Geoscience Reference
In-Depth Information
Fig. 6.5 Overlap between
projection zones
position of a point. To describe the zones in which a point lies, a zone number is
designated before the y value (assigned 500,000 m). The coordinates formed in such
way are called false coordinates, denoted by y false . To show the results, the points
are all expressed by the false coordinates, whereas in real applications, the zone
number should be eliminated and the 500,000 m value subtracted. The recovered
values are called the natural coordinates of this point. The relationship between
natural coordinates and false coordinates is shown in Fig. 6.6 .
For instance, in 6 zone 19, the natural coordinates of points A and B are:
x
4 485 076
:
81 m
x
4 485 076
:
81 m
A
:
B
:
y
2 578
:
86 m
y
2 578
:
86 m
and their false coordinates are:
x
4 485 076
:
81 m
x
4 485 076
:
81 m
A
:
B
:
y false
19 497 421
:
14 m
y false
19 502 578
:
86 m
6.4 Direct and Inverse Solutions of the Gauss Projection
and Transformation Between Adjacent Zones
6.4.1 Formula for Direct Solution of the Gauss Projection
Derivations of the Formula
The formula for the direct solution of the Gauss projection is the formula used to
compute the Gauss plane rectangular coordinates (x, y), given the geodetic coordi-
nates (L, B)or(l, q) of a point, as shown in Fig. 6.7 .
The projection equation from the ellipsoid to the plane is generally expressed as:
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