3 THE APPROXIMATE CO-ORDINATES OF 
THE POINTS 
The adjustment procedure requires the approximate value of 
the co-ordinates of the unknown points. They can be obtained 
in any possible way. One of the possible ways is then the 
procedure analogue to the aerial triangulation adjustment by 
independent models (Fangi, Thessalonic, 1999). Even with 
this computation the reciprocal visibility between the 
adjacent theodolite stations is not required. The computation 
takes place in two steps: 
1. Formation of the models: By means of the co-planarity 
algorithm the three orientation parameters of one theodolite 
station with respect to a next one, are estimated. Then, by 
intersection of lines in space the relative co-ordinates of the 
intersected points are computed. Similarly to 
photogrammetry, the locus of the intersected points can be 
defined model, that, differently from the photogrammetric 
one, is already vertical, for the intrinsic nature of the geodetic 
measurements. There are two types of models: those formed 
by three vertices (three-section) and those formed by two 
models (bi-section). The computer programme tries first to 
form the trisected models, then the bisected models, 
comparing the observations of one station with all the other 
possible ones. — 
2.The final co-ordinates of the model points are worked out 
by means of an absolute orientation (four + one parameters). 
The ground co-ordinates of two points at least are then 
needed. When the models to be oriented are more than one, 
they can be linked with to procedure similar to the aerial 
triangulation with independent models. One model is 
equivalent to a traverse side. Compared to the triangulation in 
photogrammetry, the unknown parameters are less, all the 
equations are linear, and no iteration is needed. 
No approximate value for any unknown parameter and 
coordinate is needed except the bearing of the zero reading 
for any theodolite station. It is the useful to to get it with a 
magnetic compass. 
4 THE COMPUTER PROGRAMME FOR 
ADJUSTMENT: 3Dom 
A computer programme has been written called 3Dom (the 
name means three-dimensional adjustment, while the sound 
of the pronunciation is equal to freedom: the freedom to place 
the theodolite wherever it is useful and not where it is 
required to be visible from the other theodolite positions, 
freedom on the surveyor to travel with the least equipment). 
The programme is written in Fortran Power Station. It uses 
the Cholewky algorithm for triangularisation, solution of the 
normal system and inversion of the normal matrix. The 
design matrix is reduced, and coupled with a matrix of 
addresses (Mussio, 1984). In addition to the numerical report 
3Dom has a graphical output, preparing a file with the 
extension .dxf. The ellipsoids of errors (Mussio, 1984) are 
drawn point-wise, along 20 meridians. The accuracies of the 
measuring instruments,  theodolite for angles and 
distantiometer for distances, can be input. 
5. THE CONTROL NETWORK OF THE 
GUGGENHEIM MUSEUM IN BILBAO 
In the month of April 2004 a control network for the 
photogrammetric survey of the museum Guggenheim (figure 
4) in Bilbao (Spain) has been set up. It is composed by 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
- 17 theodolite stations 
- 11:751 points 
We didn't make use of any target, choosing only natural 
points, taking advantage of the particular nature of the 
exterior panelling, composed by metallic plates of titanium, 
with very sharp edges (figure 5). The building is then an ideal 
environment to set up a very dense and accurate topographic 
network in short time. 
  
Fig. 4 —The Guggenheim Museum in Bilbao. 
From any traverse vertex the surroundings vertices have been 
observed with the help of a rod with a reflecting prism. A 
portable GPS Pathfinder Casio, with the accuracy of 10 m has 
been useful to get approximate positioning. In order to be 
able to observe the points of the top of the roof of the 
building, photographic images have been shot from the hill 
placed in the northern side of the museum. For the good 
orientation of the images taken with long focal length lenses, 
it is necessary to know the projection centre co-ordinates 
(Fangi, 1990, 1991). Therefore three theodolite stations have 
been placed rather far away from the museum, at a distance 
ranging from 500 m to 1.2 km. These stations have been 
linked to the net by resection in space. In this situation, with 
narrow angle resection, (figure 7), the geometrical 
configuration is poor and weak. Normally the determination 
leads to high values of variances of the co-ordinates. 
  
Figure 5 — The exterior panelling in tiles of titanium helped in 
the selection of the observed point coincident with the 
vertices and with the edges of the buildings 
Among the 751 observed points, some of them have been 
surveyed by irradiation (60) and mostly by intersection (691). 
We used a reflector-less theodolite. In spite of that, the 
remarkable distances did not allow the direct measure of the 
distance for mostly of the points, and we had to use the 
intersection to get the point coordinates. 
     
   
   
   
  
   
  
  
  
  
  
  
  
      
   
  
  
  
  
   
   
      
    
    
   
   
   
    
  
   
   
   
  
  
  
  
  
  
  
  
  
  
   
   
   
     
     
  
  
Th 
cor 
for 
cot 
col 
top 
ha 
ren 
bec 
ver 
ord 
tab 
tra 
Tal 
1) 
2) 
3) 
1): 
7) « 
4) 8 
3): 
In 1 
ise