4 
GIUSEPPE I N G H I LL E RI 
trary, in the semianalytical method, those rotations are computed according to 
the condition that the left taking point of the model and at least two points on the 
ground model fit in the positions determined in the preceding model. 
Let us suppose, in fact, we know the instrumental coordinates of the taking points 
and that, once determined, they should not vary during the execution of a whole 
strip. The models are formed with a relative symmetric orientation, using the para 
meters cp 1( cp 2 , x 1; x 2 and co x (or oo 2 ). The models so formed evidently have an arbi 
trary scale and angular position, but it is evident that the relative position of the 
model and of the taking points is the same that the ground and the taking points 
had at the moment of the shoot of the stereogram. 
Let us read in each model the instrumental coordinates of some transfer points, 
at least two in the preceding model and two in the successive one. 
In each model we have to compute 7 unknowns, for the calculation of the 
absolute orientation. 
Let us suppose, now, that the first model of the strip has three known points 
or, at least, the three coordinates of 2 points and the height of another point. 
Then, we shall write 7 equations and, by solving them, we shall obtain the 7 requi 
red orientation parameters. 
If we indicate by capital letters the ground coordinates and by small letters the 
model coordinates, and introduce the coordinates relative to the barycenters G 
and g of the ground and of the instrumental points, the equations are evidently of 
the type : 
X 
= X [x cos 
(* 
X) + 
y 
cos 
[y 
X) 
+ 
z cos 
(zX)] 
1) 
Ÿ 
= \[x cos 
{x 
v) + 
~y 
cos 
(.y 
y) 
+ 
Z cos 
(z Y)] 
Z 
= X [x cos 
{x 
Z) + 
y 
cos 
{y 
Z) 
+ 
Z cos 
(2 Z)] 
with 
2) 
X -- 
= Xq 4" X 
; 
Y : 
Yg 
+ 
Ÿ ; 
Z = 
= Zg + z 
and 
3) 
X 
— x ë T* x ; 
y 
4- 
y 
Z = 
The director cosines, function of the three angles d>, p and g, (rotations of the 
model in order to fit on the known points), can be given, for instance, by the following 
relations : 
COS 
(X' X) = 
cos a cos O 
+ 
sen 
G 
sen 4) sen 
4 
cos 
(Y'X) = 
sen g cos 4) 
cos 
G 
sen 0 sen 
4 
cos 
(Z' X) = 
cos nsen 0 
cos 
(X' Y) - 
— sen G cos g 
cos 
(Y' Y) = 
COS G COS g 
cos 
(Z' Y) = 
sen g 
cos 
(X' Z) = 
— cos g sen 
4- 
sen 
G 
cos sen 
4 
cos 
(Y'Z) = 
— sen g sen 
— 
cos 
G 
cos sen 
4 
cos 
(Z' Z) = 
COS (JL cos 
4)