Datum Problems - Map Projections: Cartographic Information Systems - page 542

The direct and inverse equations for a datum transforma-
tion of conformal coordinates of type Gauss-Krueger or
UTM from a local datum (regional, National, European)
to a global datum (i.e. WGS 84) are given in terms of a
bivariate polynomial representation. The polynomial coef-
ficients depend on the datum transformation parameters,
namely three parameters of translation, three parameters
of rotation, one scale parameter, and one form parame-
ter change, in total eight parameters. The form parame-
ter change accounts for the variation of the eccentricity of
the reference ellipsoid-of-revolution under the change from
one geodetic datum to another one, namely from local to
global or vice versa. The equations generating the trans-
formation of local conformal coordinates of type Gauss-
Krueger or UTM to global conformal coordinates of the
same type enable us to transform mega data sets stored in
data bases or in charts from the local datum (the datum of
the data base, the datum of the chart) to the global datum
(the datum of satellite derived coordinates by means of the
Global Positioning System, i.e. WGS 84) and vice versa.

Box 21.28 (Polynomial representation of 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,Y,ρ,t x ,t y ,t z ,α,β,γ,s,δE 2 )=
= ρ x 10 X

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

ρ − ρ − ρ −

+ x 11 X x 00 Y y 00 +

ρ − ρ −

+ x 02 Y

ρ − y 00 2

+ x 30 X

ρ − x 00 3

+ x 21 X

ρ − x 00 2 X ρ − y 00 +

y 00 3 +

+ x 12 X x 00 Y y 00 2 + x 03 Y

ρ − ρ − ρ −

+O(4) , (21.86)

y ( X,Y,ρ,t x ,t y ,t z ,α,β,γ,s,δE 2 )=
= ρ y 00 + y 10 X

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

ρ − ρ − ρ −

+ y 11 X x 00 Y y 00 +

ρ − ρ −