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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