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method controls scale, azimuth and height in a strip triangulation wit 
degree of accuracy. In the future, this method will be built into the a 
gulation. 
ha Very high 
Dalytiea] tu 
Formulas. 
In computing the relative orientation different procedures may be follow 
on the mathematical formulation of the problem. The procedure developed at 
Research Council is based upon equations of analytical geometry. 
The absolute orientation of the photographs is determined with respect to a l'ectangulay 
system of co-ordinates X, Y and Z. The differences between the X, Y and Z CO-Ordinafes 
of the projection centres of two consecutive photographs i and i+1 ina Strip are the ke 
components bx, by and bz. The co-ordinates of image points in a photograph are compita 
in a system X, Y, Z of which the axes are parallel to the axes of the X, Y andZ 
while the origin is at the projection centre of the photograph. 
When the two photographs are in the correct relative orientation, rays from em 
responding image points in two photographs intersect. The two corresponding image 
points and the two projection centres lie on these intersecting rays and must thus ] 
plane. This means that the third order determinant 
ed, depending 
the Nationg 
ystem 
ie in one 
bx by bz 
X, Y, À = 0 
Xt Y; Za ld cc (1) 
Each pair of corresponding image points produces one condition equation of this kind, 
If a given orientation of photograph i and a preliminary value for the base component 
bx are assumed, the elements of relative orientation of photograph i+1 are the has 
components by and bz and the three rotations of photograph i--1, The co-ordinates Y, T 
and Z are linear functions of the plate co-ordinates and the focal length: 
X=Le +Ly +Lf 
Y = Mx + MY Tom 
Z2 "u,* dong nf  — 0 2 (2) 
  
The co-efficients of these functions are the direction-cosines of the photograph axe: 
* and y and the camera axis. In these dircction-cosines occur the sines and cosines of the 
three rotations. The condition equations are therefore not linear in the five elements of 
relative orientation. This makes it difficult to solve them directly. 
The electronic computers can only perform the mathematical operations of addition, 
subtraction, multiplication and division. Every other mathematical operation must be 
reduced to a combination of these. This makes it feasible to solve linear equations. The 
equation (1) is therefore first made linear with respect to the elements of relative 
orientation. Let Vip Viu and f in the elements of the last row be substituted by c 
ordinates X, IJ Y: ra and Zi, „1 obtained from the equations (2) by substitution of 
approximate values for the rotations. This does not affect the validity of the equation. 
Further let the rotations be chosen as follows: « about the X-axis, q about the Y-axis and 
x about the Z-axis. 
Differentiation with respect to the elements of relative orientation then gives: 
bo byi bzi ba bj bzi ba byi ba 
X: Y. Z dw + X Y; Zz ‚do + X, Y, Z; ‚de 
0 Zi, Ti Yi, 1 Zi, +1 0 E Xj, 1 YS 1 Xs 0 
   
  
  
    
    
  
   
    
   
  
    
    
  
  
      
          
   
  
  
  
  
  
   
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