Day * 
ll ma 
7%0.N,X, FT m.n.V. -7&,.7. 
{ 101%; MD 2,148, 7 
i=l 
The direction cosines used in equation 18 are obtained by using 
the image coordinate system (Fig.8) and the rotation matrix M. 
The direction cosines of a line from the exposure station to the 
image point is 
  
Cos qw. “x, ud. where: 
S dt i i/ à 
i-i... t = : 
d, = Cos Bi = Yi/d; (19) ai the image point 
Cos Ys £74; Si = ith exposure stn 
n 2 2 2. b 
di = (x; t Yi tf; ) 
Then the direction cosines of the line from exposure station S 
to the object-point A is:- 
T 
  
  
S,A, 7 M.ig,a. , Orl f. cos o, 
i i i "i'i i T 
T 
m, | = M, | cos Bs (20) 
n; COS Yr 
The matrix of coefficients in equation 18 is symmetrical and the 
solution is obtained from these three linear equations. This 
newly developed procedure can be used for any data acquisition 
system configuration based on more than two stations. 
(ii) Optimisation using Planes 
The second method of obtaining the spatial coordinates is based 
on optimisation using the planes at the four sides of the quad- 
rustational pyramid (Fig.5). However, it should be emphasised 
that this method cannot be used for a two-station system. 
The general equation of a plane in the system is given by the 
following expression: 
X-X Y-Y Z-Z 
S S, m 
i i i 
Xp Yo Zn. = 0 (21) 
i i i 
Bx By By 
i i i 
Expanding equation 21 we get: A.X + B.Y + C,Z + D, = 0 (22) 
where 
A, =t(YR, BZ, + ZR. BY.). y, B. = "(XR. BZ, — ZR, BE.) 
á + i i i 1 i i i i 
Ci = (XR; BY, = YR; BX.) 
135