Geography Reference
In-Depth Information
Fig. 15.19.
Flow chart of the two step approach for generating the strip transformation
x
2
=
X
(
x
1
,y
1
)and
y
2
=
Y
(
x
1
,y
1
)
The strip transformation of conformal coordinates of type
Gauss-Krueger (
ρ
=1)orUTM(
ρ
=0
.
999578) for a strip
[
[80
◦
S
,
84
◦
N]) repre-
sented by
x
2
=
X
(
x
1
,y
1
)and
y
2
=
Y
(
x
1
,y
1
) is derived in
terms of a bivariate polynomial up to order five.
3
.
5
◦
,
3
.
5
◦
]
−
l
E
,l
E
]
×
[
B
S
,B
N
]=[
−
×
}
represent the conformal coordinates in the first strip of
ellipsoidal longitude
L
01
, while
{x
2
,y
2
}
represent those con-
formal coordinates in the second strip of ellipsoidal longi-
tude
L
02
.X
(
x
1
,y
1
)and
Y
(
x
1
,y
1
) are power series in terms
of
L
01
− L
02
given by (
15.123
), (
15.124
), and Box
15.12
.
Two examples (Bessel ellipsoid, World Geodetic Reference
System 1984 (WSGS84)) document the numerical stability
of the derived strip transformation.
{
x
1
,y
1
Example 15.8 (Bessel ellipsoid, strip transformation
x
2
(
x
1
,y
1
)and
y
2
(
x
1
,y
1
) of conformal coor-
dinates of Gauss-Krueger (GK) type versus direct transformations
{L, B}→{x
1
,y
1
}
with
respect to
L
01
=9
◦
and
{L, B}→{x
2
,y
2
}
with respect to
L
02
=12
◦
, TP 1.O. Bonstetten
(
L
= 1042
◦
59
3215
,B
=48
◦
26
45
435)).
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