The points surveyed in the base area are coded 
according to their height. Code L29 relates to the 
points surveyed on the core of the second order, 
while L39 refers to the third, and so forth. 
The number of points surveyed on the base and on 
the surface of the cylindrical core are as 
follows: 
order number 
first 1548 
second 246 
third 289 
fourth 287 
fifth 320 
sixth 294 
seventh 212 
eighth 264 
In point of fact only the points surveyed on the 
two edges of the dripstones and the cylindrical 
cores were processed. 
6. DATA PROCESSING 
6.1 Recording and filing 
  
The points surveyed were filed as follows: ID, X, 
Y, Z, where ID is the identifier of each point, 
and X, Y, and Z are the coordinates of the 
absolute reference system. 
The data were then subdivided into files 
containing readings on similar elements, that is 
that coded the same. Figure 5 illustrates this. 
The data was then processed using the VDIM program 
on an IBM RS/6000 system. 
6.2 The VDIM program 
This program is used extensively by AGIP in the 
analysis of simple curved surfaces and lines in 
space, starting from a random selection of 
coordinates. The shapes that are best suited to 
this treatment are: 
- circular cylinders 
- elliptical cylinders 
- truncated cones 
- three-dimensional ellipses and spheres 
- two-dimensional ellipses and circles 
Determining the optimum parameters of a cylinder 
or a cone using points which have been defined by 
means of photogrammetric techniques is no easy 
task. 
It soon becomes clear that traditional iterative 
processes are going to be of little use. Newtonian 
methods and their variations are not practical 
because of the amount of algebraic calculations 
required. 
Briefly, the program works in the following 
fashion: 
a) the "general quadric" that describes the 
points observed is defined using the "least" 
square method 
b) the generic quadric is reduced to a central 
quadric (degenerate). The directions of the 
axes and the center are calculated from this. 
c) if the sum of the points observed is 
reasonable, one of the three axes is very 
close to the axis of the cylinder or the cone 
that we are aiming to define. Thus for each 
of the axes, we define a cylinder or a cone 
and then select the one of the three for 
which the distance between the surface and 
the points surveyed are on average the 
smallest. 
Developed in Fortran 77, this program has proved 
highly-effective in tests on an extensive range of 
samples. 
The files we selected for treatment with the VDIM 
program were those which included measurements 
taken at the base, on the cores, and on the 
dripstones. As a result, it was possible to plot 
the approximate geometric figures derived from the 
points (which is to say, a cylinder for the base 
and the cores of the Tower and a circumference for 
the dripstones as in fact was done in the previous 
survey). The diameters of the dripstones and of 
the direction cosines of the perpendicular to the 
dripstones were also calculated as well as the 
direction cosines of axes of the cores and 
their diameters. The accuracy of these data was 
checked by means of a statistical survey. 
6.3 The CATIA program 
The data were then processed using CATIA 
(Computer-aided three-dimensional interactive 
application). Produced by Dassault Systemes of 
France, this modeling program enables the user to 
create correlation between two- and three- 
dimensional areas quickly and easily. All the 
views can be correlated and each modification in 
one view is reflected in the model and, as a 
result, on all of the other views. 
A modular program, inasmuch as there is a base 
unit onto which one can load separate units for 
different applications, CATIA is used within the 
AGIP company on an IBM RS/6000 in an X-Windows 
environment, or using the graphics applications 
available on the IBM 5080 system. 
First of all the data were separated into layers, 
using an interface program. One layer consisted of 
the points surveyed and the other of the geometric 
figures obtained via the VDIM program. The two 
layers could, of course, be superimposed as well 
as being see-through, and it was thus possible to 
detect the most salient anomalies. 
  
Figure 6 
CAD-derived image of point surveyed 
on the base, the cores, and the dripstone