Geography Reference
In-Depth Information
60
◦
Fig. 11.1.
Mapping the sphere to a (tangent) cylinder. Transverse aspect. Line-of-contact:
Λ
0
=
−
x
y
=
RA
cos
B
0
,
(11.1)
f
(
B
)
tan
A
=
sin(
Λ
−
Λ
0
)
,
sin
B
=cos
Φ
cos(
Λ
−
Λ
0
)
,
(11.2)
−
tan
Φ
cos
B
, Λ
2
=
f
(
B
)
Λ
1
=
cos
B
0
.
(11.3)
R
The procedure of how to set up special equations of the mapping “sphere to cylinder” in the trans-
verse aspect (transverse equidistant mapping, transverse conformal mapping, transverse equal
area mapping) can be easily deduced from the preceding chapters. Far easier, in the mapping
equations as well in the equations for the left principal stretches defined in Chap.
10
,conven-
tional coordinates
spherical longitude Λ
and
spherical latitudes Φ
and
Φ
0
are simply replaced
by their corresponding items
meta-spherical longitude A
and
meta-spherical latitudes B
and
B
0
.
Transformations of conventional spherical coordinates to meta-spherical coordinates is performed
by using (
11.2
).
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