El 
2 
2. The Invariants of the Orientation. 
  
The relative orientation of a pair of photographs is defined in an 
earlier paper (1) in terms of the base components (C, Cy, C,) and 
the Eulerian angles ? v and $. 
The condition of correct relative orientation gives the relationship 
y (C, 5— C, 5) +7 (x Cz+ C, f) -— Cy (x$ Ef) 0. .. (1) 
where (x, y) are the coordinates of the image in the left hand picture ; 
(8,7,5) are given in terms of the photo-coordinates (x', y') in the 
right hand photograph by the transformation matrix 
— L sin + cosa M sin y — sinA . — sin? ibt 
L cosy + sinA —M cosy + cosa sing cosy A2) 
sin '&- sin $ — sind cos ¢ cos 2- 
where 
L = (1 —cos®) sing , M = (1-—cos#)cos@ … .. (3) 
and 
A = y $ - the difference between the azimuthal angles. 
The value of ^ will usually be small when the principal-point bases 
are employed as x axes. The actual value can be derived by applying 
condition (1) to the principal points P: and P ET follows : 
2 
Hence, 
»7/ — (fsin?sinp, —fsin®cosy,  —f coss). 
(£5756) P, (f sin® sin sin Ÿ cosy cos 4 ) 
Substituting in Equation (1) we obtain. 
P [zz 5T 922 5 E Yezeej). 
C C. bCz.. ,b 
y/ x = re sin 9 cosy Av cos? — sin? siny ) … .. (4) 
P2(X5y202--f; X= - bb; y = 2 = 0) 
Hence, 
(5,7 3:5) P, 
( fsin? siny — b ( — L sinyy + cosa ), 
— f sin 9 cosy —b ( L cosy + sina), 
— f cos $- — b  sin$ sing)