If the scale number m, is defined as ds;/ds';, by combination with 
(5) we obtain the differential equation: 
ds; = mp + dsy' + C + Sj. * dsi. | (6) 
Since distortion depends on direction a, the following relationships c can 
be introduced: 
Xi ?94.* COS 8 , .Xi 
Sj' + cos a 
(7) 
$; + sin a 
Yi Si «Sina , yi 
where: 
X4,y4 coordinates of a point before transformation 
X4 ,y4 coordinates of the same point after transformation 
When (6) and (7) are combined, the following transformation equations 
are obtained: 
  
  
  
  
  
d m.2 + C. « X, 2 + yı2 
E v /m, v4 c tX C Jn" + Yi 
X4 - 9 Cx = 2 . Mns 
2 Cx X4 (8) 
jor -m, + /m? + 4. Cy * y4 : e /x;? + Yi2 
J4 = ’ Cy = 2 . y 2 
Qo Cy Yi 
In the example under consideration, the castle in the centre of Darmstadt 
NS taken as the central point, with m, » 1.0, m, = 1.40, 
= 9.0 [cm], c = 0.0444 [ cm-1]. Figure 4 shows “an excerpt from the 
D 25 000  $opographic map of the environs of Darmstadt before and after 
transformation with the OR1/SORA-MP system. 
7.2 Transformation from panoramic to perspective photographs 
In addition to panoramic cameras used mainly for mapping from the air, 
there are also terrestrial panoramic cameras used in advertising, 
architecture, accident, forensic documentation etc. 
In the case considered here, a panoramic photograph had to be trans- 
formed into a perspective photograph. 
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