Geography Reference
In-Depth Information
∈
E
2
A
1
,A
2
,P
0
P
Fig. 8.11.
Fundamental perspective graph.
P
∈
E
2
∪
P
P
c
P
0
P
A
1
1
− E
2
sin
2
Φ
A
1
1
− E
2
sin
2
Φ
=
cos
Φ
cos
Λ
−
cos
Φ
0
cos
Λ
0
,
Y
P
− Y
0
=
A
1
A
1
1
1
=
cos
Φ
sin
Λ
−
cos
Φ
0
sin
Λ
0
,
(8.91)
E
2
sin
2
Φ
E
2
sin
2
Φ
0
−
−
Z
P
−
Z
0
=
E
2
)
E
2
)
A
1
(1
−
A
1
(1
−
1
1
=
sin
Φ
−
sin
Φ
0
.
E
2
sin
2
Φ
E
2
sin
2
Φ
0
−
−
Substituting
g, h
,and
k
into the basic formula for the radial coordinate
r, r
is obtained as follows:
X
c
−
X
0
r
=
X
c
−
X
P
2
+
X
c
−
X
0
2
−
X
P
−
X
0
2
×
(8.92)
×
4
X
c
−
X
P
X
c
−
X
0
−
[
X
c
−
X
P
2
+
X
c
−
X
0
−
X
P
−
X
0
2
]
2
.
2
2
2
Substitute the transformation of surface normal ellipsoidal coordinates
{Λ, Φ}
,
{Λ
0
,Φ
0
,H
0
(
Λ
c
,
Φ
c
)
to the corresponding Cartesian coordinates, and you receive the new
curvilinear representation of the radial coordinates.
}
.and
{
Λ
0
,Φ
0
,H
=0
}
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