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=
1
−E
cos
Δ
E/
2
tan
2
n
,
α
r
nΛ
c
1+
E
cos
Δ
(19.16)
=
2
n
,
α
r
nΛ
c
1+
E
sin
Φ
1
−E
sin
Φ
E/
2
tan
4
−
(19.17)
Φ
1+
E
sin
Φ
1
n
E/
2
tan
π
cn
N
sin
Δ
Φ
2
Λ
1
=
Λ
2
=
4
−
.
(19.18)
−
E
sin
Φ
We here distinguish between two cases.
Δ
=0:
r
=
f
(0)
(the central point is mapped to a point)
and
Δ
=
π/
2:
r
=
f
(
π/
2) =
c
(the parallel circle-of-reference
Δ
=
π/
2or
Φ
= 0 is mapped to a circle of radius
c
)
.
There are two variants of conformal mappings.
19-221 Conformal Mapping: The Variant of Type Equidistant on the Parallel Circle-of-Reference
We first consider the variant of
type equidistant on the parallel circle-of-reference
.Inthiscontext,
let us fix the projection constant
n
by
n
:= sin
Φ
0
=cos
Δ
0
.
(19.19)
The radius of the parallel circle
p
is computed as follows.
Input :
X
2
+
Y
2
A
1
+
Z
2
A
2
= 1
(19.20)
(equation of the ellipsoid-of-revolution)
.
Output :
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