Three equations (3-5) are necessary to determine the interior 
orientation. These equations may be derived from three images which 
contain two pairs of perpendicular vectors (one condition of 
orthogonality) or from one image with three pairs of perpendicular 
vectors (three conditions of orthogonality in one photograph). If 
only the principal distance is to be calculated, one equation is 
sufficient as X, = ¥, = 0 (principal point = center of image). 
Ethrog /1/ and Rawiel /6/ give a very special description of a similar 
method. In close range photographs Rawiel uses control points on a 
rectangular frame surrounding the object, whereas Ethrog takes 
parallel and perpendicular lines on a square block to derive the 
interior orientation from one image. 
3.4 Geometrical Restrictions 
The coefficients of equation (3-4) indicate numerically weak 
positioning of images. This method fails if one pair of vectors, e.g. 
Vi, Vi, is parallel both at the object and at the image. Coefficient 
ls (3-3) which can be interpreted as the vector product of v | and UM 
vanishes if these vectors are parallel. Thus K, of equation (3-5) 
will be 0, and the "'variable' (x?«y?«c?) cannot be determined 
(Fig. 6). 059. ¢ 
y} 
  
  
Fig. 6: Parallel vectors at the image 
(Y5-Y 4) (x, -x4) - Gt -X  Gy,-Y 4) = 
X73 x X, X, i 
ys « by,-v, 
= v! ! = 1l = . 
HP 2121. 
It is necessary to avoid photographing edges of Square blocks parallel 
to the image plane as these edges define parallel vectors at the 
photograph, and cannot be used to calculate the interior orientation. 
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