15-5 Examples (Gauss–Krueger/UTM coordinates) 345
The summary concerning the Gauss–Krueger coordinates is presented in Box 15.6, the summary
concerning the UTM coordinates is presented in Box 15.7, and a comparison is shown in Box 15.8.
Box 15.6 (Summary: Gauss–Krueger coordinates).
(1)
Choose {L 0 , B 0 } such that |l| = |L − L 0 | < l max = 2
◦ , |b| = |B − B 0 | < 1
◦ , and L 0 multiple of 3
◦ .
False Easting: x(l, b) +
L 0
3 ◦ × 10
6 + 5 × 10
5 , Northing: y 0 + y(l, b).
y 0 is the length of meridian from the equator to the latitude point B 0 : B 0 = B is permitted.
(2)
Choose {L, B} out of {False Easting, Northing}.
Choose y 0 such that |y| = |Northing − y 0 | < 100 km and
|x| =
˛
˛ False Easting − 10
6 × meridian number − 5 × 10
5
˛
˛ < l max × R 0 × cos B/ρ,
ρ := 180
◦ /π, R 0 = 6 380 000 m.
Longitude: L = L 0 + l(x, y), latitude: B = B 0 + b(x, y).
B 0 is the latitude of the meridian arc y 0 , y 0 = Northing is admissible, L 0 = 3
◦ × meridian number.
Box 15.7 (Summary: UTM coordinates).
(1)
Choose {L 0 , B 0 } such that |l| = |L − L 0 | < l max = 3.5
◦ , |b| = |B − B 0 | < 1
◦ , and L 0 + 3
◦ multiple of 6
◦ .
False Easting: x(l, b) + 5 × 10
5 , False Northing: y 0 + y(l, b) +
j
0
if Northing > 0 ,
10
7 if Northing < 0 .
y 0 is the length of meridian from the equator to the latitude point B 0 : B 0 = B is permitted.
(2)
Choose {L, B} out of {False Easting, False Northing} subject to scale 0.999 578.
Choose y 0 such that |y| = |False Northing − y 0 | < 100 km and
|x| =
˛
˛ False Easting − 5 × 10
5
˛
˛ < l max × R 0 × cos B/ρ,
ρ := 180
◦ /π, R 0 = 6380000 m.
Longitude: L = (zone − 30) × 6
◦ − 3
◦ + l(x, y), latitude: B = B 0 + b(x, y).
B 0 is the latitude of the meridian arc y 0 , y 0 = Northing is admissible.