parallelpiped (points inside the parallelpiped cannot be observed since most S. T 
objects under consideration are not transparent). Accordingly, the values of 
OYt, OYt and OZt do not represent the standard deviations of the points on 
the surface of three dimensional object. The surface of three dimensional 
object can be approximated geometrically by a plane, where the object points 
are distributed, rather than a three dimensional object. This plane is the 
best fitting plane for points located on the surface of the object. The opti- 
mum position of the two theodolite stations are designed as if the surface of 
the three dimensional object is that plane. The values of the optimum base 
distance Bo, the optimum object distance Do, the theodolite elevation Eo 
OXp, OYp and OZp, for that plane, are given in Section V. Moreover, the 
optimum object distance Do must be checked verses the object distances of the 
offset points. The offset points must lie not too close to the two theodolite 
stations where oX accuracy is bad. If some of the offset points are too 
close to the theodolite stations, the optimum object distance must be increas- 
ed. 
The theodolite elevation for two or three dimensional object has to be 
taken in the field as close as possible to the middle of the object height. 
VII. CONCLUSIONS 
The accuracy of control points, obtained from theodolites intersection, 
can be maximized if the base distance between the two theodlite stations (B) 
is taken as 1.4L, the object distance (D) is taken as 0.26L and the theodo- 
lite elevation (E) is taken at the middle of the object 0.5H (where 2L is the 
length of the object and H is the object height). The expected values of oX, 
OY and 0Z of the object-coordinates for any theodolite position can be obtain- 
ed from equations 20, 21 and 22 respectively. 
ACKNOWLEDGMENT 
The author is grateful to Saudi Arabian National Center for Science and 
Technology (SANCST) and to the University of Petroleum and Minerals (UPM) for 
their support during the preparation of this paper. I also extend my sincere 
thanks to my wife Nerman Tawfik for reviewing the mathematical equations in 
this paper. 
REFERENCES 
1. Abdel-Aziz, Y.I. 1978 "Applications of Photogrammetric Techniques to 
Building Construction. Photogrammetric Engineering and Remote 
Sensing, the Journal of the American Society of Photogrammetry, Vol. 
45, No.2, 1979. 
  
2. Abdel-Aziz, Y.I. and Karara, H.M. , 1973 "Photogrammetric Potential of 
Non-metric Cameras", Civil Engineering Studies, Photogrammetric 
Series No.36, University of Iilinoís, Urbana, Illinois, U.S.A. 1973: 
  
3. Faig, W. 1972 "Design, Construction and Geodetic Coordination of Close- 
Range Photogrammetric Test Field", Civil Engineering Studies, Photo- 
grammetric Series No.36, University of Illinois, Urbana, Illinois, 
U.S.A. 1971. 
  
  
4. Malhotra, R.C. and Karara, H.M. "High Precision of Stereometric System, 
"Civil Engineering Studies", University of Illinois, Photogrammetry 
Series No.28, 1971. 
10