Rethinking Ephemeral Architecture. Advanced Geometry for Citizen-Managed Spaces

In recent years there have been a high amount of citizen initiatives that address the complex problems of the contemporary city. There are empty or disused spaces that have been reused for urban gardens, for social use, to encourage integration and civic activities activation, etc. Traditional architectural processes do not provide realistic solutions to these initiatives that, along with limited financial resources, have led to the emergence of architectures and self-constructed facilities, almost as an emergency mode, without necessary planning, media and constructive knowledge. The democratization of technology, thanks to laboratories of digital production, combined with knowledge of the properties of different surfaces through the CAD-CAM tools, offers new opportunities for the development of a lightweight, flexible and low impact architecture, very according to the needs of citizens' initiatives that naturally arise in our cities. The new existing scenario contemplates the figure of the architect, or engineer, not only as an agent of the market, but as a professional able to propose efficient solutions to problems from within, bringing their specific knowledge and serving as bridges between the new technological solutions and the challenges of society

Surface discretisation with rectifying strips on Geodesics

The use of geodesic curves of surfaces has enormous potential in architecture due to their multiple properties and easy geometric control using digital graphic tools. Among their numerous properties, the geodesic curves of a surface are the paths along which straight strips can be placed tangentially to the surface. On this basis, a graphical method is proposed to discretize surfaces using straight strips, which optimizes material consumption since rectangular straight strips take advantage of 100% of the material in the cutting process. The contribution of the article consists of presenting the geometric constraints that characterize this type of panelling from the idea of “rectifying surface”, considering the material inextensible. Experimental prototypes that have been part of the research are also described and the final theoretical results are presented

New properties about the intersection of rotational quadratic surfaces and their applications in Architecture

A graphic conjecture is presented based on a singular property stated by Archimedes [287-212 B.C.] in his work On Conoids and Spheroids. This ancient text constitutes the starting argument for graphic research that has revealed an unknown property regarding the intersection of rotational quadratic surfaces which they share one of their foci. This article shows the heuristic geometric reasoning carried out stemming from Archimedes’ text transcriptions and a conjecture that can be deduced when the initial property is generalised for the rest of the quadratic surfaces. Moreover, an explanation is offered for the possibilities of this property to be used for the discretisation of architectural surfaces through the use of parametric design and digital fabrication

Structural Models based on Minimal Surfaces and Geodesics

This article presents the results of research carried out with respect to the geometric, formal and structural adaptation of minimal surfaces. These surfaces were discretized into strips developable on geodesic curves, and then used for the construction of timber gridshells. For this project, both physical and virtual models derived from the same geometric models were used. The objective was to demonstrate the validity of the use of models and the transformation that modelling is undergoing due to the use of digital tools, both software and hardware. These include, on the one hand, drawing and analysis software and, on the other, digitally controlled fabrication tools. This research focuses specifically on the design and construction of the Scherk Pavilion, a space where the results of various experiments in which the common factor was the use of models was transferred to a real scale

Some controversies on representation of the solar shadow in 17th century: the manuscript ‘Artes Exçelençias de la Perspectiba’ in context

PreprintSome of the ‘geometric contradictions’ in certain works, especially manuscripts about perspective, can be used to understand which paradigms in the history of representation clash with each other. The manuscript Artes Exçelençias de la Perspectiba introduces us to this important chapter in the history of perspective, not only in Spain, but throughout the seventeenth century in Europe. During this period solutions were found, tested and formulated regarding the delicate problem of the graphic control of shadows produced by sunlight – or “striking” – within the perspective method

Augmented graphic thinking in Geometry: developable architectural surfaces in experimental pavilions

We will analyze how the incorporation of digital manufacturing in our schools is motivating a deep reflection about the need to be familiar with both the foundations of geometry as well as with more advanced knowledge. The reinterpretation of our inherited graphic design discipline in light of current digital tools can open up new fields of study and work, such as is occurring in the field of developable surfaces, warped surfaces and many others. In addition, through non-linear graphic processes and digital tools of parametric design, we can arrive at an "expanded graphic thinking" that we can place at the service of production and morphological research. Thus, the old descriptive geometry - geometry based on graphics – comes to serve a cybernetically enlarged mind. We will present four experimental pavilions resulting from several workshops on geometry and digital manufacturing carried out in collaboration between the University of Seville and several Ibero-American Universities. Based on the deep geometric knowledge of developable helical surfaces and surfaces of equal slope, a guided exercise is proposed to approach the design, manufacturing and assembly phases of these architectural installations on a real scale

Graphic Thinking and Digital Processes: Three Built Case Studies of Digital Materiality

Think strategic link between computer programming; digital modeling; the data; matter and CNC manufacturing in the various stages of the architectural project is key to update our discipline with new technologies. Our proposal to articulate and digital graphic thought processes; developable folded geometries and compositions is rooted in an expanded graphic thinking through multiple conceptual tools that are already part of the operational structure of our discipline

Cactus Pavilion: experimental architecture with folded developable surface

PREPRINTCACTUS PAVILION es un pabellón madera diseñado como centro de interpretación itinerante del Proyecto de Salvamento del Patrimonio Arquitectónico y Natural de Santiago de Anaya, Valle del Mezquital, México. El pabellón (Fig.1) ha sido concebido y diseñado en el Departamento de Ingeniería Gráfica de la Universidad de Sevilla, en colaboración con Fablab Donostia de la Universidad del País Vasco. Se propone una arquitectura efímera biomimética en forma de cactus hueco de madera, realizada con tiras desarrollables formada por paneles de 3mm de espesor. Al igual que en otras experiencias anteriores, el pabellón se ha diseñado con herramientas CAD-CAM y se ha fabricado digitalmente mediante una fresadora de control numérico CNC de tres ejes. Cactus Pavilion ha sido galardonado con una Mención Honorífica LAKA COMPETITION’18 https://lakareacts.com/winners/cact us-pavilion

De la Geometría Descriptiva a la Geometría Arquitectónica: aportaciones de autores clásicos al nuevo paradigma

The use of computation for architectural design, together with the application of digital fabrication techniques for materialisation, has brought a new paradigm where contributions by classic authors linked to Descriptive Geometry might seem inappropriate. This paper shows a case study of a full-scale prototype which proves how some of the classic geometric theorems and procedures can still play a role in the design computation era. Objectives: identify and analyse the usefulness of classic Descriptive Geometry contents within the computational design paradigm through the case study of a particular project. Methodology: Analysis of the conception, development and materialization processes, to identify the application and potential benefits of classic geometric contents. Results: at the different stages analysed, some classic geometric theorems and procedures were found to be useful and efficient. Practical implications: The implications of these findings involve both architectural practice and the academic sphere. Originality / value: Although initially bound to this case study, the methodology could be extrapolated to more complex projects to obtain more simple and efficient design algorithms.El uso de la computación en el diseño arquitectónico, junto con la aplicación de técnicas de fabricación digital para la materialización, ha traído un nuevo paradigma donde las aportaciones de los autores clásicos vinculados a la Geometría Descriptiva podrían parecer inadecuadas. Esta comunicación muestra un estudio de caso sobre un prototipo a escala natural que demuestra cómo algunos de los teoremas y trazados clásicos aún pueden tener un papel en la era de la computación. Objetivos: analizar la utilidad de contenidos de la Geometría Descriptiva clásica dentro del paradigma del diseño computacional a través del estudio de caso de un proyecto concreto. Metodología: Análisis de los procesos de concepción, desarrollo y materialización, para identificar la aplicación y beneficios potenciales de contenidos geométricos clásicos. Resultados: en las diferentes etapas analizadas, algunos procedimientos y teoremas geométricos clásicos resultaron ser útiles y eficientes. Repercusiones prácticas: Las repercusiones de los resultados obtenidos atañen tanto a la profesión arquitectónica como al ámbito académico. Originalidad / Valor: La metodología usada en este estudio de caso, podría extrapolarse a proyectos más complejos para obtener algoritmos de diseño más simples y eficiente

Considerations regarding the representation of the invisible: Monge’s method in four dimensions

[EN] The graphic representation of fourdimensional space, between the nineteenth and twentieth centuries, deserves a prominent place in the history of graphic thinking. As happened in the development of the Renaissance perspective, the study of polyhedra and polytopes by a few ‘graphic mathematicians’ was linked to the codification of new ways of representation. The desire to define new ways of seeing and representing the fourth dimension transcended all the spheres of aesthetic manifestations. We provide relevant testimonies regarding the evolution of the four-dimensional graphic systems. A final contribution based on Alfredo Llorens Herrero’s Thesis 1 is also included, which involves the amplification of the Dihedral System or Monge’s method through the inclusion of an extra dimension.[ES] La representación gráfica del espacio tetradimensional, entre el siglo xix y xx, merece un lugar destacado en la historia del pensamiento gráfico. Al igual que ocurrió en el desarrollo de la perspectiva renacentista, el estudio de los poliedros –y politopos– por unos pocos “matemáticos de la representación” fue unido a la codificación de novedosas formas de representar. La voluntad de definir nuevas formas de ver y representar la cuarta dimensión trascendió a todas las esferas de las manifestaciones estéticas. Aportaremos relevantes testimonios sobre la evolución de estos primeros sistemas gráficos tetradimensionales. Una última contribución se recoge en la Tesis de Alfredo Llorens Herrero 1, que supone la ampliación del Sistema Diédrico en una dimensión extra.Martín Pastor, A.; Gentil Baldrich, JM. (2019). Consideraciones en torno a la representación de lo invisible: el método de Monge en cuatro dimensiones. EGA. Revista de Expresión Gráfica Arquitectónica. 24(35):118-129. https://doi.org/10.4995/ega.2019.11551SWORD1181292435BOOTH, David (2001). "Introduction", in: Rudolf Steiner, The Fourth Dimension. Sacred Geometry, Alchemy and Mathematics. Massachusetts: Anthroposophic Press.BRAGDON, Claude Fayette (1913). A Primer of Higher Space. The fourth dimension. Nueva York: Manas Press, Rochester.CABEZAS GELABERT, Lino (2010): "El origen poliédrico de las especies de Arturo Soria y Mata: Ciencia, Pitagorismo y pensamiento estético", in: Arte y geometría, Granada: Universidad de Granada, pp. 15-48.CAJORI, Florian (1926). Origins of Fourth Dimension Concepts. The American Mathematical Monthly, 33:8, pp. 397-406. https://doi.org/10.1080/00029890.1926.11986607FLORENSKY, Pavel, Obratnaia perspektiva, 1921-1924. (trad. La perspectiva invertida. Madrid: Siruela, 2005)FREGUGLIA, Paolo (2001). "Sulle origini della geometria descrittiva quadridimensionale", in: Matematica e architettura. Metodi analitici, metodi geometrici e rappresentazioni in architettura. Florencia: Alinea Editrice, pp. 91-94.GENTIL BALDRICH, José María, MARTÍN-PASTOR, Andrés (2015). Poliedra as form of geometric knowledge: The Spanish Jamnitzer or the fourth book of 'Artes Exçelençias dela Perspectiba'. EGA, n. 25, pp. 56-65. https://doi.org/10.4995/ega.2015.3677GENTIL BALDRICH, José María (2013). La prospettiva: 'un buco nella tavoletta'. Disegnare idee immagini, 46, pp. 22-29.GIBBONS, T.H. (1981). Cubism and 'The Fourth Dimension' in the context of the late nineteenthcentury and early twentieth-century revival of occult idealism. J. Warburg Courtauld Inst. 44, pp. 130-147. https://doi.org/10.2307/751055HALSTED, G. (1897). Bibliography of hyperspace and non-euclidean geometry. American Journal of Mathematics 1, pp. 261-276. https://doi.org/10.2307/2369314HENDERSON, Linda Dalrymple (1983). The fourth dimension and non-euclidean geometry in modern art. Princeton: Princeton University Press. https://doi.org/10.1086/355234HINTON, Charle Howard (1912). The Fourth Dimension, Londres: Georges Allen. Original in: Harper's Monthly Magazine, julio de 1904.JOUFFRET, Esprit Pascal (1903). Traité élémentaire de géométrie à quatre dimensions Paris: Gauthier-Villars. (1906) Mélange de géométrie à quatre dimensions. Paris: Gauthier-Villars.LAWRENCE, Snezana (2015). Life, Architecture, Mathematics, and the Fourth Dimension. Nexus Network Journal, 17, pp. 587-604. https://doi.org/10.1007/s00004-014-0221-9LUECKING, Stephen (2010). A man and his square: 11b Kasimir Malevich and the visualization of the fourth dimensión. Journal of Mathematics and the Arts, 4:2, pp. 87-100. https://doi.org/10.1080/17513471003744395LLORENS-HERRERO, Alfredo (2016). Larepresentación gráfica del espacio tetradimensional euclídeo. La ampliación del método diédrico a cuatro dimensione. Unpublished doctoral thesis, Universidad de Sevilla. Available in full text in: https://idus.us.es/xmlui/handle/11441/52367PANOFSKY, Edwin (1927). Die Perspektive als «Symbolische Form». Leipzig-Berlin: Teubner (trad. 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Bibliography of Non-Euclidean Geometry, Including the Theory of Parallels' the Foundations of Geometry, and Space of n Dimensions. Londres: Harrison & Sons.STRINGHAM, Washington Irvin (1880). Regular Figures in n-Dimensional Space. American Journal of Mathematics, Vol. 3, No. 1, pp. 1-14. https://doi.org/10.2307/2369441VAN OSS, Salomon Levi (1899). Das regalmässige Sechshundertzell und seine selbstdeckenden Bewegungen. Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam, 7, (1). Amsterdam: Müller.VERONESE, Giuseppe (1882). Sulla Geometria Descrittiva a quattro dimensioni. Atti del Regio Istituto Veneto di Scienze Lettere ed Arti, (5), 8, pp. 987-1024