Geoscience Reference
In-Depth Information
Projection of an Arbitrary Geodesic
Arbitrary geodesics are projected as curves that are concave towards the central
meridian and poles.
Distortion of Projection
It can be seen from Fig. 6.8 that the projected meridians appear more curved and
distorted the further away they are from the central meridian. Thus, distortion
increases further away from the central meridian.
Practical Formulae
This section provides the practical formula for the direct solution of the Gauss
Projection, which is suitable for computations based on computer programming.
Parameters relevant to the Krassowski Ellipsoid, GRS75 Ellipsoid, and GRS80
Ellipsoid, respectively, are also provided for practical use.
Formulae for the Direct Solution of the Gauss Projection (Accurate to 0.001 m)
l ˀ
In ( 6.28 ), we set m
ᄐ cos B
180 to obtain:
2
4
3
5
9
=
m 4
m 6
1
2 m 2
1
24
1
720
t 2
2
4
58t 2
t 4
x
X
þ
Nt
þ
5
þ
9
ʷ
þ
4
ʷ
þ
61
þ
2
4
3
5
,
;
m 3
m 5
1
6
1
120
t 2
2
18t 2
t 4
2
2 t 2
y
Nm
þ
1
þ ʷ
þ
5
þ
þ
14
ʷ
58
ʷ
ð
6
:
29
Þ
where the meridian arc with length X is computed according to (5.41) if the
Krassowski Ellipsoid is adopted; if the GRS75 or GRS80 Ellipsoid is adopted,
X is computed according to (5.42) or (5.43), respectively. Computations continue to
the eighth-power term in (5.41), (5.42), or (5.43).
Formulae for the Direct Solution of the Gauss Projection (Accurate to 0.1 m)
l ˀ
180
In ( 6.27 ), we set m
cos B
to obtain:
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