Geography Reference
In-Depth Information
F
R
arcsin(
)
2
B
c
sin 2
c
sin 4
c
sin 6
c
sin 8
c
sin 10
(67)
2
4
6
8
10
B
sin 2
B
sin 4
B
sin 6
B
sin 8
B
sin 10
B
2
4
6
8
10
q
arctanh(sin
)
Expanding
q
as a power series of the eccentricity at
e
by means of Mathematica yields
the direct expansion of the transformation form authalic latitude function to isometric
latitude
0
F
R
arcsin(
)
2
(68)
q
arctanh(sin
)
l
sin
l
sin 3
l
sin 5
l
sin 7
l
sin 9
1
3
5
7
9
where
1
1
11
107
1513
2
4
6
8
10
l
e
e
e
e
e
1
3
30
1890
32400
1663200
1
61
2321
1021
4
6
8
10
l
e
e
e
e
3
90
11340
907200
831600
1
5
151
6
8
10
l
e
e
e
(69)
5
756
4032
166320
71
41
8
10
l
e
e
7
302400
123200
61
1197504
10
l
e
9
4.4 Accuracies of the direct expansions
The accuracies of the indirect and direct expansions given by Yang(1989, 2000) derived by
the author has been examined choosing the CGCS2000 reference ellipsoid.
The results show that the accuracy of the indirect expansion of the transformation from
meridian arc to isometric latitude is higher than 10
-3
″, while the accuracy of the direct
expansion (53) is higher than 10
-7
″. The accuracy of the indirect expansion of the
transformation from isometric latitude to meridian arc is higher than 10
-2
m, while the
accuracy of the direct expansion (56) is higher than 10
-7
m. The accuracy of the indirect
expansion of the transformation from meridian arc to authalic latitude function is higher
than 0.1
10 k
. The
accuracy of the indirect expansion of the transformation from authalic latitude function to
meridian arc is higher than 10
-2
m, while the direct expansion (62) is higher than 10
-4
m. The
accuracy of the indirect expansion of the transformation from isometric latitude to authalic
latitude function is higher than 0.1
2
5
2
km
, while the accuracy of the direct expansion (59) is higher than
2
km
, while the accuracy of the direct expansion (65) is
