Diseño digital y fabricación de grupos de superficies arquitectónicas complejas, eficientes y continuas = Digital Design and Fabrication of Clusters of Complex, Efficient and Continuous Architectural Surfaces

Andrés Miguel Rodríguez, Jesús Anaya

DOI: https://doi.org/10.20868/ade.2020.4497

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El auge y desarrollo de las herramientas de diseño, edición y fabricación digital en la producción arquitectónica, ha permitido que arquitectos e ingenieros puedan materializar elementos con una gran complejidad programática y formal y con un comportamiento estructural eficiente. La aplicación a la producción arquitectónica de los principios que están presentes en las superficies mínimas con estructura cristalina es de interés para el diseño, edición y fabricación digital de nuevas soluciones arquitectónicas basadas en superficies continuas, complejas y eficientes con una alta capacidad de prefabricación. La investigación presenta como pueden obtenerse y fabricarse con métodos digitales avanzados de diseño y fabricación, como la impresión 3D aditiva, una gran variedad de nuevas topologías arquitectónicas modulares, que pueden conformar en ocasiones agrupaciones complejas y porosas


The rise and development of design, editing and digital manufacturing tools in architectural production has allowed architects and engineers to materialize elements with great programmatic and formal complexity and efficient structural behavior. The application to architectural production of the principles that are present in the minimum surfaces with crystalline structure is of interest for the design, edition and digital fabrication of new architectural solutions based on continuous, complex and efficient surfaces with a high prefabrication capacity. The research presents how a wide variety of new modular architectural topologies can be obtained and manufactured with advanced digital design and manufacturing methods, such as additive 3D printing, which can sometimes form complex and porous clusters

Palabras clave

Morfología; diseño y fabricación digital; superficies complejas; estructuras de membranas; Morphology; design and digital fabrication; complex surfaces; membrane structures


Rodríguez, A.M.; Anaya, J. (2017). Morphogenesis of continuous, efficient and complex architectural surfaces associated to crystal systems. International Association for Shell and Spatial Structures (IASS), Proceedings of IASS Annual Symposia, Vol. 2017 (23) 1-10.

Fischer, W.; Koch, E. (1984). On 3-periodic minimal surfaces. Zeitschrift für Kristallographie-Crystalline Materials 179(1-4), 31-52.

Rodríguez, A.M.; Anaya, J. (2018). From simplicity to complexity: clusters of complex continuous efficient surfaces from simple doubly ruled surface patches. International Association for Shell and Spatial Structures (IASS), Proceedings of IASS Annual Symposia, Vol. 2018 (13) 1-8.

Schwarz, H.A. (1890). Gesammelte mathematische Abhandlungen, vol. I,

Springer H.A. Schwarz, Gesammelte mathematische Abhandlungen, vol. I, Springer.

Schoen, A. H. (1970). “Infinite periodic surfaces without self-intersections”, NASA TN D-5541. Springfield, VA: Federal Scientific and Technical Information.

Schoen, A. H. (2012). “Reflections concerning triply-periodic minimal surfaces”, Interface focus, vol 2(5), 658-668.

Fischer, W.; Koch, E. (1990). Crystallographic aspects of minimal surfaces, Le Journal de Physique Colloques, 51, C7 131-147.

Karcher, H.; Polthier, K. (1996). Construction of triply periodic minimal surfaces, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 354, 2077-2104.

Lord, E. A.; Mackay, A. L. (2003). Periodic minimal surfaces of cubic symmetry, Current Science, 85, 346-362.

Lord, E. A. (1997). Triply-periodic balance surfaces, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 129, 279-295.

Kawasaki, T. (2003). Classification of spatial polygons that could possibly generate embedded triply periodic minimal surfaces, Tokyo Journal of Mathematics, 26(1), 23-53.

Fujimori, S.; Weber, M. (2009). Triply periodic minimal surfaces bounded by vertical symmetry planes, Manuscripta Mathematica, 129(1) (2009) 29-53.

Fujimori, S.; Weber, M. (2008). A construction method for triply minimal surfaces, Proceedings of the 16th OCU International Academic Symposium, OCAMI Studies, 3 (2008), 79- 90.

Pearce, P.J. (1990). Structure in nature is a strategy for design. The MIT Press, 1990.

Lalvani, H. (1995). Families of Multi-directional Periodic Space Labyrinths, Structural Topology 21, 47-58.

Burt, M. y Korren, A. (1996). Periodic Hyperbolic Surfaces and subdivision of 3-Space, Katachi Symmetry, Springer Japan, 179-183.

Burt, M. (2007a). Periodic Sponge Surfaces and Uniform Sponge Polyhedra in Nature and in the Realm of the Theoretically Imaginable, Mathematical Institute SASA, Visual Mathematics, 36, 0-0.

Burt, M. (2007b). Periodic Sponge Polyhedra-expanding the Domain, ISIS-Symmetry, In Form and Symmetry: Art and Science, 500-504.

Burt, M. (2008). Uniform Networks in 3-dimensional Space, Mathematical Institute SASA,Visual Mathematics 39, 10-15.

Korren, A.; Burt, M. (1995). Self-Dual Space Lattices and Periodic Hyperbolic surfaces, Symmetry: Natural and Artificial. Budapest: Symmetrion. ISIS Symmetry, Symmetry: Culture and Science, 6 (1).

Korren, A. (2001). Identical Dual Lattices and Subdivision of Space. Mathematical Institute SASA, Visual Mathematics 12(3).

Tenu, V. (2009). Minimal surfaces as self-organizing systems: a particle-spring system simulation for generating triply periodic minimal surface tensegrity structure, Tesis Doctoral, UCL (University College London).

Meeks III, W. H. (1990). The theory of triply periodic minimal surfaces Indiana University Math Journal, vol. 39(3), 877-936.

Karcher, H. (1989). The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions, Manuscripta Mathematica, Springer 64(3), 291-357.

Brakke, K. A. (1992). “The surface evolver”, Experimental mathematics vol. 1(2), pp. 141-165.

Fischer, W.; Koch, E. (1989a). New surface patches for minimal balance surfaces. I. Branched catenoids, Acta Crystallographica Section A: Foundations of Crystallography, 45(2), 166-169.

Fischer, W.; Koch, E. (1989b). New surface patches for minimal balance surfaces. II. Multiple catenoids, Acta Crystallographica Section A: Foundations of Crystallography, 45(2), 169-174.

Fischer, W.; Koch, E. (1989c). New surface patches for minimal balance surfaces. IV. Catenoids with spout-like attachments, Acta Crystallographica Section A: Foundations of Crystallography, 45(8), 558-563.

Fischer, W.; Koch, E. (1989d). New surface patches for minimal balance surfaces. III. Infinite strips, Acta Crystallographica Section A: Foundations of Crystallography, 45(7), 485-490.

Ros, A. (2001). The isoperimetric problem, Global theory of minimal surfaces 2, 175-209.

Wohlgemuth, M.; Yufa, N.; Hoffman, J.; Thomas, E. L. (2001). Triply periodic bicontinuous cubic microdomain morphologies by symmetries, Macromolecules, 34(17), 6083-6089.

Brakke. K. (2018). Susquehanna University, Mathematics Department, http://facstaff.susqu.edu/brakke/evolver/examples/periodic/periodic.html, (accessed 15 February 2018).

Blender (2018). Blender software, https://www.blender.org/, (accessed 15 February 2018).

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