The process of tiling, also referred to as ‘tessellating’, involves the development of figures or shapes that when assembled together form a coherent plane without gaps or overlaps. Such tiles may have any geometric shape provided they fit together, even if the tiles change in size and shape across the plane itself. The patterned, tiled surfaces found in architecture are directly analogous to the mesh patterns defined using digital tiling tools. As with contouring, the history of tiling is long established in traditional manual craftsmanship – producing mosaics, stained-glass windows and other types of surface ornamentation. Time-consuming and labour-intensive, these precedents required the configuration of myriad fragments to form an intricate yet uniform design. Despite this, the cumulative result afforded considerable variation in terms of geometry, tone and overall image. One of the many advantages of digital design and fabrication methods is that they can effectively overcome the previous investment of time and also provide ways in which patterns may be generated and optimized to gain maximum impact both visually and materially – especially concerning the reduction of waste. During this book’s first section, we discussed the use of meshes to approximate curvilinear geometry from polygons and triangulation. In the context of digital fabrication, the possibilities of translating design information from digital meshes to machines that produce components from sheet materials is immediately apparent. Therefore, this method of making complex three-dimensional forms and surfaces from a kit of essentially two-dimensional components has enabled architects to overcome one of greatest obstacles in fabricating this type of design. The development of mass customization and non-standard components, owing to the efficiency with which digital technologies may integrate these, has vastly expanded the field of design inquiry and options for modulation. As a result, designers can fabricate components with much more differentiation than hitherto, which, when combined, may produce effects in aesthetic, material and experiential terms that are much more transformative than the simple sum of their parts.
Tiling as a geometric strategy is used extensively in the built environment, as shown by the tessellated pattern of this infrastructure element for the reshaping of the A2 ring road, Den Bosch (Netherlands), by UNStudio. The design’s identity and coherence is expressed through the efficiency of the various elements, via a simple concept that lends itself to repetition. The concrete sound barriers are clad in a continuous relief, while the transparent barriers are printed with this same pattern – an abstracted migrating bird, which alludes to the identity of the A2 as a section of the trans-European Amsterdam–Palermo route.
In Reiser + Umemoto’s West Side Convergence project, the flowing design is structured using a triangulated tiling spaceframe that not only alludes to physical support and span but also reinforces the concept of uninterrupted, continuous information and material flux across the urban landscape of Manhattan.
The canopy of the Aurora installation by Future Cities Lab features a tiling pattern to optimize the distribution of openings across its panels and maximize the variety of spatial effects through incorporated lighting elements.
3XN’s design for Horten’s new Copenhagen headquarters, completed in 2009, demonstrates innovative use of three-dimensional tessellation to address design issues. The façade elements were developed specifically for this building’s complex geometry and based on a tiling pattern intended to facilitate a positive working environment, offering baywindow views towards the water while avoiding direct sunlight.
Tiled surfaces may either be smooth and precise, or faceted and primitive, factors that correspond to the degree of resolution. While it may appear preferable to always use a highly defined model, this can result in a very large file size, making it difficult to process and handle. Software platforms are increasingly adept at enabling designers to evaluate the resolution and size of the tiles in relation to the overall geometry, fabrication method and materials to be employed. This process of translation facilitates the design intentions to be calibrated with the proposed system of construction. Given the nature of tessellated patterns they are able to accommodate a wide range of tile and field designs, which has led to extensive application as a strategy for making complex form.
Case study Tiling as surface strategy
Barkow Leibinger – Trutec Building, Seoul, 2006.
This design uses digitally controlled 2D laser cutting to form 3D polygonal façade panels. The aluminium window extrusions, developed from a tiled surface geometry, transform a potentially ordinary office building by employing a custom- fabricated façade. Because the building’s context was yet to be constructed, the façade was produced for optimal effect, forming a proactive ‘camouflage’ reflecting light, weather, people, traffic, etc. in its proximity. Through the use of CNC cutting, standard off-the-shelf extrusions at angles were made, which were then connected to create shallow-depth 3D crystalline glazing panels. This process resulted in three basic types: a 2D panel, a 3D panel and a 3D panel rotated through 180 degrees. The combination of these types via a complex organizational matrix generated significant variation across the façade.
A Physical model of shallow-depth 3D panel.
B CAD drawing illustrating triangulated geometry, dimensions and tiling pattern formed through the transformation of rotation.
C, D, E, F, G AND H Study models produced at scale to evaluate lighting effects in relation to various tiling configurations.
I Weather testing, using a water turbine to assess the performance of several full-size prototype panels and the connections between them.
J Final panels being hoisted into place on site.
Case study Tiling to fabricate complex curvilinear form
Studio Gang – Marble Curtain, National Building Museum, Washington D.C., 2003.
An exploration of the structural capacity of stone, the Marble Curtain hung in tension from the museum’s vaulted ceiling. Stone performs best when subjected to compressive loads. By linking pieces of stone together in a series of jigsaw-like chains, however, the Marble Curtain places the material in tension from the ceiling downwards, without any skeletal support or frame. No technical data exists for stone in tension; its capabilities were discovered by breaking stone types in a testing laboratory. Water-jet cutting allowed for intricate puzzle-shaped cuts. For structural redundancy, each piece was laminated with a fibre-resin backing. The Marble Curtain was 5.5m tall, comprised 620 pieces and weighed just 680kg. The stone was only 10mm thick, which allowed the design to explore its translucency.
A CAD drawing, indicating overall geometry of the design scaled within proposed context.
B Physical scale model, produced to evaluate the structural chains’ positions.
C Testing of prototype ‘jigsaw’ pieces to understand performance of stone under tension.
D Jigsaw components are hung on the structural chains using a timber frame, which was subsequently removed once the curtain was fully hung.
E The final installation, demonstrating the resultant curved form and the translucence of the stone owing to its minimal thickness.
STEP BY STEP TILING AND MASS CUSTOMIZATION
Surface deformations and curvilinear geometries are often mutually interdependent aspects of digital design. The fabrication techniques available to architects have enabled them to pursue explorative and innovative design inquiry and inform its realization. Faulders Studio’s Deformscape project in San Francisco is a permanent outdoor living space at the rear of a private dwelling. Situated in a tightly packed neighbourhood, the single large Japanese Maple tree is used to establish a ‘gravitational’ pattern of grooves focused towards it.
1 To generate the optically shifting pattern, a three-dimensional deformation is produced in 3D modelling software and then the wireframe grid is projected upward onto an implied 2D surface.
2 This is diagrammatically flattened to provide the pattern for CNC milling the individual marinegrade-plywood tiles, which are then painted.
3 The grid is also projected upward onto the rear wall, to create a geometric backdrop and further emphasize the optical illusion. The individual components are fixed to a porous fibre-reinforced polymer-grated surface to allow rainwater to drain laterally along the grooves to the tree’s roots.
4 Once constructed, the flattened perspective regains its original, warped three-dimensionality. However, in reality the surface is entirely horizontal, enabling maximum use of the space.
STEP BY STEP TILING TO CREATE OPTIMAL VARIATION
Metal is an ideal material for folding since it retains shape, and complex and multiple folding is achievable via digital machines. This explorative project by Barkow Leibinger demonstrates the potential of metal tiles to create a three-dimensional surface, produced using a simple module that, once assembled with other identical counterparts, appears non-repetitive.
1 The tessellated pattern of the units’ geometry is developed in CAD prior to application with material. The scripting technique enables mass-customized assembly from identical pieces to form a unique surface-making system.
2 The metal components are then two-dimensionally laser cut from flat stock and folded using the Trumabend machine.
3 Each component ‘nests’ into the next one in the surface composition, with 24 possible variations in which, when combined in a field as shown here, any repetition is concealed by the myriad permutations across the overall surface.
Case study Tiling as generative and fabrication processes
Future Cities Lab – Xeromax Envelop{e}s, various locations, 2010.
Future Cities Lab is an experimental design-andresearch office based in San Francisco. Their work questions technology’s role in contemporary society, exploring the intersections of design with advanced fabrication technologies, robotics, responsive building systems and public space. The Xeromax Envelop{e}s installation is an interactive and intricate geometric surface that pulsates in response to the movement of people close by.
For this project, digital design and fabrication allows the production of non-standard components and – although initially designed, fabricated and tested in San Francisco – the installation was then sent by standard post to New York, meaning it needed to be as light, modular and deployable as possible. The project was first modelled and fabricated using a combination of Grasshopper and Firefly (both plug-ins for Rhino). Its components were parametrically modelled and then individual pieces were flattened, tagged and organized on to digital-cut sheets that were laser cut. The primary construction materials were a synthetic waterproof paper and 2mm-thick clear and yellow sheets of polyester PET-G. The hexagonal surface comprises thousands of interconnected laser-cut pieces folded, notched, assembled and then hand sewn together using a fine stainless-steel cable. The robotic heads were constructed from both PET-G and cast-acrylic frames that held the electronics including LEDS, IR sensors and servomotors. All the electronics were custom fabricated by Future Cities Lab, and became an integral part of the installation’s aesthetic. The final installation was suspended from the gallery ceiling using light-gauge aircraft cable.
A Digital-cutting pattern sheets, showing ‘flat’ geometry that when connected will form three-dimensional, hexagonal composites.
B Physical sketch models illustrate various ideas investigated during the design-development process. Different materials and geometrical configurations were produced, to interrogate their suitability for the overall system.
C Assembly of the modules, from two-dimensional cut pieces to three-dimensional faceted objects.
D Testing the circuits and programming of servomotors.
E Electronic circuitry is combined with the installation’s plastic infrastructure.
F Connecting the laser-cut panels to form the responsive surface membrane.
G The layout of modules prior to integration into a continuous surface.
H Connecting the surface modules together.
I Suspending the installation within the gallery space.
J View from behind the surface.
K Final installation: surface becomes further articulated as it responds to the movement of people within its domain.
