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For long distance triangulation the necessary check points can be obtaine 
using many oblique photographs. In this case different methods are available, One could 
for instance, keep each individual plane z strictly vertical and build up a System UR 
ling a traverse by determining the angles between corresponding great cireles and the 
distances using the triangulation results. The insufficient accuracy of the determination 
of the angles seems the weak point of this approach. Another procedure was accepted i 
the present investigation. A straight line is extended throughout the Strip of oblique 
photographs by always transferring two points of the established portion of the line t 
the succeeding photograph. The fact that these points must be in coincidence in the 
cylindrie map projection permits the step by step joining on the map of the groups of 
check points determined from different oblique photographs. 
The intersecting figure of plane z and any other plane is, of course, a Straight ]ine, 
  
  
  
Z 
À 
0 P T m 
/ / ' 
7 y, ) Jl] Jj, / | \ 
gi /4 L1] L H 7] / / : N 
71] / | LAR 
FELL NE: 
1 ~~ 
l 
I 
| 
l 
i 
C +=. oN T ef X 
A 
/ 
Fig.1 
Let us consider the horizontal plane (zr) which includes the nadir point of the oblique 
photograph (Fig. 1). Intersection of z and r is line I’. When the line I’ is projected to the 
cylinder all projection rays lie in a plane 4 which includes the line in question and the 
center of the earth. The intersection of plane 1 and the cylinder, line I, is the projection 
of I’. It is fairly simple to establish the equation of line I in a rectangular geocentric 
coordinate system z,%,z. This can be transferred to the previously defined coordinate 
system having the nadir point as origin and X and Y measured on cylindrical surface. 
The Z-coordinate axes is still in coincidence with the vertical line through the nadir 
point (CN). 
Let us next consider a point P which is in plane z but outside of plane r. A straight 
line m’ which is parallel to I” can be constructed through the point P. 
Line m is the projection of m' on the cylinder. The differences between | and m can 
be determined by differentiating the equation of line I. This gives 
Z h—Z X2 (1 
dY — —Y,. h (a = REZ 2H + +) 
where Y, is the Y value at which // crosses the Y-axes, h is the flight altitude above the 
cylindric surface and R is the radius of the latter. 
     
    
  
   
    
  
  
    
   
  
  
  
   
   
  
   
  
  
  
      
  
  
  
  
  
   
  
   
    
  
  
     
   
    
     
   
    
    
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