whereby the transformation matrix of the two vector triplets is: 
  
  
1 1 k 
1 11 15 ik 
j 2.8 & | (8) 
ki kj kk 
Denoting, for example, the two rotational angles between the two vector 
triplets according to Figure 2 with a and w, we obtain: 
u=X cos @ - y sin Q sin o * c*sin Q cos o 
V = cos OQ + c sin w (9) 
Ww - -X sin Q - y cos Q Sin à 4 c cos Q cos w 
From Figure 5 we obtain: 
X --x- xp) cos K -(y- Y sin x (10) | 
<<i 
= -(x - x gin Kk + - cos K 
(x - x) (y - XQ) eo 
where x and y are the plate coordinates of an image point in an arbitrarily 
oriented rectangular reference system (plate coordinate system). 
Substituting (10) into (9) and using (6) we have: 
(2) | (x-x, A, * (3-5 +c 9] ; 
  
  
  
  
X = | X, 
S (11) 
Ys (a) | 62235, + (y-y_)B, +c E] is 
Q o 
with Q = (x-x JC, + (y-y,)¢, *cF 
and 
lm | G04, + (Y)B, + (2), ] it 
s P (12) 
c [ Q4, + (Y)B, + (2)c,] 
y= 3 * Yo 
with q = (X) D + (Y) E + (Z) FP’ 
13