21-4 Gauss–Krueger/ UTM coordinates:from a local to a global datum 477
Box 21.20 (Polynomial coefficients of a conformal series of Box 21.11 of type Gauss–Krueger or UTM after
a curvilinear transformation, Easting X(l − l 0 , b − b 0 , ρ, t x , t y , t z , α, β, γ, s, δE
2 ), second version).
U 00 =
A 1
a 1
ˆ`
x 10 + x 10,e 2 δE
2 ´
δL + x 11 δLδB
˜
,
U 10 =
A 1
a 1
`
x 10 + x 10,e 2 δE
2 + x 11 δB
´
,
U 01 =
A 1
a 1
x 11 δL ,
U 20 = 3
A 1
a 1
x 30 δL ,
U 11 =
A 1
a 1
`
x 11 + x 11,e 2 δE
2 + 2 x 12 δB
´
,
U 02 =
A 1
a 1
x 12 δL ,
U 30 =
A 1
a 1
`
x 30 + x 30,e 2 δE
2 + x 31 δB
´
,
U 21 = 3
A 1
a 1
x 31 δL ,
U 12 =
A 1
a 1
`
x 12 + x 12,e 2 δE
2 + 3 x 13 δB
´
,
U 03 =
A 1
a 1
x 13 δL .
(21.77)
Box 21.21 (Polynomial coefficients of a conformal series of Box 21.11 of type Gauss–Krueger or UTM after
a curvilinear transformation, Northing Y (l − l 0 , b − b 0 , ρ, t x , t y , t z , α, β, γ, s, δE
2 ), second version).
V 00 =
A 1
a 1
h
y 00 + y 00,e 2 δE
2 + y 00,e 2 e 2
(δE
2 )
2
2
+ ( y 01 + y 01,e 2 δE
2 )δB + y 20 δL
2 + y 02 δB
2
i
,
V 10 = 2
A 1
a 1
y 20 δL ,
V 01 =
A 1
a 1
`
y 01 + y 10,e 2 δE
2 + 2 y 02 δB
´
,
V 20 =
A 1
a 1
`
y 20 + y 20,e 2 δE
2 + y 21 δB
´
,
V 11 = 2
A 1
a 1
y 21 δL ,
V 02 =
A 1
a 1
`
y 02 + y 02,e 2 δE
2 + 3 y 03 δB
´
,
V 30 = 4
A 1
a 1
y 40 δL ,
V 21 =
A 1
a 1
`
y 21 + y 21,e 2 δE
2 + 2 y 22 δB
´
,
V 12 = 2
A 1
a 1
y 22 δL ,
V 03 =
A 1
a 1
`
y 03 + y 30,e 2 δE
2 + 4 y 04 δB
´
.
(21.78)