Geography Reference
In-Depth Information
Box 15.9 (Optimal dilatation factor for a Universal Transverse Mercator mapping of an
ellipsoid-of-revolution
E
A
1
,A
2
according to
Grafarend
(
1995
, pp. 459-461),
l
E
:=
L
−
L
0
eastern longitude difference,
B
S
and
B
N
southern latitude and northern latitude).
Strip width [
−
l
E
,l
E
]
×
[
B
S
,B
N
] :
Optimal dilatation factor:
3
.
5
◦
,
+3
.
5
◦
]
[80
◦
,
84
◦
]
,
[
−
×
0
.
999578
,
(15.111)
2
◦
,
+2
◦
]
[80
◦
,
80
◦
]
,
[
−
×
0
.
999864
.
As outlined by
Grafarend et al.
(
1996
, pp. 279-284), the inversion of the bivariate homoge-
neous conformal polynomial (
15.109
)and(
15.110
) leads us to the bivariate homogenous polyno-
mial (
15.112
)and(
15.113
) with coecients
{
l
ij
,b
ij
}
summarized in Box
15.11
.
l
1
=
L
−
L
01
=
y
1
ρ
− y
0
+
l
30
x
1
3
=
l
10
x
1
ρ
+
l
11
x
1
+
(15.112)
ρ
ρ
y
1
ρ
−
y
0
2
+
l
12
x
1
+O
4
l
,
ρ
b
1
=
B
−
B
01
=
=
b
01
y
1
y
0
+
b
20
x
1
ρ
2
+
b
02
y
1
y
0
2
ρ
−
ρ
−
+
(15.113)
+
b
21
x
1
ρ
2
y
1
ρ
− y
0
+
b
03
y
1
ρ
− y
0
3
+O
4
b
.
Box 15.10 (Meridian arc
y
0
=
M
(
B
0
)).
y
0
=
A
1
(1
− E
2
)
B
0
0
E
2
sin
2
B
)
3
/
2
=
A
1
B
0
1
−
d
B
1
3
4
E
2
64
E
4
−
(1
−
16384
E
8
5
175
256
E
6
−
−
−
8
E
2
1+
1
512
E
6
sin 2
B
0
3
4
E
2
+
15
35
128
E
4
−
−
256
E
4
1+
3
64
E
4
sin 4
B
0
+
15
4
E
2
+
35
−
(15.114)
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