Geography Reference
In-Depth Information
y
=
r
lntan
π
=
4
+
β
2
=
r
ar tanh(sin
β
) =
(16.2)
=
r
ar tanh[cos
i
sin
B
−
sin
i
cos
B
sin(
L
−
Ω
)]
,
tan
x
r
=
(16.3)
=cos
i
tan(
L
−
Ω
)+sin
i
tan
B/
cos(
L
−
Ω
)
,
tanh
y
r
=
(16.4)
=cos
i
sin
B
−
sin
i
cos
B
sin(
L
−
Ω
)
.
16-1 The Equations Governing Conformal Mapping
The equations governing conformal mapping and their fundamental solution. Korn-
Lichtenstein equations and Laplace-Beltrami equations. Universal Mercator Projection
(UMP) and Universal Polar Stereographic Projection (UPS).
2
A
1
,A
2
(“ellipsoid-of-
revolution”), “spheroid”, semi-major axis
A
1
, semi-minor axis
A
2
) embedded in a three-
dimensional Euclid manifold
We are concerned with a conformal mapping of the biaxial ellipsoid
E
3
=
3
,δ
ij
}
E
{
R
with standard “canonical” metric
{
δ
ij
}
,theKronecker
delta of ones in the diagonal, of zeros in the off-diagonal, namely by means of
A
1
cos
B
cos
L
x
1
=
1
,
E
2
sin
2
B
−
A
1
cos
B
cos
L
1
− E
2
sin
2
B
x
2
=
,
(16.5)
E
2
)sin
B
1
− E
2
sin
2
B
x
3
=
A
1
(1
−
,
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