12-2 Special mapping equations 291
Fig. 12.2. Mapping the sphere to a cylinder: oblique aspect, equidistant mapping, B 0 = 45
◦ , oblique Plate
Carr´ ee projection.
12-22 Conformal mapping (oblique Mercator projection), compare with Fig. 12.3
x
y
= R cos B 0
A
ln cot
π
4 −
B
2
= R cos B 0
A
ln tan
π
4 +
B
2
=
= R cos B 0
A
1
2 ln
1+sin B
1−sin B
=
= R cos B 0
A
ar tanh(sin B)
,
(12.5)
Λ 1 = Λ 2 =
cos B 0
cos B
.
(12.6)
12-23 Equal area mapping (oblique Lambert projection), compare with Fig. 12.4
x
y
= R
A cos B 0
sin B
cos B 0
,
(12.7)
Λ 1 =
cos B 0
cos B
, Λ 2 =
cos B
cos B 0
.
(12.8)