X Y Z 
S S. S 
1 1 1 
Dy = = 12% YS. Zp 
1 À 1 
B B B 
Xi Yi Zz; 
Length of perpendicular line from the optimum point 
(X_,Y¥ ,%2 ),to each plane is 
  
  
pp Pp 
A.X TB.Y +C,2 -D. 2 2 2 
L, = 2.20 P. . where T, - A^ 4 B? 4 cC (23) 
i /T. 1 1 + 1 
i 
We assume that 4 
= s 2 
Emly (24) 
Beit . 99. . 30 O0 . 
then by minimising c, we get: mU TU O (25) 
p p p 
Equation 25 can be written in the following form: 
A. ? A.B. A.C, X A. D, 
i i'i i'i p ii 
à mc] AR Bi B,C, Y = X = B; D, (26) 
i=l. 4} ** p i-i i^a 
AC, BOC 0.2 Z C." D. 
i i i'i i p i d 
Again the coefficients matrix is symmetrical and the optimum 
point is obtained by solving these linear equations. 
EXPERIMENTAL VERIFICATION 
In order to verify the practicability and to investigate the 
resulting accuracy of the quadrustational System, a series of 
tests were carried out. In all experiments, the two short-range 
UMK cameras referred to before were used for data acquisition. 
A digitised Zeiss Jena Steko 1818 Stereo-comparator was used for 
measurements and data were processed using CYBER and facilities 
of UMRCC (University of Manchester Regional Computer Centre). In 
order to fulfil the control requirements, a precise control 
field was constructed, a detailed description of which is given 
by Babaei-Mahani (1981). 
DATA ACOUISITION AND DATA REDUCTION 
The camera stand was set up parallel to the control field with 
the camera axes perpendicular to the base. A one second theodo- 
lite was used for the orientation of the stereometric Stand to 
achieve the normal case. Pairs of photographs were taken by the 
UMK short-range cameras with equal vertical and horizontal bases. 
Measurements were taken on Stereopairs S.-79., S Sy 5175; and 
S578 using the Zeiss Jena Steko 1818 stére8comBaritor] In data 
pfocéssing, the space coordinates of each point appearing in all 
photographs were computed separately using the quadrustational 
136