1.152. Error distribution after the coordinate transformation 
For this investigation we have to assume that the positions of the 
control points are known. We shall demonstrate the procedure in detail 
for two control points 4 and 5 in the following positions (fig. 2). 
ry = b Ly = 0 
(12) 
Yi =D yg mm — b 
The differential formulae (3) and (4) above for these two points become 
dx, = Sdz, (13) 
dy, = S (— da, + dx; + dy,) (14) 
dz, — Sdz, (15) 
dy, = S (dx; — dx; 4- dy;) (16) 
The differential formulae of the wellknown coordinate transformation 
procedure are as follows 
db 
dx = dz, + % $ ydx (17) 
) 
db 
dy = dy, + y b + xda (18) 
db 
In these formulae dz, and dy, are the two translations, + is the scale 
) 
change and dx is the rotation. 
Applying the formulae (17) and (18) to the control points (12) we 
find 
dx, = dx, + db — bdx (19) 
dy, = dy, + db + bdx (20) 
dx; = dx, + bdx (21) 
dys = dy, — db (22)