(3) 
lized 
be 
Any 
be 
imply 
d as 
dered 
metry. 
  
Consequently, it must be possible to develop an analytical solution for the 
most general problem of photogrammetry, based solely on formulas which express 
the geometrical properties of an individual ray belonging to a bundle of rays, 
formed according to the concept of the central perspective. 
The corresponding relation is the condition that the center of projection 
O, the image point'r and the object point R are collinear. (Fig. 2) 
From Figure 2 we obtain: 
Hs u.T, where ju is a scale factor ; (4) 
The projection of the vectors T and R respectively into the three coordinate 
planes gives the component equations: 
X = X, + pu 
Y Y, + WW (5) 
2 =2 + |W 
o 
The triplet of formulas (5) is the analytical expression for the condition 
that, the points O, r and R lie on a straight line. 
By eliminating the scale factor p in formulas (5) we obtain: 
where (X) = X - X, 
(X) = (z) = 
(Y) * Y - Y, (6) 
(Y) » (z) Z 
(2) = 2 - 2, 
From Fig. 2 we read directly: 
F = lu + jv + kw = 1x + 3 + £e (7) 
11