CI PA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
Is it possible to build a topology with these drawings? Some 
would say so, but, although these “wires” can be spatially 
organised as well-connected and well-defined entities, this 
topology must be considered incomplete, as it only allows to 
distinguish whether a point forms part of a certain linear entity 
or not. This implies that when an ashlar stone of a monument is 
drawn as a complex of line strings, it behaves as a cage and we 
can’t even distinguish for sure the inner space from the outer. 
The models in which surfaces are interpolated by means of a 
triangle irregular networks (TlNs) or squared grids are very 
commonly used in the context of aerial Photogrammetry. Also, 
the so called digital terrain models (DTM) have a wide range of 
application in the fields of civil engineering, agronomy, 
environmental studies and so on. Computers’ brute force has 
made these models possible which are now considered to be 
their most efficient product in the context of digital topographic 
cartography. So why not try to use them in the field of 
architecture? 
2. HOW? 
The DTM are topological idealizations which describe the 
terrain surface. They are often called digital models of elevation 
(DEMs) and this leads us to think that, although they are built 
taking into account the three dimensions, one of them is of 
bigger relevance in their calculation: the elevation, the reason 
for this is simply gravity, which gives their universal sense to 
the concepts of up and down, whereas the position with 
reference to the other two fundamental axis are, in practice, 
impossible to distinguish. (Their association to geographic, 
magnetic, or any other kind of axis is just conventional). From 
the structural point of view. Gravity obviously also has a 
peculiar meaning in the field of architecture. However, 
architecture constantly defies it by making verticality the norm , 
whereas in nature everything tends to the minimum of potential 
energy, to the lower possible position, to horizontality. While in 
a terrain it is very uncommon to find conditions of inverse 
slope, and almost all the land’s surfaces are visible from the 
eagles point of view, in architecture, the most significant 
surfaces (façades) are invisible from the aerial point of view. 
The programmes for terrain modelling make use of this 
fundamental distinction applying the scheme 3D=2D+1D and 
they are unable to form continuous models of architectural 
objects. However, they can be locally used for façades if the 
direction normal to these surfaces takes the role of privileged 
direction. This is normally solved in practice by folding down 
the façade on the horizontal level. 
3. AN EXPERIENCE 
Los Milafros aquae duct, in Mérida ( Spain), where this trick has 
been tested, offers a great structural systematism. That’s why, 
as it often happens in the so called linear civil works (roads, 
trains, canals,...) great advantages can be granted to a system of 
reference which has three fundamental directions related to this 
structure. Gravity’s direction will be the inevitable axis, 
whereas the direction of the pillars alignment will be the second 
one, which we have agreed to called longitudinal axis. The third 
one could only be the one perpendicular to the two above 
mentioned. Bearing in mind its form, the aqueduct can be 
described as a succession of pillars of squared plan linked by 
arches in three different heights. I the past a horizontal canal 
was found along the top but it has been destroyed by time. Each 
pillar can obviously be studied in its four different sides which 
can be dealt with separately: two on the sides (right and left) a 
frontal and a back side, which can be identified once we’ve 
established a station increasing sense. The local origin of 
coordinates have been placed at the centre of each pillar and the 
two axis described above have been drawn at an integer value 
of elevation. These axis should serve as hinges to fold each side 
down on the horizontal level. By doing so we could deal with 
them as if they were terrains from which we could obtain 
DEMs. 
The turn of each can easily be reversed about the same pivot 
and the digital skin can be driven back to the erected position. 
4. HOW IS A SURFACE DIGITAL MODEL MADE? 
In a cartographic context, the terrain is modelled from linear 
and punctual features extracted during the photogrammetric or 
land surveying. Some of the linear entities represent break lines 
in the curvature of the land surface, hard variations of the slope, 
while some others are not noticeable in terms of relief but just 
lie down on the ground as it occurs with spot elevations and 
other punctual features. Elevation, shape and type (breakline or 
random) of all these elements will allow us to figure out the 
topography of the terrain. Terrain modelling programmes use 
them also to interpolate a mathematical surface formed by 
triangles connected by their sides. The programme only needs 
some rules to handle the graphic entities whether as breaklines 
or random usually by means of association between behaviour 
graphic codes (level, colour, style, stroke). 
In the architectonic case the something similar can be done in 
terms of modelling surfaces. By differentiating through graphic 
codes one could establish those graphic entities which represent 
disruptions in the curvature of the surface and those that simply 
lie on it. J 
In the project of 
restoration of the 
aqueduct the criteria for 
the coding was primarily 
based on thematic 
aspects. As a result, to 
each building material 
used (granite, quartzite, 
ceramic, rubble concrete, 
metal...) corresponded a 
layer or group of layers. 
Some thematic layers 
gathered non-structural 
features such as paint 
stains, moss, lichen, oxide 
or they served to 
demarcate zones with 
different degrees of