Geography Reference
In-Depth Information
Case 3
(normal equiareal cylindric mapping, equidistant on the equator):
Φ
B
A + B
( A + B cos Φ )d Φ =
f ( Φ )=
0
Φ
Φ
B 2
A + B
B 2
A + B sin Φ.
AB
A + B
AB
A + B Φ +
d Φ +
d Φ cos Φ =
=
(14.69)
0
0
Mapping equations and principal stretches:
x
y
=
, Λ 1 = F (0)
( A + B ) Λ
A + B
A + B cos Φ ,
F ( Φ ) =
B 2
AB
A + B Φ +
A + B sin Φ
Λ 1 = A + B cos Φ
1
Λ 2 =
.
(14.70)
A + B
Let us now “switch” from the polar aspect of the mapping “ellipsoid-of-revolution to cylinder”
to the transverse aspect of the mapping “ellipsoid-of-revolution to cylinder”.
 
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