Geography Reference
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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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