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
