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apply certain corrections to every direction, transforming the curves into the
corresponding straight lines, and then to reduce the known elements in the geodetic
network to the plane and convert the geodetic coordinates of the initial point to the
plane coordinates. We compute the plane coordinates of other geodetic points, e.g.,
the plane coordinates of P
2
0
(Fig.
6.11b
), with:
x
2
ﾼ
x
1
þ
D
12
cos T
12
,
y
2
ﾼ
y
1
þ
D
12
sin T
12
One also needs to determine all the side lengths and grid azimuths of the plane
triangle, such as D
12
and T
12
, etc.
From the above analysis, we can see that the reduction of the geodetic network
on the ellipsoid to the Gauss plane consists of the following computations.
Direct Solution of the Gauss Projection
We reduce the geodetic coordinates (L
1
, B
1
) of the initial point P
1
to the Gauss
plane rectangular coordinates (x
1
, y
1
) of the corresponding projection point P
1
0
.
This is known as the direct solution of the Gauss projection.
Arc-to-Chord Correction
We convert the interior angles of the ellipsoidal triangle to that of the plane triangle
formed by the corresponding straight lines. Actually, we convert the direction of the
curve projected from a geodesic to the direction of its chord, and we obtain the
angular difference between the projected curve and the chord, which is known as
the arc-to-chord correction or curvature correction or direction correction, denoted
by
ʴ
12
,
ʴ
13
, and so on.
Distance Correction
We reduce the geodesic distance S
1.2
of the initial side P
1
P
2
on the ellipsoid to the
length of chord D
1.2
of the corresponding projected side P
1
0
P
2
0
on the plane, where
the correction applied is called the correction of distance, denoted by
Δ
S.
Computation of Grid Convergence
We convert the geodetic azimuth A
1.2
of the initial side on the ellipsoid to the plane
grid azimuth T
1.2
of the corresponding projected side P
1
0
P
2
0
, which is known as the
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