Geography Reference
In-Depth Information
been worked out, but it is lengthy and does not offer too much of an insight. Instead we have
dealt with the integral (
23.114
)by
numerical integration.
Box 23.24 (The generic steps of a map projection for a given structure of the map (
23.99
)of
type circular cylinder
C
2
g
(
V
)
).
The left Jacobi map
J
l
=
x
U
x
V
=
g
V
0
0
(23.100)
y
U
y
V
f
subject to the orientation conservation
|J
l
|
=
x
U
y
V
− x
V
y
U
>
0
↔ f
>
0
(23.101)
The left Cauchy-Green map
(23.102)
C
l
:
J
l
G
r
J
l
=
g
2
V
0
0
=
a
2
[
f
2
(
n
+1)
]
n
/
(
n
+1) 0
0
n
(23.103)
f
2
subject to the right metric tensor G
r
=
I
2
of the developed circular cylinder
The general eigenvalue problem
(23.104)
C
l
−
Λ
2
G
l
= 0
(23.105)
subject to left metric of the church tower of the onion shape
G
l
=
g
2
(
V
)
0
(23.106)
g
2
(
V
)+
h
2
(
V
)
0
subject to
g
(
V
)=
acos
n−
1
V
[
cos
2
V
(
n
+1)
−
n
]
h
(
V
)=(
n
+1)
cos
n
VsinV
(23.107)
G
11
=
g
2
(
V
)=
a
2
cos
2
n
Vsin
2
V
G
12
= 0
(23.108)
G
22
=
g
2
(
V
)+
h
2
(
V
)=
cos
2(
n−
1)
V
(
n
+1)
2
cos
2
Vsin
2
V
+
α
2
[
cos
2
V
(
n
+1)
n
]
2
−
Λ
2
G
l
=
g
2
V
C
l
Λ
2
g
2
(
V
)
−
0
−
=0
↔
(23.109)
f
2
− Λ
2
(
g
2
(
V
)+
h
2
(
V
))2
0
g
V
g
(
V
)
=
[
n/
(
n
+1)]
n/
2
1
cos
n
VsinV
Λ
1
=
√
n
+1
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