Dividing equations (108), (109) and (107) by E1Lyz: FiLyz and GL? respectively, 
we obtain: 
  
  
  
  
  
  
  
Dvz is Xx. 
E = E (110) 
ilvz 1 
Dyz Yt c 
TI = P (111) 
1 x27 1 
oo 2 Art 
Brees. 1 au 
lY 1 : 
But from equation (87), it is seen that: 
Xi Xe Yi Ye 2, Zo 
= = F m G m 8, e. (113) 
j 1 f 
Hence, it follows that: 
Dyz = = = Day = 8 . (114) 
Ely Filyz Ober 1 
Equations (113) and (114) provide a convenient set of expressions for relating 
the camera station coordinates to dimensions in the object space, the connecting link being 
the quantity 6 This quantity must necessarily be positive for images in the positive 
1 
photograph plane. Hence, the sign of Lys Luz or Ly in equation (114) must be chosen so 
as to make 91 positive. 
c Ye or Ze is involved in the 
computation, either as a known or as a sought quantity, the corresponding object point 
It is evident from equation (113) that whenever X 
coordinate, Xi, Yi or Zi» must be known. Fortunately in practice, the object space 
coordinate system can often be chosen such that one of Xi» Yi or 2, is zero. 
Relationships Between Two Dimensions in the Object Space 
Dimensions Dy? Dy, and De are representative dimensions in planes parallel to 
the XY, YZ, and XZ coordinate planes. The endpoints of each of these dimensions are 
designated by points 1 and 2. Three more dimensions are now introduced. Diy is another 
dimension in a plane parallel to the XY coordinate plane (but not necessarily the plane 
in which Duy lies), Dj, is another dimension in a plane parallel to the YZ coordinate 
YZ 
plane, and Diy lies in a plane parallel to the XZ coordinate plane. The endpoints of 
X 
each of these new dimensions are designated by points 3 and 4. 
In addition to the K-values defined by equations (92) through (97), the following 
K'-values are introduced: 
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