Pavilion Ditebius Torus - Torcuato Di Tella University

School of Architecture and Urban Studies - Torcuato Di Tella University

Digital Tectonic



Matías Imbern



Eugenio Tenaglia



Luciana Garcia Campos

Felipe Ginevra

Agostina Giovo

Agustina González Morales

Gastón Hermida

Tomás Meneghetti

Victoria Nicolich

Agustina Suar

Magdalena Viegener

Gabriela Zarwanitzer

Martín Zemma 



MASISA   |   30


YEAR 2016



The course is oriented toward exploration in digital design and interpolated digital/analogue manufacturing, understanding the growing progress of digital media as a generator of new design possibilities. The main objective is the development of skills and design techniques, as well as the conceptual understanding and the application of digital processes, keeping a speculative and innovative attitude, emphasizing the relationship between computation and procedure.

The analysis and rigorous documentation of case studies is the beginning of the research project, which digs into geometric orders and material techniques in order to provide tools for the development of new tectonic systems. The rethinking of existing systems through the introduction of digital processes seeks to optimize traditional material, programmatic and/or formal logics.

The construction of digital models of associated geometry initiates the development of the project, constituting an instrument to generate alternative variations of these systems. This results in a research-project phase, which gives new innovative possibilities, generating interfaces between digital models and physical prototypes.

Through the fabrication of prototypes, combining digital manufacturing techniques with analog techniques, students will be able to explore new capacities and potentialities offered by digital tools in architecture.



The system is developed from the investigation of reciprocal structures of wood, using elements of square section and combined geometric patterns. The three-dimensional assembly of elements that support each other, with a certain coefficient of friction, defines the reciprocal structure. Each element rests on the next and so on until the last one rests on the first, forming a closed, self-contained system. This type of structures has the capacity to cover great spans with small elements, generating a stable and versatile structure, without the need of aggregated elements.

The system begins with the development of a bi-dimensional module, combining both horizontal and vertical lines forming a grid. Then, in order to generate thickness and inertia, two patterns are set in opposite faces, incorporating transverse pieces that sew both layers. Each of the original lines is subdivided and exploited according to the number of intersections with the lines in the opposite direction.

From this, the definitive grid is generated: in the superior face, in the horizontal direction, it is composed by a sequence of three true-nine false in each horizontal line, displaced one of the others, upwardly, three modules to the right. The vertical pattern is conformed by one false-two true, starting at the beginning of each horizontal line. Regarding the inferior pattern, horizontally, it is equal to the upper one, and four modules are displaced to the right. The lower vertical sequence differs from the upper one. This is composed of a pattern of four true-three false, shifted from one another, from left to right, one module up. It is inserted with the pattern at different times of the horizontal curve. Finally, the cross pieces are those that sew both patterns. The joints between the two layers are always made between vertical pieces in the upper side and horizontal pieces in the bottom side. They are located in the horizontal pieces, at the beginning of the third module.



The system consists of a module that is instantiated repeatedly, in relation to the guiding coordinates of a generating surface (U, V, W). At the same time, the system is versatile enough to allow its adaptability to different curvatures according to diverse initial parameters: open curves, closed curves, surfaces and volumes. Therefore, the module can be accommodated in a wide variety of geometries, from open lines, which is the generic of the system, moving towards more complex structures such as surfaces and volumes, which allow the evolution of the system to more intricate levels.

For each of these studies, three possible differentiations of the system are analyzed. On the one hand the subdivision of the original curve and incorporation of polygons in its center for the application of the pattern, and on the other hand, the rotation of the same, which allow manipulating the performance of the pavilion. The third differentiation depends on the context in which it is implanted, the transition between bases and unions as structural reinforcement of the system. The latter is necessary for a three-dimensional control of the system, working with wood, which allows generating systems that constantly challenge the structural conventions of the material.



The system is adapted to a closed curve, generatrix of a "moebius torus". The original curve is subdivided and in each subdivision a polygon is located. Next, a total rotation is introduced in the series that completes the 360º, so that each polygon rotates a certain percentage depending on the number of subdivisions, in order to generate surface continuity along the entire geometry. Once the pattern of the adaptable module is instantiated, it naturally rotates with the movement of the moebius torus. The upper and lower horizontal and vertical elements, opposite each other, operate on two sides. In the other two, the cross pieces are located.

Each variable of adaptability: subdivision of the initial curve, rotation of the system, and scale of bases and unions is studied individually in five variants, looking for a balance of both performance and structural efficiency. The final geometry finds two moments of support in the lower parts of its base, while the rest of the geometry increases its height and eccentricity as it moves away from them. The scale of the bases and unions means the increase of size of the base polygons and decrease of size of the arch polygons as the height of the global geometry increases.



Before the fabrication process, the digital model, developed in Rhinoceros / Grasshopper, is analyzed by finite element method as a preliminary structural verification. The objective of this operation is to obtain partial confirmations of the overall behavior of the system, as well as simulation of possible deformations as project feedback, in order to understand which regions should be reinforced. Karamba (a plug-in for Grasshopper) is the software used to carry out this process, working iteratively. Once the results are released, the changes are introduced in the regions with higher deformation, and they are re-evaluated until the system reaches a satisfactory range of deformation.  The initial readings detect the critical points, determined by the eccentricity and the consequent torsion of both arcs. Therefore, a series of measures are taken:

A- By modifying the code, the contact surface between the moebius torus and the floor is widened, thus increasing the number of pieces in contact with the ground and reducing the span of the arches.

B- The section of the arches is reduced, generating a small number of elements, reducing their weight and the torsion.

C- Some extra pieces are placed in sectors where the code produces certain discontinuities of the pattern that weaken the structure.



The different pieces that form the reciprocal system are interlocked as linking method among them. This resource has 2 great advantages: On the one hand, it notably increases the rotation range between the pieces, and on the other hand, it provides clear constructive information regarding direction and position of the different pieces within the set. This constructive information is extremely useful, especially in the case of systems of mass differentiation, in which all the pieces and their geometrical positions in the system (beyond their hierarchical position to form the pattern) are unique.

The interlocking geometry is calculated by the code dividing the resulting volume from the intersection between two pieces, and assigning a part to each piece. Nonetheless, its geometry sometimes becomes impossible to mill with the technology available: a 3-axis router, which moves freely in the XY plane, but only moves vertically on the Z axis, without any degree of rotation. Therefore, the entire system work with MDF of 15mm thickness, so each piece is divided into 2 slats, a geometric decomposition much easier to be milled.

Finally, due to the presence of geometry with 'undercuts' (sectors to which the router can not access), a larger quantity of material had to be removed, which was later replaced by small wooden wedges at during the assembly.



The digital manufacture of the pieces is the culmination of a series of digital processes through which their geometry is refined. After the pattern is instantiated in the stipulated trajectory / surface, the codes calculates the intersection between pieces. Next, another code defines the geometry of each interlock, and each piece is divided into 2 or more slats (depending on the direction in which the interlocks are given) of 15mm. thickness. Then, using a Rhinoceros plugin called RhinoNest, the pieces are optimally placed (to produce the least material waste) inside the MDF boards of 2.6x1.83m. The geometry is exported to another software, called AlphaCAM, which allows digital simulation of router behavior prior to final milling. The milling process consists of 3 processes: the numbering of the pieces, the milling of the interlocks and finally, the cutting of each slat. To simplify the whole process, the pavilion was divided into 3 cutting lots, which are each divided into 2 sublots.

Then, the process continues analogically, sorting and selecting the slats according to their numbering, gluing them to shape the pieces (using clamps to accelerate the drying process) and then removing the surplus chip material that leaves the milling process.

Finally, in order to assure the interlocks, they are glued and stapled. As an aid to the assembly, a series of supports are used that were milled together with the pieces. They serve as jigs to control the height and rotation of some pieces of the pavilion simplifying both, its geometric precision and its support while the assembly moves forward, until the system is complete and the reciprocity begins to function.