15-6 Strip transformation of conformal coordinates (Gauss–Krueger/UTM mappings) 355
Example 15.8 (Bessel ellipsoid, strip transformation x 2 (x 1 , y 1 ) and y 2 (x 1 , y 1 ) of conformal coordinates 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 = 1 2
◦ , TP 1.O. Bonstetten (L = 1 0
◦ 4 2
5 9 .
3 2 1 5
,
B = 4 8
◦ 2 6
4 5 .
4 3 5 5
)).
{L, B} → {x 1 , y 1 }:
L 01 = 9
◦ ,
dilatation factor ρ = 1 ,
B 0 = 4 8
◦ ,
x 1 = 1 2 6 9 6 7
.2 4 8 3 3 m
, y 1 = 5 1 0 0 5
.5 6 9 2 4 m
,
y 0 (B 0 = 4 8
◦ ) = 5 3 1 7 8 8 5
.2 3 2 3 2 m
.
C onventional G auss–K rueg er coordinates:
N orthing y GK = y 0 + y 1 = 5 3 6 8 8 9 0
.8 0 1 5 5 m
,
F
alse E asting
x GK =
L 01
3 ◦ × 1 0
6 m + 5 0 0 0 0 0 m +
x 1 = 3 6 2 6 9 6 7
.2 4 8 3 3 m
.
{L, B} → {x 2 , y 2 }:
L 02 = 1 2
◦ ,
dilatation factor ρ = 1 ,
B 0 = 4 8
◦ ,
x 2 = −9 4 9 4 2
.3 7 1 1 4 m
, y 2 = 5 0 3 7 8
.0 1 5 5 1 m
.
C onventional G auss–K rueg er coordinates:
N orthing y GK = 5 3 6 8 2 6 3
.2 4 7 8 2 m
,
F
alse E asting
x GK =
L 02
3 ◦ × 1 0
6 m + 5 0 0 0 0 0 m +
x 2 = 4 4 0 5 0 5 7
.6 2 8 8 6 m
.
{x 1 , y 1 } → {x 2 , y 2 }:
B 0 = 4 8
◦ ,
x 2 = −9 4 9 4 2
.3 7 1 1 0 m
, y 2 = 5 0 3 7 8
.0 1 5 5 1 m
,
End of Example.