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