P
SO,
an
d
th
e
p
er
p
en
d
icu
lar
m
et
h
o
d
s
ar
e
s
h
o
w
n
b
y
th
e
co
lo
r
s
r
ed
,
g
r
ee
n
a
n
d
b
lack
,
r
esp
ec
tiv
el
y
4
.
5
.
T
he
P
ro
ba
bil
it
y
o
f
t
he
O
pti
m
a
l
A
ux
i
lia
ry
P
o
int
being
Aro
un
d
t
he
P
er
p
endic
ula
r
L
i
ne
Co
nn
ec
t
ing
So
urce
a
nd
Dest
ina
t
io
n
Fig
u
r
e
8
illu
s
tr
ates
t
h
e
r
atio
o
f
th
e
d
is
tan
ce
to
t
h
e
p
er
p
en
d
icu
lar
lin
e
to
t
h
e
d
is
ta
n
ce
b
et
w
ee
n
t
h
e
s
o
u
r
ce
an
d
d
es
tin
a
tio
n
i
n
ter
m
s
o
f
p
er
ce
n
ta
g
e.
E
ac
h
b
ar
o
f
t
h
e
f
i
g
u
r
e
r
ep
r
esen
ts
t
h
e
te
n
p
er
ce
n
t
to
tal
o
f
th
e
v
alu
e
s
.
Fo
r
ex
a
m
p
le;
t
h
e
t
h
ir
d
b
ar
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
p
o
in
ts
w
h
o
s
e
p
er
ce
n
ta
g
e
is
b
et
w
ee
n
2
0
an
d
2
9
.
As
it
i
s
clea
r
f
r
o
m
Fi
g
u
r
e
8
,
th
e
co
n
ce
n
tr
atio
n
o
f
o
p
ti
m
al
a
u
x
i
liar
y
p
o
in
t
is
m
o
r
e
ar
o
u
n
d
th
e
p
er
p
en
d
icu
lar
.
T
h
e
v
alu
e
o
f
ze
r
o
f
o
r
th
e
p
o
in
ts
m
ea
n
s
t
h
at
th
e
y
ar
e
o
n
th
e
p
er
p
en
d
icu
lar
.
I
n
o
r
d
er
t
o
ex
a
m
i
n
e
f
e
w
er
p
o
in
t
s
,
th
e
p
o
in
ts
o
n
th
e
p
er
p
en
d
icu
la
r
in
s
tead
o
f
t
h
ep
o
in
t a
r
o
u
n
d
it
ar
e
co
n
s
id
er
ed
.
Fig
u
r
e
8
.
th
e
r
atio
o
f
th
e
d
is
ta
n
ce
to
th
e
p
er
p
en
d
icu
lar
li
n
e
t
o
th
e
d
is
tan
ce
b
et
w
ee
n
th
e
s
o
u
r
ce
an
d
d
esti
n
atio
n
in
p
er
ce
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
O
ff
in
e/On
lin
e
Op
timu
m
R
o
u
tin
g
o
f a
UA
V
Usi
n
g
A
u
xilia
r
y
P
o
in
ts
(
A
b
b
a
s
F
a
d
a
vi
)
399
4
.
6
.
A
Co
m
pa
riso
n
w
it
h o
t
her
M
et
ho
ds
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
w
as
co
m
p
ar
ed
w
it
h
t
h
e
t
w
o
m
et
h
o
d
s
o
f
P
SO
[
8
]
an
d
GA
[
1
4
]
.
Fo
r
t
h
is
r
ea
s
o
n
all
th
e
t
h
r
ee
m
e
th
o
d
s
w
er
e
r
u
n
a
h
u
n
d
r
ed
ti
m
es
i
n
d
i
f
f
er
en
t
e
n
v
ir
o
n
m
en
t
s
a
n
d
w
it
h
d
i
f
f
er
en
t
s
o
u
r
ce
s
an
d
d
esti
n
atio
n
s
.
I
n
th
is
p
ap
er
,
th
e
o
f
f
er
ed
m
eth
o
d
ti
m
e
w
a
s
c
o
n
s
id
er
ed
as
t
h
e
r
ef
er
e
n
ce
v
al
u
e
it
w
a
s
co
m
p
ar
ed
w
it
h
t
h
e
ti
m
e
s
o
b
tain
ed
f
r
o
m
o
th
e
r
m
et
h
o
d
s
.
T
ab
.
1
s
h
o
w
s
th
e
av
er
ag
e
o
f
th
e
o
b
tain
ed
r
es
u
lts
.
T
o
im
p
le
m
en
t
P
SO
th
e
s
a
m
e
s
etti
n
g
s
as
s
p
ec
if
ied
in
r
ef
er
e
n
ce
[
8
]
w
er
e
u
s
e
d
.
I
n
s
o
m
e
i
m
p
le
m
e
n
tatio
n
s
P
SO
is
ca
u
g
h
t
i
n
th
e
lo
ca
l
m
i
n
i
m
u
m
an
d
v
i
s
u
al
l
y
s
p
ec
if
ied
as
f
ail
in
g
to
r
ea
c
h
a
s
atis
f
ac
to
r
y
s
o
lu
t
io
n
.
Fu
r
t
h
er
i
m
p
le
m
en
ta
tio
n
o
f
P
SO in
th
i
s
ca
s
e
d
o
es
n
o
t
h
av
e
a
g
o
o
d
r
es
u
lt.
T
o
allev
iate
th
e
p
r
o
b
lem
,
t
h
e
n
u
m
b
er
o
f
p
ar
ti
cles
w
a
s
i
n
cr
ea
s
ed
.
T
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9
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Feb
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9
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401
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CO
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ti
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s,
IEE
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T
ra
n
sa
c
ti
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,
v
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l.
41
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p
.
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[6
]
L
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ip
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.
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u
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ri,
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.
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g
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"
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l.
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p
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.
[7
]
I.
K.
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.
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.
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a
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n
is,
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.
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T
so
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sta
ra
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[8
]
J.J.
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2
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3
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lso
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4
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stra
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ter
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a
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p
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5
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ss
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ll
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o
rv
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A
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telli
g
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n
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m
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6
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h
i
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n
s
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v
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l.
2
,
p
p
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-
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,
2
0
0
4
.
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Evaluation Warning : The document was created with Spire.PDF for Python.