FA 
    
   
  
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
  
  
  
  
  
    
    
  
  
  
  
  
   
   
   
   
  
  
  
  
  
z 
  
  
  
  
  
  
  
  
   
4 
and for dependent pairs 
bd Pa (10) 
dbzs = — Pu (11) 
2. The influence of the relative orientation upon the elevations 
The influence upon the elevations of the model from (8) — (11) is 
obtained from the wellknown differential formulas 
h? 4- x? h2 + (x — b)? x—b 
lh = — loi 7 leo + Za 2 
d b de, b deo b dbz, (12) 
Hence we find from (8) — (9) for independent pairs of pictures 
h 
dh = — b2d (2x2 — 2bx + 2h2 + h°)p, (13) 
and from (10) — (11) for dependent pairs of pictures 
h 
dh = — bad (2x2 — 3bx + 2h + b2)p, (14) 
(13) and (14) demonstrate the influence upon the model elevations of 
the distortion via the elements of the relative orientation only. 
In order to find the final influence upon the elevation we have to 
take the compensating effect of the absolute orientation into account. 
The number and the location of the elevation control points will of 
course play a most important role. After the absolute orientation has 
been performed, the final effect upon the model elevations must be 
exactly identical for both the methods of the relative orientation. 
3. The compensating effect of the absolute orientation 
The differential formula of the elements of the absolute orientation 
is wellknown. 
We have dh = dh, + xd n 4- yd £ (15) 
where dh, is the translation of the model. 
d# and d £ are the rotations of the model around the axes x = 0 and 
y = 0 respectively. 
For three arbitrarily located elevation control points 1—3 we have’ 
dhy =dh + x, d'y + y4d€ 
dhs — dh, + xd n + y2d € (16) 
dh, — dh. c xad N d yad £