Geography Reference
In-Depth Information
14-31 Special Normal Cylindric Mapping (Equidistant: Equator, Set
of Meridian Circles)
We start off by the postulate of an equidistant mapping on the set of parallel circles. This leads
to the following result.
d
f
=
F
2
(
Φ
)+
G
2
(
Φ
)d
Φ,
f
(
Φ
)
F
2
(
Φ
)+
G
2
(
Φ
)
=1
Λ
2
=1
⇒
⇔
(14.50)
f
(
Φ
)=
Φ
0
F
2
(
Φ
)+
G
2
(
Φ
)d
Φ
+const
., f
(0) = 0
⇒
const
.
=0
,
=
, Λ
1
=
F
(0)
x
y
F
(0)
Λ
0
F
2
(
Φ
)+
G
2
(
Φ
)d
Φ
F
(
Φ
)
, Λ
2
=1
.
(14.51)
14-32 Special Normal Conformal Cylindric Mapping (Equidistant:
Equator)
Alternatively, let us start off by the postulate of a conformal mapping. Similar as before, this
leads to the following result.
d
f
=
F
(0)
F
2
(
Φ
)+
G
2
(
Φ
)
F
(
Φ
)
f
(
Φ
)
F
(0)
F
(
Φ
)
=
F
2
(
Φ
)+
G
2
(
Φ
)
⇔
Λ
1
=
Λ
2
⇒
d
Φ,
(14.52)
F
2
(
Φ
)+
G
2
(
Φ
)
F
(
Φ
)
f
(
Φ
)=
Φ
0
d
Φ
+const
., f
(0) = 0
F
(0)
⇒
const
.
=0
,
=
F
(0)
, Λ
1
=
Λ
2
=
F
(0)
x
y
Λ
0
√
F
2
(
Φ
)+
G
2
(
Φ
)
F
(
Φ
)
.
(14.53)
d
Φ
F
(
Φ
)
14-33 Special Normal Equiareal Cylindric Mapping (Equidistant +
Conformal: Equator)
Here, let us depart from the postulate of an equiareal mapping. Step by step, this leads to the
following result.
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