O.M.I. Homologo-Comparator for the Survey of Spatial Lines 
by 
Ing. LUIGI RONCA 
FOREWORD. 
In this study, there is expounded, in an exclusively qualitative manner, the theoretical 
principles on which the new instrument and its employ are founded. In the subsequent study 
the matter will be treated instead in an analytical manner, thereby arriving at the formulae 
of setting and of plotting. 
The OMI homolog-comparator is a universal plotter according to the classical numerical 
method for the stereophotogrammetrical survey of spatial lines, and particularly of 
trajectories or linearform objects having tridimensional development. 
Besides performing the work of a normal centesimal orthogonal comparator for 
stereograms and of a normal radiai principal point triangulator, it is also a homologoscope, 
since it permits to actuate the projective identification, by pricking or by photographie 
polar coordinates, of the pair of homologous points on the two conjugated images of a 
stereogram. 
Its universality manifests itself in reference to the take arrangement inside ample 
limits of convergency, of asymetry, of difference of heights of the take centers, and of 
obliquity. 
The theoretical outlines of the homolog-comparator and its various uses are founded: 
1) Upon the considerations of the take diehedral, as the intrinsical geometrical support 
of the take arrangement of the two phototheodolites, and on its subsequent development 
in a plane. 
2) Upon the invariance of the nuclear fulerums, particular points analytically identifiable 
on the faces of the takes diehedral and characteristic of the reciprocal external orientation 
angle of the frames of the photographic perspectives. 
3) Upon the consideration (non-essential) of a particular system of intrinsical reference 
bound to the take dihedral for the practical execution of the numerical plotting. 
I THE TAKE DIHEDRAL AND ITS SCALE OF REPRESENTATION. 
a) Relations between dihedral and take arrangement. 
The planes of the two photographie perspectives (negatives) generally intersect each 
other giving place to a dihedral that we shall call the take dihedral. The negative frames 
of the perspectives must be considered; the consideration of positive frames is equivalent. 
We wish to state here that the two particular cases, in which the take dihedral 
degenerates into a single plane (normal take arrangement, that is plates coplanary) and 
into a pair of parallel planes (oblique take arrangement), are simpler than the usual case. 
In the usual case of the dihedral that does not degenerate, the take arrangement is 
intrinsically determined on its faces by the following six parameters of reciprocal external 
orientation: 
» — Semi-opening angle (orthogonal section) of the dihedral; 
d,, d, — distances of the principal points P and P’ of the two photographic perspectives 
from the edge of the dihedral; 
g,, g,— swing, in the photogrammetrical sense, of the two frames of the perspectives in 
respect to the edge of the dihedral; 
1— distance between the bases of the lowered perpendiculars from the principal points 
from the edge of the dihedral (staggering). 
These parameters are directly deduced by the following current topographical para-