Digital design and fabrication of clusters of complex, Efficient and continuous architectural surfaces

The emergence of digital design and edition tools in architectural production has allowed the development of typologies and forms that were extremely complicated to draw and represent previously. They are based on surfaces with high degree of formal indetermination and complexity, in which the geometry is a fundamental analytic and support tool for their accomplishment and understanding. All this, in conjunction with the implementation of digital manufacture technics, has enabled that architect and engineers can materialize elements with great formal and programmatic complexity and efficient structural behaviour. The application to architectural production of the principles that are present in the morphogenesis and epigenesis of minimal surfaces with crystalline structure [1], triply periodic minimal surfaces [2], especially those that contain straight lines, is of interest to the digital design, edition and manufacture of new architectural solutions based on continuous, complex and efficient surfaces with high prefabrication degree. These surfaces emerge from a simple hyperbolic patch when the operations of the associated crystallographic group related to Bravais lattices are applied to it, and produces a tiling of Euclidean three-dimensional space. This patch is an n-sided skew polygon, whose borders can correspond to those straight lines previously mentioned, and in many cases, these patches could even be identified with doubly ruled surfaces, with the advantages that this implies. Different authors have investigated these surfaces since nineteenth century and they have presented different construction methods and varieties of surfaces. Schwarz [3], Neovius, Schoen [4], Fischer and Koch [5], Karcher and Polthier [6], Lord and Mackay [7], Weber and Fujimori [8] stand out among all of them. In twentieth century, many architects have made different architectural research and proposals related to these surfaces or similar surfaces. This could be observed in the works of Haussermann, Chanéac, Michael Burt [9], Peter J. Pearce [10], Haresh Lalvani, Ami Korren [11], Toyo Ito, Vlad Tenu, Leeser Architecture, Vincent Callebaut, UNStudio and Studio RAP. The research present how can be obtained and fabricated a great variety of new modular architectural typologies, that even can constitute complex and porous clusters, with advanced digital design and manufacture methods, as the additive 3D printing. They will be formed by complex, continuous efficient surfaces with high replicability level through the application of the principles that are present in the construction of triply periodic minimal surfaces, especially those that contain straight lines and whose patch can be assimilated in some cases with doubly ruled surfaces. Likewise, conclusions that connect their geometry and their adaptive.