Geography Reference
In-Depth Information
19-2 Special Conic Projections Based Upon
the Ellipsoid-of-Revolution
Normal mappings of type
equidistant, conformal
,and
equal area
. The mapping equations and
the principal stretches. Lambert mapping and Albers mapping.
In this section, we present special normal mappings of type
equidistant, conformal
,and
equal area
as second postulates.
19-21 Special Conic Projections of Type Equidistant on the Set
of Parallel Circles
Let us transfer the postulate of an equidistant mapping on the set of parallel circles. As it is
shown in (
19.9
), we get a typical
elliptic integral
of the second kind.
Λ
2
=1 and
Λ
2
=
f
(
Δ
)
M
⇒
f
(
Δ
)=
M
(19.8)
⇔
E
2
)
A
(1
−
f
(
Δ
)=
E
2
cos
2
Δ
)
3
/
2
,
(1
−
E
2
)
(1
E
2
cos
2
Δ
)
−
3
/
2
d
Δ
f
(
Δ
)=
A
(1
−
−
(19.9)
E
2
)
Δ
0
E
2
cos
2
Δ
∗
)
−
3
/
2
d
Δ
∗
.
=
A
(1
−
(1
−
19-22 Special Conic Projections of Type Conformal
Here, we depart from the postulate of conformality. After integration-by-parts and after applica-
tion of the addition theorem, we are finally led to (
19.15
).
N
sin
Δ
=
f
(
Δ
)
nf
(
Δ
)
f
f
nM
N
sin
Δ
Λ
1
=
Λ
2
⇒
⇒
=
M
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