Geography Reference
In-Depth Information
x
=
x
(
Λ, Φ
)=
RΛ
cos
Φ
f
(
Φ
)
=
R
2
Λ
cos
Φ
,
d
y
d
Φ
(13.9)
y
=
y
(
Φ
)=
Rf
(
Φ
)
,
Λ
S
=
1
2
f
4
(
Λ
2
f
2
sin
2
Φ
+
f
6
+
f
2
+
Λ
2
f
2
cos
2
Φ
+2
Λ
2
f
f
sin
Φ
cos
Φ
)
=
±
(13.10)
1
4
f
8
(
Λ
2
f
2
sin
2
Φ
+
f
6
+
f
2
+
Λ
2
f
2
cos
2
Φ
+2
Λ
2
f
f
sin
Φ
cos
Φ
)
2
±
−
1
,
(
Λ
S
)
1
,
2
=
√
2
2
2+
Λ
2
sin
2
Φ
+
Λ
sin
Φ
4+
Λ
2
sin
2
Φ,
=
±
(
Λ
S
)
3
,
4
=
(13.11)
√
2
2
2+
Λ
2
sin
2
Φ
Λ
sin
Φ
4+
Λ
2
sin
2
Φ.
=
±
−
13-2 Special Mapping Equations
Special mapping equations for pseudo-cylindrical equal area mappings of the sphere. Sinu-
soidal pseudo-cylindrical mapping, elliptic pseudo-cylindrical mapping, parabolic pseudo-
cylindrical mapping, rectilinear pseudo-cylindrical mapping.
The special mapping equations to be considered are the mapping equations of the sinusoidal
pseudo-cylindrical mapping, the elliptic pseudo-cylindrical mapping, the parabolic pseudo-
cylindrical mapping, and the rectilinear pseudo-cylindrical mapping. Let us study these special
mapping equations in the sections that follow.
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