b) all equations are of the type: 
e- £(M,,M;j) 0 i,j=1..n, 
- £(M;,N;) 0 i=i..n, j=1..q. 
il 
So, block adjustment by independent models 
belongs to the sub-class of problems 
satisfying the definition 1.1. 
Since every model is rapresented by the 
seven orientation parameters M; and every 
control point known in altimetry or 
planimetry by the added variables N; 
every node has a physical meaning, as 
underlined later too. 
Let' s now define 
V=ini, e 5 z/ün-/An+17 e. ‚Nn+q} 
and, if: 
Ej = {(n;,n;)|i,j=1...n, 3 one point 
connecting model 'i' and 'j'} 
Ey = {(n;,ny)|j=n+l...n+q, i71...n if the 
control point known in planimetry or 
altimetry has the image coordinates in the 
model 'i') 
GRAFICO DELLE STRISCIATE € DE! PUNTI Di APPOGGIO 
tenon 
Tiganametia: LAs 8 3° erane 
  
  
  
  
  
   
— Jd 
Puts © 0000400 © plenmane à quete 
oco» Hn 
Punk & 0990005 & soie quel 
‘ 
f 
| 
| 
| 
| 
| 
| 
  
  
  
  
then, the set of the edges is: 
E = Eı U E» 
The above definitions of the sets V and E 
summarize an immediate way to build the 
graph, underlining at the same time that 
the graph is properly related to the 
nature of the problem instead of the 
matrix of the linear or linearized system. 
Although this, the reordering of the 
variables done to preserve the order of 
numbered nodes determines the location of 
not null coefficients and, so, the 
structure of the matrix. Infact, the 
generic equation f(x,,X,,X3,X,)=0, after 
linearization, becomes: 
a1Xx; + a2xı + a3x3 | aaXa = b 
where 81,82;à83,84 and b are the 
coefficients whose position within the 
matrix is determined by the location of 
the variables and not by the value of the 
coefficients which depends on the type of 
the equation. 
| 
  
SCALA 125000 
Figure 1. Scheme of photos ralating to the experimental example of block adjustment by 
independent models for the realization of numerical cartography in the Friuli-V.G. 
region. 
Figure 1 reports the scheme of the photos 
and the control points for an experimental 
example of block adjustment relating to 
the realization of numerical cartography 
in the Friuli-V.G. region; figure 2 shows 
the graph relative to the example reported 
103 
in figure 1. Note how the location of the 
models is repeated within the distribution 
of the nodes, how the edges describe 
precisely which models get together the 
connecting points and in which model the 
control points lie.