Geoscience Reference
In-Depth Information
Fig. 3.3 Traversing
Triangulation
A series of points P 1 , P 2 , P 3 ...
, each point intervisible with its adjacent points, are
chosen and connected in the form of a triangulation network, as shown in Fig. 3.4 .
Determine the length of P 1 P 2 and its azimuth as the initial length and azimuth of the
network, respectively; observe the angles in each triangle and reduce these lengths
and angles to a plane. Assume the given coordinates of point P 1 are (X 1 , Y 1 ), the
length and grid bearing of P 1 P 2 are D 12 and T 12 , respectively, and the observed
angles are A i , B i , and C i . The lengths and grid bearings of each side can be obtained
from P 1 P 2 :
sin B 1
sin A 1 ,
D 13 ¼
D 12
T 13 ¼
T 12 þ
C 1 :
sin B 2
sin A 2 ,
D 14 ¼
D 13
T 14 ¼
T 13 þ
C 2 :
...
The coordinates of points in the entire network can be obtained according to
these side lengths and azimuths, namely:
x 3 ¼
x 1 þ Δ
x 13 ¼
x 1 þ
D 13 cos T 13 ,
y 3 ¼
y 1 þ Δ
y 13 ¼
y 1 þ
D 13 sin T 13 :
...
This is the fundamental principle of establishing the horizontal control network
by triangulation.
Trilateration and Combination of Triangulation and Trilateration
Establishing the horizontal control network using trilateration is almost the same as
when using triangulation. The difference is that while using trilateration we only
measure the side lengths of the triangle in the network. The interior angles are
obtained through computation. If some or all lengths are also measured apart from
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