Geography Reference
In-Depth Information
Fig. 21.9.
Polynomial diagram, the polynomial representation of latitude increments
b
−
b
0
, conformal coordi-
nates
of type Gauss-Krueger or UTM, the
solid dots
illustrate non-zero monomials, the
open circles
zero
monomials, according to
Cox et al.
(
1996
, pp. 433-443)
{
x, y
}
Box 21.23 (Coecients of a bivariate series inversion of conformal type, the ellipsoidal lon-
gitude increments
l
−
l
0
).
l
10
=
(1
−
e
2
sin
2
b
0
)
1
/
2
a
1
cos
b
0
,
l
11
=
tan
b
0
(1
−
e
2
sin
2
b
0
)
,
(21.80)
a
1
cos
b
0
e
2
sin
2
b
0
)
3
/
2
(1 + sin
2
b
0
−
3
e
2
sin
2
b
0
+
e
2
sin
4
b
0
)
l
30
=
−
(1
−
,
6
a
1
(1
−
e
2
)cos
3
b
0
l
12
=
+(1
−
e
2
sin
2
b
0
)
3
/
2
(1 + sin
2
b
0
−
3
e
2
sin
2
b
0
+
e
2
sin
4
b
0
)
.
2
a
1
(1
−
e
2
)cos
3
b
0
Box 21.24 (Coecients of a bivariate series inversion of conformal type, the ellipsoidal latitude
increments
b − b
0
).
e
2
sin
2
b
0
)
3
/
2
a
1
(1
b
01
=
(1
−
,
−
e
2
)
e
2
sin
2
b
0
)
2
b
20
=
−
tan
b
0
(1
−
,
2
a
1
(1
−
e
2
)
3
e
2
cos
b
0
sin
b
0
(1
e
2
sin
2
b
0
)
2
b
02
=
−
−
,
(21.81)
2
a
1
(1
−
e
2
)
2
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