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From the point of view of numerical 
graphics, the elements were divided into 
three categories: 
3DPOINT Points defined with three coordi- 
nates; 
3DPOLY Three dimensional  polylineal, 
generally closed; 
3DFACE Three dimensional surfaces of 
which the edges and cha- 
racteristic points are defined. 
In this case successive automatic 
processings make it possible to 
perform either polynomial 
approximation to define the trend 
of the surface equation, or 
identify plane triangles to 
create  triangulated structures 
with successive approximation for 
the final computerized display. 
The first code described (PERCONCI) is 
the basic one that identifies the points 
on the border of the basic unit, while 
the second (INTCONCI) codes the points 
with heights within the quoin. 
The other surfaces identified within the 
quoin were then, as already stated, 
plotted as closed and coded polylineals, 
taking account of the different style or 
constructional characteristics of the 
portion of monument examined. 
To complete the restitution phase, the 
operation of graphics data editing, 
managed by the same software that manages 
the plotter (MACROS), becomes 
particularly useful if one works with the 
restitution system described above. 
It is possible to perform a whole series 
of operations on the unit (partial or 
total cancellation, displacement of 
vertices, construction of a unit 
connecting isolated points and so on) 
which are often necessary for correction 
Of errors or to make up for the 
inevitable omissions in the restitution 
phase. A typical example is the 
construction (made mandatory in editing) 
of the unit referring to the lateral 
surfaces of the architectural 
decorations, obtaining by joining single 
points belonging to different planes. 
At the end of these operations one 
obtains an ASCII file of coordinates 
which forms the starting point for 
subsequent processing. 
4. DATA THINNING, 
The research also revealed the importance 
of defining modalities of distribution 
and appropiate density for points 
acquired, in order to achieve the best 
ratio between amount of data and 
Closeness to reality, according to the 
scale of restitution desired. The 
question becomes particularly important 
in architectural work, in which a wrong 
density could lead to definition of lines 
differing from the real ones, with all 
  
  
the consequences that would be entailed 
in both historical interpretation and 
analysis of statics. Too low a density of 
points, for example, could be 
counteracted by execution of a subsequent 
spline, with a definition of curvatures 
that might be completely different from 
the original. Attention must therefore be 
given to the acquisition phase, ensuring 
that it is compatible with a possible 
subsequent thinning operation. In our 
research various techniques have been 
used, which are described briefly below, 
and methods that can be extended to most 
cases have been tested. 
4.1 Recording systems 
  
The ordinary acquisition systems used in 
numerical plotters, based on various 
types of real-time recording (single 
point, space increment, time increment, 
mixed space and time, vector) involve 
different modalities to which there 
correspond differing amounts of data 
recorded for the same object. Problems of 
memory occupation apart, these may also 
generate  differeing approximations to 
reality, depending on both the algorithm 
and the increments imposed by the 
operator. Even when working on the same 
object, it is therefore easy to produce 
totally non-homogeneous configurations of 
data amounts and approximations. 
Hence the need for a procedure to check 
and where necessary thin, one that will 
make it possible to store data 
corresponding to the characteristics of 
the object and to specific prescriptions, 
in a way fully analogous to acquisition 
of non-photographer 2D data, such as 
digitalization of existing graphics. In 
the restitution performed, a vector 
recording system with 5 gon increments 
was used. It is interesting to analyze 
the methods developed for automatic line 
generation in changing the scale of 
maps. Researches in the field of pattern 
generation, image processing and computer 
vision is particularly concerned with the 
problems of detecting corners, and its 
findings are studied for application in 
problems of digitalized data compression. 
In our case such research can be adapted 
to the problem of finding the principal 
angles to insert in the approximate 
geometry of finite element calculation. 
A method proposed in 1988 (Thapa, 1988) 
"zero crossing algorithm" identifies the 
critical points to record for different 
degrees of generalization due to the 
change of scale. Application of this 
algorithm, however, is laborious, as it 
requires an initial transformation from 
vector to raster form (for example by the 
Bresenham algorithm (Bresenham, 1965)) 
and a subsequent filter type analysis to 
reduce noise. Perhaps more interesting 
for our purpose is the CVD algorithm 
(Commutator Vertex Detection, detection 
of vertexes by commutating operators) by 
Anderson and Bezdeck in 1984 (Anderson et 
Al., 1984). 
This was tried by Thapa (Thapa, 1990) and 
adapted to problems of compressing data