Specifications
Coordinate Transformation 65
Coordinate
The generic formula used to translate and rotate from coordinate system 1 to
coordinate system 2 is as follows:
where
ε
rx
=
ε
x
expressed in radians, similarly for ε
ry
and ε
rz
.
Example: Define local datum as the WGS-72 datum
$PASHS,UDD, 0,6378135.0, 298.26,0,0,4.5,0,0,-0.554,0.23
$PASHS,DTM,UDD
This implements the transformations listed in Table 5.2 and below.
∆
x=
∆
y=0
∆
z= 4.5 meters m= 0.23ppm
ε
x
=
ε
y
=0
ε
z
= –2.686
x
10
-6
radians = –0. 554 in the following equation:
Table 5.2: Ellipsoid Parameters for WGS-72 and WGS-84
Datum Reference Ellipsoid a[m] 1/f
WGS-72 WGS-72 6378135.0 298.26
WGS-84 WGS-84 6378137.0 298.257223563
x
y
z
2
∆x
∆y
∆z
1 m
6–
×10+()
1 ε
rz
ε
ry
–
ε
rz
–1ε
rx
ε
ry
ε
rx
–1
x
y
z
1
+=
x
y
z
WGS 84–
0
0
4.5
10.23
6–
×
10
+()
12.686–10
6–
× 0
2.686 10
6–
× 10
001
x
y
z
WGS 72–
+=