GEOGRAPHICAL SURVEY OFFICE OF SWEDEN NO A 34
7
2.2. The differential formulas.
The x-obliquity (x-deviation) and the width-correction (y-deviation) have
the following influence upon the image coordinates in the A 7 and A8 accord
ing to Lycken [3] :
ta'. -■ÉBL-dt+i-dl
s s
dy * = - — dt - dl
J s s
( 1)
x' and y' are the coordinates in the grid plane, where the origin of the
coordinate system is located in the projection centre, s = \J x'^ + (g-y') 2
and g = 230 mm (A7) , g = 240 mm (A8) • The well known differential formulas
relating the image and the machine coordinates are as follows;
2
dx=-dx + — dz + y dpe + (l + — 0 ) zdcn - ¿SL den
OZO ¿. ' z
z
2
dy = - dy + -^ dz - x d9e + d<p - (l + ^ ) zden
( 2)
x and y are the machine coordinates, dx Q , dy Q and dz Q are the translations.
These translations can be written as follows;
ta o = Ô ^ ^
ây 0 - f % - %
( 3 )
dz = — dc - dz
o c
After inserting formula (l) into (2) and formula (3) into (2) the following
working correction equations are obtained in the image scale;
^2 , , , ,
v x “ "^p + *” < k^ ,+ ~àc- “d2H- y 'dae +(l+ ) edep - ~^-dcj - ^^L-dt+ ^dl-dx'
c
. / /
*2
( 4 )
v' ss -dyp+ -^dy^+^dc- ^dz- x'dae + -df -(l+ edej - -fdt- ■^^-dl-dy"
dx'— — x ^ = X ^ _ x ^
z measured given
<3y'= - 7' = y
measured
- 7
given