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in Boxes
21.18
and
21.19
. In consequence, upon a replacement of global coecients by local
coecients of Box
21.18
in the coecients of Boxes
21.19
and
21.15
, we derive the second version of
global conformal coordinates (
21.70
) in terms of local ellipsoidal coordinates with the coecients
of Boxes
21.20
and
21.21
.
Box 21.14 (Polynomial representation of conformal coordinates of type Gauss-Krueger or
UTM after a curvilinear datum transformation).
b
0
)=
=
ρ
[
U
00
+
U
10
(
l − l
0
)+
U
01
(
b − b
0
)+
U
20
(
l − l
0
)
2
+
U
11
(
l − l
0
)(
b − b
0
)
+
U
02
(
b
X
(
l
−
l
0
,b
−
b
0
)
2
+
−
l
0
)
3
+
U
21
(
l
l
0
)
2
(
b
b
0
)
2
+
U
30
(
l
−
−
−
b
0
)+
U
12
(
l
−
l
0
)(
b
−
b
0
)
3
]+
+O(4)
,
+
U
03
(
b
−
Y
(
l
−
l
0
,b
−
b
0
) =
(21.70)
l
0
)
2
+
V
11
(
l
=
ρ
[
V
00
+
V
10
(
l
−
l
0
)+
V
01
(
b
−
b
0
)+
V
20
(
l
−
−
l
0
)(
b
−
b
0
)
+
V
02
(
b − b
0
)
2
+
l
0
)
3
+
V
21
(
l
l
0
)
2
(
b
b
0
)
2
+
V
03
(
b
b
0
)
3
]+
+
V
30
(
l
−
−
−
b
0
)+
V
12
(
l
−
l
0
)(
b
−
−
+O(4)
.
Box 21.15 (Polynomial coecients of a conformal series of type Gauss-Krueger or UTM after
a curvilinear datum transformation, Easting
X
(
l
−
l
0
,b
−
b
0
), first version).
U
00
=
X
10
δL
+
X
11
δLδB,
U
10
=
X
10
+
X
11
δB,
U
01
=
X
11
δL,
(21.71)
U
20
=3
X
30
δL,
U
11
=
X
11
+2
X
12
δB, U
02
=
X
12
δL,
U
30
=
X
30
+
X
31
δB,
U
21
=3
X
31
δL,
U
12
=
X
12
+3
X
13
δB,
U
03
=
X
13
δL.
Box 21.16 (Polynomial coe
cients of a conformal series of type Gauss-Krueger or UTM after
a curvilinear datum transformation, Northing
Y
(
l − l
0
,b− b
0
), first version).
V
00
=
Y
00
+
Y
01
δL
+
Y
20
δL
2
+
Y
02
δB
2
,
V
10
=2
Y
20
δL,
V
01
=
Y
01
+2
Y
02
δB,
(21.72)
V
20
=
Y
20
+
Y
21
δB,
V
11
=2
Y
21
δL,
V
02
=
Y
02
+3
Y
03
δB,
V
30
=4
Y
40
δL,
V
21
=
Y
21
+2
Y
22
δB, V
12
=2
Y
22
δL,
V
03
=
Y
03
+4
Y
04
δB.
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