Analysis for Single Mutually Orthogonal Axes in Object Space 
The orientation matrix of a photograph can be determined if the interior orienta- 
tion elements (xs Yo? f) are known and the images of the X, Y and Z axes, including the 
origin, are imaged in the photograph. Figure 7 shows such a photograph, the X, Y and Z 
axes being formed by the edges of a building. 
y 
  
  
| x 
  
  
  
  
  
Figure 7 
For convenience, the image coordinate system is chosen with origin at the 
principal point; that is, x Yo 0. The origin of the object space coordinate system, 
XYZ, is imaged at j. Points a, b and c are suitably selected points on the images of 
the X, Y and Z axes. 
For the time being, let us presume that image point j is at the principal point, 
Z 3 = Y4 = 0 and x, = 0. This is a 
very special case of the problem which seldom occurs, but which is useful in developing 
o, and vanishing point n, is on the y-axis; that is, x 
the analysis for the general case. The vanishing points Bu» My and n, must be on image 
Z 
lines ja, jb and jc respectively. Hence: 
By = Ay «n 
4" (35) 
x. x 9 (49) 
in which dy 7 Y and dy 7 ^ 
m