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')
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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.
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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.