1€ 
1€ 
  
  
x’ (sin @ cos x + 
  
  
Fig. 2. First arrangement of the coordinate systems and the rotations. 
cases first the complete projective relations between corresponding 
points in the two planes after the three rotations will be demonstrated 
and then the general differential formulae of these relations will be 
derived. We will also distinguish between the two cases as demon- 
strated by the formulae (1)—(2) and (3)—(4) respectively. In accord- 
ance with practical application to photogrammetry the first case will 
be denoted the projection case and the second one the photography case. 
1. The projection case 
1.1. Rotation sequence Q9, 0 and X. 
If the x’ y'-plane is rotated through arbitrary angles p, o and x in 
this sequence the relation between the coordinates of an arbitrary 
point P and the coordinates of the corresponding point P' would become: 
' (eos o cos x 
h (— x' eos o sin x 4- y' eos o eos x — esin o) 
sin y sin o sin x) 4- y' (cos g sin x + sin sin œ cos x) + € sin @ cos c) 
cos g sin o sin x) 4- y' (cos g sin o cos x — sin o sin x) + e cos o 
x’ (sin © cos x + cos sin w sin x) + y’ (cos g sin o eos x — sin g sin x) + € COS P COS © 
cos o) 
(6) | 
- 
D |