Geoscience Reference
In-Depth Information
longitude of the central meridian L 0 is given, and l
L 0 can be computed), the
Gauss plane coordinates (x, y)ofP can be calculated according to ( 6.27 ).
The functional relationship between (x, y) and (L, B) expressed in ( 6.27 ) has
determined the specific form of f 1 and f 2 in ( 6.19 ).
When l
L
3.5 , the computation according to ( 6.34 ) is accurate to 0.1 m. If the
desired accuracy is 0.001 m, the series in ( 6.27 ) can be further expanded. The
process is not shown here. The computational formula is directly given as:
<
9
=
l 00 4
N
N
24
l 00 2
sin B cos 3 B 5
t 2
2
4
x
X
þ
sin B cos B
þ
þ
9
ʷ
þ
4
ʷ
ρ 00 2
ρ 00 4
2
l 00 6
N
720
sin B cos 5 B 61
58t 2
t 4
þ
þ
ρ 00 6
:
;
l 00 3
ρ 00 5 cos 5 B 5
N
ρ
N
N
120
cos Bl 00
ρ 00 3 cos 3 B 1
t 2
2
18t 2
y
þ
þ ʷ
þ
00
6
2 t 2 l 00 5
t 4
2
þ
þ
14
ʷ
58
ʷ
ð
6
:
28
Þ
For the most accurate formulae and for new methods, some literature is
recommended for further reading (Karney 2011; Kawase 2011; Kawase 2012;
Deakin, et al. 2011).
Formula Analysis
Analyzing ( 6.27 ), one can get the shapes of the meridians and parallels on the
ellipsoid after the projection (cf. Fig. 6.8 ).
Projections of the Central Meridian and Equator
When B
0, and y changes with l, it indicates that the equator is projected as
a straight line, i.e., the abscissa axis. When l
0, x
X it indicates that the
central meridian is also projected as a straight line, i.e., the ordinate axis. There are
no distortions in the projection. The point of intersection of the projected central
meridian and equator is the origin of the plane coordinate system.
0, y
0, x
Meridian Projection
Setting l as constant, we can get the parameter equation of curves of the projected
meridians in terms of parameter B. When the value of B increases, x increases while
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