CIPA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
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definition of the terrain-like pillar faces were simultaneously 
defined. This implied that, in addition to the need of digitising 
features for construct conventional plans of elevation, it was 
needed the digitisation of random points on the faces of the 
ashlars to record the roughness of their surface. We also traced 
line-strings along sharp edges or around the hollows made by 
the quarrymen's for the rock grab and following the deep 
heading joints between the stone courses as well. 
Once these “topographic” features have been digitised and 
properly coded for their classification, the computer programme 
needs to be set up so that it will be able to distinguish which of 
these groups of layers gather random elements and which others 
contain breaklines. That’s how, once each side of the complete 
drawing has been folded down, a triangle mesh can be 
interpolated in very few seconds. 
Fig. 3. Triangle mesh model of a pillar face. 
5. APPLICATONS OF THESE MODELS. 
5.1 Obtaining sections. 
Probably one of the most common problem derived from the 
lack of a surface-topology in the graphic documents obtained 
by photogrammetric restitution is the difficulty to section these 
objects. This is specially an obstacle when they present blunt 
and bulky shapes and their representation with lines is a 
simplification biased by the point of view of the stereo-plotter 
operator or draftsman (in fact, in most cases, if the 3D-drawing 
are shown rotated, the lines no longer make sense and it is 
difficult to recognize the figures). For example, a bas-relief 
composed of human figures would be digitized as a few 
silhouettes and some more linear work defining some features 
and folds. If we wanted to obtain a section we would have first 
to decide the position of the cutting plane while doing the 
Figure 5. The digital surface model of an ideal reconstruction 
of the ashlars can be faced to the current estate. 
restitution and we would have to go along the section line with 
the floating mark / pointer, which would often mean a great 
deal of difficulty. 
But once the TIN (triangular irregular network) has been 
created by means of the drawn elements as a mathematical 
representation of the surface, it can easily be sectioned along 
any direction. 
Fig. 4. For each pillar face we obtained horizontal sections at 
one meter interval and three vertical. 
The triangles cover the whole surface so that one can know the 
third coordinate “elevation” of any desired point so that it is 
possible to solve intersections between regular surfaces and the 
network. 
We consider that the constructed surface represent a good 
approach to the true shape of the stone structure better than the 
line-strings plotted during restitution. The interpolated lattice 
makes objective the way-of-doing of the operator and makes 
uniform the merge of sessions done by different people. 
5.2 Volume calculations 
Volume calculations enclosed by regular figures is a geometric 
problem which involves a reasonable degree of difficulty. 
However, the problem when trying to measure volumes of 
shapes in sculpture figures, or any other irregular shapes (also 
weathered pieces that have lost their original regularity) 
becomes almost unsolvable. This difficulty is often work 
rounded by the simplification or generalisation of the form and 
assuming the error coming from the method itself. 
From the triangular mesh models and through some 
mathematical processes we can derivate other models of 
regular square grids, which are very adequate for volume 
measurement. 
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