Datum Problems - Map Projections: Cartographic Information Systems - page 545

21-43 Numerical Results

Here, we depart from the polynomial representation of the global conformal coordinates { X,Y }

in terms of local conformal coordinates due to a curvilinear datum transformation and its

inverse by Boxes 21.31 and 21.32 . In our case studies, we concentrate on the State of Baden-
Wurttemberg. The transformation of 50 BWREF points from a global to a local datum and vice
versa has been computed. Table 21.2 summarizes those datum transformation parameters that
areavailabletous.

{ x, y }

Box 21.31 (Polynomial representation of the global conformal coordinates { X,Y } in terms of

local conformal coordinates due to a curvilinear datum transformation, Gauss-Krueger

conformal mapping or UTM, polynomial degree three, Easting X,x , Northing Y,y ).

{ x, y }

X = X ( x, y, ρ, t x ,t y ,t z ,α,β,γ,s,A 1 ,E 2 ,a 1 ,e 2 )=
= ρ x 00 + x 10 x

ρ + x 01 y

y 00 + x 20 x
ρ

2 y

ρ −

y 00

+ x 11 x
ρ

ρ −

+ x 02 y y 00 2

ρ −

+

+ x 30 x
ρ

3

+ x 21 x
ρ

2 y
ρ −

y 00 + x 12 x
ρ

y
ρ −

y 00 2

y 00 3 +O(4) ,

+ x 03 y

ρ −

(21.90)

Y = Y ( x, y, ρ, t x ,t y ,t z ,α,β,γ,s,,A 1 ,E 2 ,a 1 ,e 2 )=
= ρ y 00 + y 10 x

ρ + y 01 y

y 00 + y 20 x
ρ

2 y

ρ −

y 00 + y 11 x

ρ

ρ −

+ y 02 y y 00 2

ρ −

+

ρ − y 00 3

+ y 30 x
ρ

3

+ y 21 x
ρ

2 y

ρ − y 00 + y 12 x

y

ρ − y 00 2

+ y 03 y

ρ

+O(4) .

Box 21.32 (Polynomial representation of the local conformal coordinates { x, y } in terms of

global conformal coordinates due to a curvilinear datum transformation, Gauss-

Krueger conformal mapping or UTM, polynomial degree three, Easting X,x , Northing Y,y ).

{ X,Y }

x = x ( X,Y,ρ,t x ,t y t z ,α,β,γ,s,A 1 ,E 2 ,a 1 ,e 2 )=
= ρ x 10 X

ρ − x 00 + x 01 Y ρ − y 00 + x 20 X ρ − x 00 2