Geography Reference
In-Depth Information
Fig. 14.2.
Vertical section. The example of a torus
Box 14.4 (Summary).
Case 1
(normal cylindric mapping, equidistant on the equator and the set of parallel circles):
f
(
Φ
)=
Φ
0
x
y
=
(
A
+
B
)
Λ
.
B
d
Φ
=
BΦ,
(14.66)
BΦ
Case 2
(normal conformal cylindric mapping, equidistant on the equator):
f
(
Φ
)=(
A
+
B
)
Φ
0
B
A
+
B
cos
Φ
d
Φ
=
=(
A
+
B
)
Φ
0
d
Φ
AB
−
1
+co
s
Φ
=
(14.67)
B
2
arctan
tan
2
√
A
2
=
2
B
(
A
+
B
)
−
B
2
√
A
2
.
A
+
B
−
Mapping equations and principal stretches:
=
, Λ
1
=
Λ
2
=
F
(0)
F
(
Φ
)
x
y
(
A
+
B
)
Λ
√
A
2
−B
2
arctan
tan
2
√
A
2
−
B
2
2
B
(
A
+
B
)
A
+
B
A
+
B
A
+
B
cos
Φ
.
=
(14.68)
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