Geography Reference
In-Depth Information
⎡
⎤
⎡
⎤
X
Y
Z
X
Y
Z
⎣
⎦
=
R
3
(
−γ
)
R
2
(
−β
)
R
1
(
−α
)
⎣
⎦
.
⎡
⎤
a
(
cosV
)
n
sinVcosU
a
(
cosV
)
n
sinVsinU
−
⎣
⎦
=
R
3
(
−γ
)
R
2
(
−β
)
R
1
(
−α
)
(23.96)
(
cosV
)
n
+1
The oblique orthogonal projection, in consequence, is defined by Box
23.23
where (
x, y
) are the
Cartesian
coordinates of the
oblique plane
which cover
2
.
R
2
).
Box 23.23 (Oblique orthogonal projection of the onion
Z
x
=
Y
y
=
Z
(23.97)
Z
1.5
-1.5
-1
-0.5
0
0.5
1
X+
22
-0.2
-0.4
-0.6
-0.8
-1
Fig. 23.22.
T
he
onion function
√
X
2
+
Y
2
=
aZ
n/
(
n
+1)
√
1
−
Z
2
/
(
n
+1)
with respect to the
onion constants
∈
1
,
√
2
,
2
,
3
,
4
,
5
n
=3
,a
Next we aim at a
conformal mapping,
an
equiareal mapping
and an
equidistant mapping
of the
church tower of onion shape
Z
2
onto a circular cylinder
parallel to the 3-axis (normal placement)
which is
in
vertic
al contact
with
Z
2
. The radius of the cylinder is determined by the maximal
radius
√
X
2
+
Y
2
=
g
(
V
)=max(
V
)ofthe“
onion function
”, namely by means of
(i)
g
(
V
) = 0 (necessary condition),
(ii)
g
(
V
)
<
0 (suciency condition).
(iii)
g
(
V
)=0
↔−ncos
n−
1
Vsin
2
V
+
cos
n
+1
V
=0
↔ cos
n−
1
V
−n
+(
n
+1)
cos
2
V
=0
n
n
+1
,
cos
2
V
=
cos
n−
1
V
↔
=0
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