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Fig. 21.7.
Polynomial diagram, the polynomial representation of the conformal coordinate Northing
Y
in a
global frame of reference 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)
Box 21.13 (Synthesis matrix S of a curvilinear datum transformation close to the identity,
decomposition S(
h
)=S
0
+
h
S
1
+O(
h
2
)).
e
2
sin
2
b
)
1
/
2
,
n
(
b
):=
a
1
/
(1
−
e
2
)
/
(1
e
2
sin
2
b
)
3
/
2
,
m
(
b
):=
a
1
(1
−
−
E
2
sin
2
b
)
1
/
2
,
q
(
b
):=[
A
1
(1
− E
2
)(1
− e
2
sin
2
b
)
3
/
2
]
/a
1
(1
− e
2
)(1
− E
2
sin
2
b
)
1
/
2
.
e
2
sin
2
b
)
1
/
2
]
/a
1
(1
p
(
b
):=[
A
1
(1
−
−
s
10
=0
,
13
=0
,
17
=0
,
s
11
=
=+sin
l/
[(
pn
+
h
)cos
b
]=
=+sin
l/
[
pn
cos
b
]
h
sin
l/
[
p
2
n
2
cos
b
]+O(
h
2
)
,
s
12
=
−
cos
l/
[(
pn
+
h
)cos
b
]=
=
−
cos
l/
[
pn
cos
b
]+
h
cos
l/
[
p
2
n
2
cos
b
]+O(
h
2
)
,
s
14
=
=
−
(21.68)
=
−
tan
b
cos
l
[
n
(1
−
e
2
)+
h
]
/
(
pn
+
h
)=
e
2
)
/p
+
h
tan
b
cos
l
(1
e
2
p
)
/
(
np
2
)+O(
h
2
)
,
=
−
tan
b
cos
l
(1
−
−
−
s
15
=
e
2
)+
h
]
/
(
pn
+
h
)=
=
−
tan
b
sin
l
[
n
(1
−
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