In Figure 3, we introduce an error for the projection centre 
coordinates in relation to the rotation axis. The amount of error is 
one project unit in X-direction. The offset causes the rotation to 
form a geometry where each camera location has a different 
projection centre. This means that each sub-image has its own 
perspective view of the scene. The result is the diverging bundle 
of observation rays. Our program calculates the error as the 
divergence of the observation ray in relation to the case where the 
projection centre lies in the rotation axis. Thus, the width of the 
spread of an observation ray bundle at the second target plane is 
half of the error our simulation program outputs. 
Point 1 
Point 2 
  
Figure 3. Eccentric sub-image panoramic frame camera geometry 
with one project unit offset in X-direction and 20? increments. 
Figure 4 illustrates the case in which the offset of the projection 
centre is one project unit in the Z-direction. We can see that the 
width of the spread of an observation ray bundle is similar than 
in Figure 3, but the deformation of the image changes. However, 
in practice the FoV limits the usefulness of such an analysis. 
That is because when we have rotated the camera more than half 
of our FoV of 53.13°, we run into a situation where we cannot 
see our target anymore assuming the target was in the centre of 
the image when the rotation started. Our simulation draws the 
observation lines from each projection centre coordinates, 
whether the camera actually sees the target or not. The program 
can be modified to take this into account and draw only the lines 
which resects with the image plane. 
If we increase the offset further, we can see how the projection 
centre coordinates deviate further from the rotation axis. In 
Figures 5 and 6, the offset is five units and a camera constant is 
four. Especially in Figure 6 this makes it hard to comprehend 
how the image plane geometry is formed. The blue lines are the 
image axes and at the end of each blue line is the projection 
centre. Starting from each projection centre there are two 
observation rays, red and green, going to the first target plane 
and continuing to the second plane. At the other end of the blue 
line, is the image plane. 
  
  
    
    
  
  
   
  
   
   
     
  
    
    
  
  
  
  
  
  
  
  
   
   
     
   
  
  
   
  
    
In the case of five unit offset in Z-direction, the deformation is so 
large that the cylinder we can see near the rotation axis are 
actually the backsides of the image planes facing the rotation 
axis and image axes are pointing outwards. 
Point 1 
Point 2 
Figure 4. Eccentric sub-image panoramic frame camera geometry 
with one project unit offset in Z-direction and 20° increments. 
Point 1 
Figure 5. Eccentric sub-image panoramic frame camera geometry 
with five project unit offset in X-direction and 20° increments. 
  
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