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