13 
e. 
5. Basic Formulas 
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5.1. PROJECTIVE RELATIONS, PHOTOGRAPHY CASE 
Our mathematical model is based on the general relations of a central pro jec 
tion of points in a three-dimensional space on a two-dimensional image plane. 
If we define the co-ordinate system 1 ) with axes and rotations as in Fig. 3 the 
Fig. 3. 
Definition of axes and ro 
tations. The right hand 
system X, Y, Z gives the 
positions of points P in 
object space. The exterior 
projection centre has the 
co-ordinates Y 0 , Z Q in 
this system. The image co 
ordinate system x, y is lo 
cated at a distance c from 
the interior projection cen 
tre. In this figure the image 
is placed in positive posi 
tion, so that the interior 
and exterior projection 
centres coincide. The ima 
ge plane is rotated around 
this point through the 
angles co, cp, x. The co-rotation is primary, the ^-rotation is secondary and the «-rotation is 
tertiary. In the figure the principal point (the foot of the perpendicular of length c) and the 
origin of the image co-ordinate system x, y coincide, but generally the principal point has the 
co-ordinates x 0 , 
X 
general formulas are 
Ml 
(Z) 
in 
(z) 
*o “b c 
y = y 0 + C 
5.1.1 
5.1.2 
*) The co-ordinate system can be chosen arbitrarily. This is the system used in the instruments 
from the Wild Company.