(3) 
US à. (4) 
Between, small changes of the elements of the inner and outer orientation of the projector 
there are the following well-known relations: 
  
hdx, 
my WC dx, (5) 
hdy,’ 
gm dy, (6) 
dz, — fdg, (7) 
dy, = fdo, (8) 
hdf = —fdz (9) 
where dx," and dy, are the translations of the grid coordinates, dx,” and dy,’ are the 
translations of the principal point of the projector caused by rotations dy and do of the 
image plane around the y'- and x'-axis. dx is identical in the two systems. 
The connection between small changes in the outer orientation and the corresponding 
translations of projected points is given by the following well-known differential formulas: 
dd y xy y? 
dy = dy, + i dz, + xdx + f dg +11 + AR hdo, (10) 
X x2 | xy ; 
dx = dx, + * dz, — ydx + (1 + AE hdg + "E do. (11) 
If the machine coordinates x and y are replaced by the image coordinates we get: 
  
zn 
X = Y 
yh 
Y= f ? 
y x'h x'y'h y? 
dy = dy, + "f de, + = dx + E. de + (1 + =) hdc, (12) 
dx = dx, + 2. dz, — gr dx + (a + 7 hdp + Sr do, (13) 
f=? f f£ 7? 
dy * y nensured 7 Ygiven IN the projection plane, 
dæ = “measured 77 “given IN the projection plane. 
If superfluous observations are present we write the formulas: 
y x'h xy’ h y? 
9,7 du, t "E. dz, + FE dx + Ye de +11 + A] hdw — dy, (14) 
a" yh a2 «^y (15) 
v. = dx, + a de, — fn dx + 1 + tig hd + PE hdw — da. t 
   
  
   
    
    
    
    
   
  
     
     
    
   
     
     
    
      
    
    
      
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