6 
GIUSEPPE BIRARDI 
/ — THEORETICAL FORMULATION 
The rigorous procedure. 
4. — Let us suppose to have observed and bridged, by means of any spatial 
triangulation procedure — analogical or analytical — all strips forming a block ; 
and to have referred to a single origin the instrumental observed coordinates of 
each strip, after correction for earth sphericity. If we divide up the strips into 
short stretches (each of 5-6 models at the most) following the criteria set out in 
a preceding paper ( 1 ), the block may considered to be formed by a total of n stret 
ches, to each of whom corresponds a model M l (i — 1, 2, ... n) sufficiently rigid and 
indeformated in respect to reality, but with an unknown absolute orientation and 
dimension. 
We must evaluate, for each M 1 stretch, the seven parameters of absolute 
orientation and dimension which allow to transform the relative coordinates 
into absolute coordinates, i.e. : 
X' o , , a 1 = s 1 sen D- 1 , (3* = s 1 cos fr 1 (planimetry) 
Z’* , Acp 1 , Aop (altimetry) 
The above will be assumed as unknowns of the problem ; in the whole block 
we shall therefore have 7 n unknowns. 
5. — The constraints to which the M l models are subjected may be divided 
into : 
— external constraints, mainly consisting of known points variously distri 
buted within the stretch, and around which the M l model will have to adhere in 
the best possible way to the actual ground surface ; 
— internal constraints, consisting of photographic points common to se 
veral stretches and independently observed within each of them, around which 
we shall impose, in the best possible way, the juxtaposition of Mi .... models 
concerned. 
From these constraints we shall derive the equations to calculate the un 
known quantities; they will be of two different types (external constraint equa 
tions, or external equations, and internal constraint equation, or internal equations) 
which will bring about a generated system of the type : 
(1) Birardi G., Triangolazione aerea a modello rigido. « Bollettino di Geodesia e Scienze affini» 
dell’ I. G. M., n° 2, 1962.