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Correction: Monge Surfaces. Generation, Discretisation and Application in Architecture
Gonzalez‑Quintial F., Martín-Pastor A.
Q1
Monge Surfaces. Generation, Discretisation and Application in Architecture
Gonzalez‑Quintial F., Martin‑Pastor A.
Q1
AbstractThis paper describes a revision of so-called Monge surfaces through using digital graphic tools, based on the synthetic conception exposed by Gaspard Monge in the 18th and 19th centuries, through their geometric relation with polar surface. As a starting point, we propose a graphical system that integrally solves the generation of these kind of surfaces, their rationalization and discretization, with the objective of their specific application in architecture. The geometric system described allows the generation of a type of surface in which the pair of curves -generatrix and directrix- give rise to the network of principal lines of curvature (LCP) of the final surface. In this way, we propose a process that follows a bottom-up generative system based on Monge surfaces, which offers wide possibilities of formal exploration, while imposing geometrical-constructive properties that are very useful in fabrication and assembly processes.
Gothic Vaulting in Spanish Military Architecture from the Eighteenth Century
Lluis-Teruel C., Lluis i Ginovart J., Ramírez González S., Bravo Nieto A.
Q1
The construction of gunpowder magazines, undertaken by military engineers in Spain throughout the eighteenth century bears testament to the Enlightenment’s construction ethos in the different domains forming the Hispanic Monarchy. In the study on the typological classification that we have performed on 271 projects involving these magazines, 31 designed using gothic vaults have been unearthed. The geometric study into this constructive system unveils that 68.97% of these pointed arches feature centres placed below the impost, suggesting that the angle of incidence on the vertical faces is below 90º, thus sharing this property with catenary vaults. Viewing the appraisals given in La théorie et la pratique de la coupe de pierres (1738) by Frézier on the structural coherence of these figures, it can be concluded that this pointed system employed by Hispanic military engineers is a simplified attempt to standardise the gothic vault in line with the catenary model.
Diego De Riaño and the Transition to the Renaissance at the Collegiate Church of Osuna
Rodríguez Estévez J.C., Ampliato Briones A.L.
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El Escorial, Derand and Guarini: About Formal Control of Ribbed Spherical and Elliptical Vaults
Calvo-López J.
Q1
AbstractGuarino Guarini’s ribbed vaults have been connected with Islamic sources. However, this connection relies almost exclusively on plans and visual observations from the church floor. By contrast, the vertical layout, although clearly shown in Guarini’s Dissegni di architettura civile ed ecclesiastica, and the intrados surface of the ribs have not been taken into account, except by Marco Boetti (Guarino Guarini, Umberto Allemandi, Torino, 2006). In this contribution, I will deal with some possible sources of Guarini’s designs for the ribbed vaults of Sainte-Anne-la-Royale in Paris, Padri Somaschi in Messina, San Lorenzo in Turin and San Gaetano in Nice. I will take into account not only the plan layout of the ribs, but also their shape in space, and the nature of the intrados surface, analysing such possible sources as the stereotomic treatise of François Derand and several Spanish stonecutting manuscripts connected with El Escorial.
The Singular Brick Vault by Slices in Tower J17 from the Aurelian Walls in Rome
Aliberti L., de-Miguel-Sánchez M., González-Uriel A.
Q1
AbstractThe lower chamber of tower J17 from the Aurelian Walls in Rome is covered by a singular brick vault by slices that is almost completely preserved. This kind of vault is unusual in a Roman context and specifically in Aurelian Walls. Brick vaults by slices were extensively studied by the French engineer Auguste Choisy, who mainly scrutinized their ease of construction that doesn’t require formwork and can adapt to different plans to achieve lowered vaults. The best-known examples are in Byzantium and generally in the Eastern Roman Empire, while we don’t know many cases dating from late Roman antiquity on the Italian peninsula. Based on a rigorous photogrammetric survey and thorough data management, a detailed analysis of this vault allows us to establish a hypothesis about its construction process and to deepen the knowledge of this type of structure.
Land- and Skyscapes of Hegra: An Archaeoastronomical Analysis of the Nabataean Necropoleis
Belmonte J.A., González-García A.C., AlMushawh M.A., Urrutia-Aparicio M., Rodríguez-Antón A.
Q1
The archaeological World Heritage Site of Hegra (Mada´in Salih, Al-Hijr), in Saudi Arabia, is often considered the southern capital of the Nabataean Kingdom. Positioned just northeast of the AlUla Valley (where ancient Dadan is located), the Nabataeans recreated several aspects of their northern capital, Petra. They carved more than 130 tombs into the sandstone outcrops of which nearly a hundred had a monumental character with ornate façades of exceptional beauty and deep sense of enduring. In February 2023, our international, multidisciplinary research team conducted a field campaign in Hegra. Our objective was to measure the orientation of Nabataean tombs and sanctuaries in the area, which could offer new clues to aspects of Nabataean culture and religion that we had studied in earlier works at Petra, and elsewhere in Nabataea. This paper includes the analysis and interpretation of the data on the orientation of 113 tombs, including all monumental ones, the largest coherent set of Nabataean tombs ever analyzed. The results show that the tombs were not randomly orientated but followed a series of patterns, most probably emphasizing the skyscape, within the framework of the Nabataean lunisolar calendar religious festivals, and, on occasions, also the local landscape.
On Vaulting: Heron’s Manuals and Their Role in Roman Dome Design
Roca A., Juan-Vidal F., Cipriani L., Fantini F.
Q1
AbstractThe subject of domes in the Roman world is complex and can be studied from different perspectives. In this paper we focus on the relationship between Heron of Alexandria's manuals and the vaulting systems of the Hadrianic age. Our aim is to compare a selection of formulae from the critical edition by Johan Ludvig Heiberg with a series of buildings recently documented using photogrammetric and laser scanner technologies. The collection of writings Heronis Alexandrini opera quae supersunt omnia (mainly books IV and V) presents an interesting set of formulae for calculating vaults and domes: volumes and areas of niches, spherical segments, lunettes, as well as empirical strategies for calculating complex shapes. This approach, which integrates practical knowledge with Vitruvian graphic schemes, allows us to clarify the work of the ancient architect and consequently to investigate the architectural problem within the more general framework of archaeology with new conceptual tools.
Study of the Effects Created by the Sunlight Passing Through the Rose Windows of Mallorca Cathedral
Samper A., Moreno-García D., Herrera B.
Q1
AbstractThis paper shows the light effects and geometric alignments created by the sunlight passing through the stained glasses of the eastern rose window in Mallorca Cathedral and projecting on the inner side of the cathedral's main façade and on the cathedral's floor. As well as providing more accurate information about these already known light effects, this paper makes use of laser scanning techniques and astronomical and geographical concepts in order to graphically display other novel effects which occur in coincidence with certain religious festivities throughout the year.
Computing the Spatial Explorations of Roberto Matta
Domínguez Gómez P., Celis D’Amico F., García Alvarado R.
Q1
Generative design tools are occasionally employed in architecture to produce shapes. They can also provide researchers with different analysis capabilities by enabling new approaches and interpretations of case studies. This contribution presents the research on some artworks of the Chilean surrealist artist Roberto Matta Echaurren (1911–2002) using software applications coded with the Processing creative programming language. The selected works belong to Matta’s spatial exploration dating between 1936 and 1938 and consist of six architectural illustrations and the essay ‘Mathématique sensible—Architecture du temps’ (1938). The methodology employed in developing these applications entails digitally analyzing the artist’s work by extracting computable elements and subjecting them to computing mechanisms (sorting, combinations, randomization, etc.) that produce configurations similar to those designed by Matta.
Correction to: Heron’s Legacy: An Example of Ancient Calculations Applied to Roman Imperial Architecture
Roca A., Juan-Vidal F., Cipriani L., Fantini F.
Q1
Geometrical Analysis of a Brick Vault by Slices from the Aurelian Walls in Rome
Aliberti L., de-Miguel-Sánchez M., González-Uriel A.
Q1
AbstractThis work focuses on the analysis of a singular case of brick vault by slices from the Aurelian Walls in Rome. The study is based on an accurate survey carried out through automated photogrammetry. This analysis aims to determine the geometry of the vault and compare it with the theoretical model of its type.
Geometric Operations in Mario Botta’s Architectural Work
Ronco F., Bertola G., Pupi E.
Q1
AbstractThis paper investigates the role of primary plane figures, primary solids, and geometric operations in Mario Botta’s architectural works during fifty years of his career. Through the selection of three case studies, the research allows the creative process to be discretized and analyzed from a geometric-mathematical point of view.
Heron’s Legacy: An Example of Ancient Calculations Applied to Roman Imperial Architecture
Roca A., Juan-Vidal F., Cipriani L., Fantini F.
Q1
AbstractHeron of Alexandria is a well-known author in the field of mathematics and engineering, but his work is of great interest for understanding ancient construction problems related to architecture. The formulas translated and commented on by Heiberg (1914a, b) are analyzed through geometric diagrams and applied to famous Roman domed architecture.
Light Effects of the Rose Windows in Mallorca Cathedral
Samper A., Moreno D., Herrera B.
Q1
AbstractThis research shows the light effects and geometric alignments created by the sunlight passing through the stained glasses of the Eastern rose window in Mallorca cathedral and projecting on the inner side of the cathedral’s main façade. Besides, we show other novel effects which occur in coincidence with certain religious festivities.
About the Sources of the Vaults of San Lorenzo in Turin
Calvo-López J.
Q1
AbstractThis contribution deals with the late 17th century baroque church of San Lorenzo in Turin, designed by Guarino Guarini; it discusses the geometry and possible sources of the vaults of the church, including stellated polygons, raised oval arches and conical approximations to the oval intrados of these arches.
Lefe Lacework Carpentry and the Mudejar Set Square of 5
Redondo Buitrago A.
Q1
The research concerns the geometric aspects of the style of carpentry developed during the Mudejar period (Spain, 12th -16th centuries) traditionally called carpintería de lo blanco, focusing in its characteristic wooden ceilings with lacework designs based on the 10-fold rosette, known as lefe. The unknown origins of the peculiar Mudejar approximation of the 36º angle are traced.
Octagonal Layouts: Project Genesis of the Cathedral of Valencia
González C.L., García-Valldecabres J.L., Meseguer L.C.
Q1
AbstractOctagonal layouts are widely used in medieval architecture. In Spain, the Cathedral of Valencia is an exceptional example because of its compositional arrangement and early date of construction. The study of this cathedral serves not only to propose the regulatory layout and geometric process to develop the transept, the ambulatory, and the dome but allows the empirical establishment of the complex properties and characteristics of the octagon. By surveying the planes with a 3D laser scanner, the graphic procedures used in the original design of the temple were verified, as were the geometric theories pertaining to the figure of the octagon in architecture, set by the golden ratio.
A Virtual Reconstruction of Gaudi’s Skyscraper Hotel Attraction Using Physics-Based Simulation
Luque-Sala A., del Blanco García F.L.
Q1
AbstractThis article aims to provide a virtual reconstruction of the skyscraper Hotel Attraction based on the original documentation, which makes it possible to analyze the project and propose hypotheses regarding the contradictory information in the original drawings. The geometry of the project has been defined using a physics-based simulation, emulating Gaudí’s methodology in his models. To define the curves, a model based on weighted hanging chains has been generated, using a system with springs and particles. This method has made it possible to precisely control the catenary deformation, avoiding the definition of each curve independently in favor of a unified approach. Over 300 m tall, the Hotel Attraction would have been the tallest skyscraper in the world at the time.
Approaching Developable Surfaces Through Shadow and Penumbra
Martín-Pastor A., González-Quintial F.
Q1
AbstractThis paper enquires into the relationship between the rigorous graphic construction of penumbra and shadow and the idea of a developable surface circumscribed to two cores (whether these are curves or surfaces). The first rigorously constructed graphic representations of shadow and penumbra appearing in different historical treatises are contextualised and contrasted with the first works addressing the mathematical description of such surfaces. We describe how artisans and artists have employed physical and mechanical models to construct circumscribed developable surfaces, examining both their formal exploration and constructive formalisation. Next we extrapolate the mechanisms for generating circumscribed surfaces to digital and parametric models. The two procedures presented here evince the existing geometric limits of this way of generating a surface, thus influencing its constructive applications. Lastly, several examples of ephemeral architecture based on such procedures are offered, in which the digital design and manufacturing of experimental pavilions with circumscribed developable surfaces are addressed.
Proportion and Disproportion in the Late Gothic Layout of the Charterhouse of Jerez (Cádiz, Spain)
Castellano-Román M., Pinto Puerto F.
Q1
The construction of a large and complex monastery such as the Charterhouse of Jerez required a precise geometric plan, the layout, which once deployed on the ground becomes the shape control system of the construction process. The basic geometric figure that supports the layout is the square and the variations derived from the ratio between its side and its diagonal. This paper presents the graphic definition of this geometric layout and analyses its persistence over more than three centuries of architectural evolution (fifteenth through eighteenth centuries). During this lengthy process, it has been possible to characterise how the rigour of geometric abstraction, the natural conditions of the ground on which the monastery was founded, and the functional and symbolic demands of the Carthusian order have been balanced. Likewise, there has been an analysis of the situations in which disproportion is imposed: the alteration or abandonment of the geometric plan. These undesirable situations reveal the imposition of existing conditions and the evolution of artistic concepts.
A Hexagonal Pattern in the Paraninfo at the Universidad de Alcalá
De-Miguel-Sanchez M., Gonzalez Duque C., Chías Navarro P., Abad Balboa T.
Q1
In the sixteenth century, the assembly hall, or Paraninfo, at the recently inaugurated Universidad de Alcalá was known as the pieça del theatro. This study focuses on the layouts and proportions designed for this hall, which could be the key to understanding the whole project as a Renaissance theater that was singularly inspired by Roman models. Specifically, the hexagonal pattern of the coffered ceiling represents a genuine formal exploration in comparison with other wooden ceilings having similar geometric bases. All this led us to study this uncommon masterpiece as a proposal for a new model toward an intellectual and architectural recovery of the Antiquity, in the core of the Universidad, conceived for the representation of academic ceremonies and humanistic theater.
Rules of Geometries of Control in Muslim Architecture: Emergence and Conflicts of a Research Field in France (1863–1899)
Girón Sierra F.J.
Q1
In the second half of the nineteenth century, studies and hypotheses on the geometric rules used in the past for setting up buildings experienced a growing momentum, fueled by the demands of a discipline in the making: the history of architecture. One area yet to be studied was the regulating geometric lines of Muslim architecture. This article describes how this research emerged and developed in France, highlighting its protagonists, hypotheses, and conceptual framework. The research was carried out by a small group of architects, engineers, and diplomats tied by professional or personal links: Vogüé, Mauss, Dieulafoy, and Choisy, being all of whom were in some way influenced by Viollet-le-Duc. Also discusses is why their sustained efforts failed to achieve a consistent overall picture. At the end of the nineteenth century, the task of describing the geometric of Muslim architecture and finding its place in the universal history of architecture was still open.
Surface Ornamentation Techniques and Spatial Distortion
Martin J., Martín Fuentes D.V.
Q1
Several different types of surface-related ornamentation that are capable of distorting the perception of space have been developed and used since ancient times. Some examples of these are di sotto in sù, quadratura, trompe l’oeil and foreshortening. These techniques throw into question the limits of space and architecture and our understanding thereof. However, until now, there has been no clear classification or designation of these distortive techniques. Therefore, this article focuses on the identification and classification of three different ornamental techniques applied to surfaces that can distort the perception of space and looks to the work of various contemporary artists to exemplify the proposed taxonomy.
Proportions and Deformations in the Mosque-Cathedral of Cordoba
Cantizani-Oliva J., Reinoso-Gordo J., Gámiz-Gordo A.
Q1
This research presents a dimensional analysis of the arcades of one of the most emblematic spaces of the Mosque-Cathedral of Cordoba: its central nave, located besides the mihrab in the ambitious extension carried out by Al-Hakam II. In order to accomplish this survey, a digital model was created from the point cloud obtained with a 3D laser scanner. Subsequently, earlier theories of architectural proportions related to this monument have been reviewed. The comparison of these earlier drawings with the corresponding digital models allows the precision of their different hypotheses to be assessed. Architectonic deformations not considered by the scientific literature are also quantified here. Finally, this research indicates certain partial order relations close to the proportion 1.3, though it should be noted that not all the arcades share the same dimensions and thus no general theory applies to their proportions.
