Geography Reference
In-Depth Information
P
2
onto a developed cylinder
C
0
Fig. 23.21.
Equidistant mapping of
23-4 Mapping the Onion Surface: Projected Geometrically
onto a Church Tower
2
,
is comparatively represented
in terms of charts of type
oblique orthogonal projection versus cylindric,
namely of type
conformal,
equiareal and equidistant.
Computer graphical examples are given.
As a
surface of revolution
the
church tower of onion shape
may be defined by
The
church power,
geometrically described as the
onion surface
Z
a
2
Z
2
/
(
n
+1)
1
Z
2
/
(
n
+1)
=0
,a
2
:=
3
X
2
+
Y
2
+
,n
Z
{
X
∈
R
|
−
−
∈
R
∈
N
}
,
3
for instance represented in the chart
{
onion longitude U, onion latitude, V
}∈{
R
|
0
<U<
2
π,
0
<V <π/
2
}
by means of
X
=
a
(
cosV
)
n
sinVcosU
=
g
(
V
)
cosU
Y
=
a
(
cosV
)
n
sinVsinU
=
g
(
V
)
sinU
(23.95)
(
cosV
)
n
cosV
=
(
cosU
)
n
+1
=
h
(
V
)
Z
=
−
−
Figures
23.22
,
23.23
,
23.24
,and
23.25
are a computer gra
phic illust
ration of the
church tower
of onion shape
, firstly by means of the “
onion function
”
√
X
2
+
Y
2
=
aZ
n/
(
n
+1)
√
1
− Z
n/
(
n
+1)
and
secondly
by means of an
oblique orthogonal projection
which is generated in the following
way: A rotation around the 1-axis, 2-axis and 3-axis parameterized by means of
Cardan angles
{
α
∈
[0
,
2
π
]
,β
∈
[0
,π
]
,γ
∈
[0
,
2
π
]
}
transforms (
X
,
Y
,
Z
)into(
X
Y
Z
), namely
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