a = 
^S 
TX. P M. 
M PHBL LE "t 
   
We suppose that all bundle models in a block are approximately simi- 
lar to the area of the object (terrain) photographed. In that case, 
the triangulation (adjustment included) involves the application of 
spatial similarity transformation to each model in a block, taking 
into account all tie and ground control conditions. 
The spatial similarity transformation. 
Let Xij» Yij» Zij be the coordinates of an object point 
j measured in the orthogonal model coordinate system xj, y, 
2; of an arbitrary model (i) and u, and 
U WE uU. v oo, 
ij ij ij 1j ij 1j 
EU 9:3! ti the transformed model coordinates after rotations 
wi, $i and kí about the X-, Y- and Z-axes of the orthogonal 
object coordinate system XYZ, respectively. 
   
    
   
    
   
   
  
   
   
   
   
   
     
  
   
    
  
  
  
  
  
  
    
    
     
We get 
= 0 o | Fr. 4 Fs. 
i 1 *13 _ 
0 cosu -sinw y. . = Va (a) 
ij 1j 
i i - 
0 sinu cosu 2 Ww 
1j 1j 
>; PS Rl. TT 
cos 0 sing Ui; u 
0 : 1 0 : ST = "i (1b) 
sind 0 cosd Was 8 i 
eme — —— wm E m. 
cosk* -sink! 0 u r 
1j 1j 
stad coset 0 V S (ic) 
13 ij 
0 0 1 Wi toi 
ij 1j 
Let Xi, Yi, Z1 be the object coordinates of the object point 
J» Xi» Yi, Zi the object coordinates of the origin i of the 
model coordinate system xj, yj, z, and A, a scale factor. 
We then get 
x. - X, Iti 
- =X 1d 
Y: Y: i $5 (1d) 
By - Z. tij 
We know a model can be levelled by a combination of the rotations 
wl and qi about the X- and Y-axes, respectively. We therefore 
eliminate the coordinates u,,, Vi, and wi; from the equations (la) 
and (lb). This gives 
cosd - sind” sinet - sind: cOSw" X.. NEA 
i ij 13 
i i 
0 COS Ww - sino Yi j = Sij (1e) 
sing“ cos à} sinl cos fr cosut Zi j Wi3