Geography Reference
In-Depth Information
Fig. J.6.
Minimum distance mapping of a point
P
on the Earth's topographic surface to a point
p
on the
International Reference Ellipsoid
E
2
A
1
,A
2
+
e
2
+
H
(
L, B
)
cos
B
sin
L
A
1
1
(J.48)
E
2
sin
2
B
−
+
e
3
A
1
(1
+
H
(
L, B
)
sin
B,
E
2
)
1
− E
2
sin
2
B
−
X
=
A
1
+
H
(
L, B
)
cos
B
sin
L,
1
− E
2
sin
2
B
Y
=
+
H
(
L, B
)
cos
B
sin
L,
A
1
1
(J.49)
E
2
sin
2
B
−
Z
=
A
1
(1
+
H
(
L, B
)
sin
B.
E
2
)
−
1
E
2
sin
2
B
−
In order to solve in algorithmic form the characteristic normal equation by means of a constraint
minimum distance mapping given earlier, we outline the first and second forward step of reduc-
tion, which leads us to a univariate polynomial equation of fourth order in terms of Lagrangean
multipliers. As soon as we have implemented standard software to solve the fourth order equation,
we continue to determine with the backward step the Cartesian coordinates
{
x
1
,x
2
,x
3
}
of the
2
A
1
,A
2
point
p
∈
E
, which has been generated by means of the
minimum distance mapping
of a
Search WWH ::
Custom Search