Proportions and Deformations in the Mosque‑Cathedral of Cordoba

Vol.:(0123456789) Nexus Network Journal (2023) 25:145–165 https://doi.org/10.1007/s00004-022-00622-y RESEARCH Proportions andDeformations intheMosque‑Cathedral ofCordoba JuanCantizani‑Oliva1 · Juan‑FranciscoReinoso‑Gordo2 · AntonioGámiz‑Gordo3 Accepted: 11 June 2022 / Published online: 11 July 2022 © The Author(s) 2022 Abstract 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. Keywords Proportion· Geometry· Measurement· Virtual architecture Introduction The Mosque-Cathedral of Cordoba, its monumental core and its surroundings, included in the World Heritage List in 1984,1 has undergone different transformations throughout history in order to be adapted to new times, but preserving the essential * Antonio Gámiz-Gordo [email protected] 1 Electrical andAutomatic Engineering Department, University ofCordoba, 14071Cordoba, Spain 2 Architectural andEngineering Graphic Expression Department, University ofGranada, 18071Granada, Spain 3 Architectural Graphic Expression Department, University ofSeville, 41012Seville, Spain 1 Historic Centre of Cordoba [World Heritage List]. Available online: https:// whc. unesco. org/ en/ list/ 313(accessed on 9 January 2022). 146 J.Cantizani-Oliva et al. features of its architectural identity (Moneo-Vallés 1985). This history comprises three different defined stages described hereunder (Nieto-Cumplido 2001). The first Umayyad Mosque was built in the eighth century by Abd al-Rahman I. Its structure of parallel arcades and naves enabled a first extension towards the south by Abd al-Rahman II, and a subsequent one by Al-Hakam II. In the tenth century Almanzor ordered the last extension of the monument towards the east, completing an astonishing interior composed of columns and double arches. The second stage was started after the conquest of Ferdinand III in 1236, when the edifice was consecrated as a Christian church. Towards 1313 the Royal chapel was built to host the tomb of Ferdinand IV of Castile, beside the Villaviciosa Chapel. Between 1523 and 1607 a large, central volume was erected, and consequently the monument was greatly altered; the inner perimeter was occupied by chapels, and in the eighteenth century new skylights were opened and plaster vaults were added in several naves. The third stage, starting in the early nineteenth century, saw numerous reformations, juxtaposing architectonic fragments of miscellaneous historical periods (Herrero- Romero 2016). It is helpful to highlight the extension commissioned by Al-Hakam II (Chueca- Goitia 1965) planned around a central nave located between the Royal Chapel and the mihrab, whose arcades are the subject of this study (Fig.1). The aim of this research is to analyze the dimensions of the arcades of the central nave in the extension built by Al-Hakam II in order to assess the accuracy of three notable theories about arcade proportions in the monument. The purpose is also to quantify their architectonic deformations, considering that the building has undergone numerous transformations and restorations for centuries. To illustrate this, a novel graphic construction was created from the point cloud obtained insitu with a 3D scanner. Likewise, thorough graphic transcriptions of the Fig. 1 Floor plan and frontal perspective of the mihrab area. Al-Hakam II extension 147 Proportions andDeformations intheMosque‑Cathedral of… descriptive drawings of the three proportion theories were elaborated to superimpose them upon the digital model of the monument’s current state and thus evaluate their precision. Finally, several charts and graphic diagrams were developed to display the main data of the deformations analyzed. Model Construction froma3D Laser Scanner The major plans of the Mosque-Cathedral of Cordoba, elaborated throughout the history with traditional drawing techniques and compiled in an influential work by Nieto-Cumplido and Luca-de-Tena in (1992), were reviewed together with other varied selections (Gámiz-Gordo 2019). The publications of computerized plans based on measurements manually obtained were also reviewed (Ruiz-Cabrero 2009; Almagro-Gorbea 2015; Messina 2017). The digitization of the architectural heritage has experienced a major breakthrough in recent years thanks to the development of new technologies for capturing metric data. Late research in the Mosque-Cathedral has applied photogrammetry techniques (Fuentes-González 2019) or 3D laser scanners (Gámiz- Gordo etal. 2021) as the basis for precise graphic documentation. In any case, the survey precision must be adjusted according to the scale used and the dimensions of the model, considering the objectives proposed here. In this study, a point cloud from the Mosque-Cathedral area enlarged by Al-Hakam II was obtained using two laser scanners, the Leica C10 and the Leica BLK360, with the technical features detailed hereafter. The Leica C10 possesses a dual axis compensator for levelling with an accuracy of 1ʺ, and 6mm in the 3D positioning of a point. It is able to station on a specific point thanks to its laser plumb line. Its scanning field is 360º horizontally and 270º vertically. The density of points can be set to different values; for example, a medium density captures points every 10cm on a plane located at 100m. The Leica BLK360 is not able to station at a specific point nor be levelled; its scanning field is 360º. Medium quality capture density is 10mm at 10m. By stationing at mq1, the C10 scanner was used to create the reference system and level the point cloud (see Fig.2). Using mq1 as the origin and the mihrab nave as the X axis, the reference scan was performed stationing in mq1. Also, mq7 was observed from mq1. Four different trajectories were performed with the BLK, using the C10 scan over mq1 as the origin to record each trajectory. Figure 2a shows the scans from the C10 (yellow) and the four trajectories followed with the BLK (white); the number 1 corresponding to the central nave is focused on in the present study. Additionally, Fig.2b shows the scanner positions symbolized by spheres and the corresponding registered point cloud. All scans were accomplished using a medium resolution, which implies a separation between captured points of 1cm at 10m distance. In the quality of the registers of the scans the following variables were considered: overlap (quantity of volume shared between two registered scans, measured in %), balance (measure of the homogeneity in the points distribution through the 3 perpendicular directions 148 J.Cantizani-Oliva et al. of the space) and the points percentage with an error less than 6mm in each of the registers. The geometric model of the current state of the building was produced by importing the point cloud to CAD and using it as a reference. The sections were extracted from the point cloud and projected orthogonally to obtain the corresponding orthoimages. To define the geometry, some commands were used to obtain lines or edges, as well as planes and intersections from the orthoimages. Each element was defined according to the degree of precision and definition of the analysed model (Fig.3). Theories onProportions intheMosque‑Cathedral ofCordoba There are several studies devoted to the field of proportions of the Mosque-Cathedral of Cordoba. Some of them focus on the general floor plan (Fernández-Puertas 2000; Hoz-Arderius 1991; Hoz-Arderius 1991), and others discuss elements such as the Villaviciosa Chapel (Fuentes-González 2019), Puerta de San Esteban (Hoz-Arderius 1991; Fernández-Puertas 1999; Fernández-Puertas 2008b), or the Puerta de los Deanes (Fernández-Puertas 2009). The main theories about the proportions of the arcades, analyzed and graphically transcribed here, are the following three: one by Emilio Camps-Cazorla2 [Camps] which analyzes the relation between the arch modules in the area of the original construction commissioned by Abd al-Rahman I (Camps Cazorla 1953); another Fig. 2 Reference system and scanner trajectories: a plan view, b perspective view of the scanner positions represented by spheres 2 Emilio Camps-Cazorla, born in Fuensanta de Martos (Jaén) on October 31st, 1903, and deceased in Madrid on January 28th, 1952. PhD in History of Art by the University of Oviedo in 1949, he never practiced as Professor, as he was appointed Director of the National Archaeological Museum. He is the author of numerous publications about Romanesque and Islamic art (Gentil-Baldrich 2021: 315-316). 149 Proportions andDeformations intheMosque‑Cathedral of… Fig. 3 Digital model on the point cloud and actual geometry. Central nave sections 150 J.Cantizani-Oliva et al. by Rafael de la Hoz-Arderius3 [Hoz], based on the relation 1.300, known as the proporción cordobesa (Doblado-González 2008; Hoz-Arderius 1991); and finally one developed by Antonio Fernández-Puertas4 [Fernández], also around the area built by Abd al-Rahman I, which proposes that the monument was conceived and drawn using Pythagorean proportions (Fernández-Puertas 2008a). Each of these theories was graphically transcribed using a geometric reconstruction, taking the intercolumn found in the area ordered by Al-Hakam II as a reference. The relations between the architectural elements in the theory by Camps were represented with a Cartesian modulated grid, in the theory by Hoz with slanted lines and numbered nodes to identify their relations, and in the one by Fernández with a sequence of geometric forms, a square that serves as the base for two equilateral triangles and an upper rectangle. The main aspects of each theory are detailed below. Theory byEmilio Camps‑Cazorla [Camps] The book Módulo, proporciones y composición en la arquitectura califal cordobesa (Camps-Cazorla 1953) poses the existence of an arithmetic modular. It focuses on the primitive Mosque built by Abd al-Rahman I, where the author claims that “the arches of the primitive arcades, though following the Hispano-Visigothic tradition, possess however such a simple structure which does not allow any evolution, so they remain essentially unaltered in their subsequent repetitions.”5 The arcades are comprised of two levels of arches, the lower having horseshoe shaped buttress arches with a stilt height equal to 1/3 of the radius. This research considers stilt as the vertical displacement of the horseshoe arch center. This typology is also seen in some earlier Hispano-Visigoth arches. The upper level has semicircular arches of extra thickness, with modillions and mouldings. Regarding the question of proportions, Camps considers two modules with no common divisor (see Fig.4). The semicircular arches conform to the division of the total width in six equal parts, “module b”, and the horseshoe arches in five, “module a”, their radii being five and four times their respective modules (5b and 4a). The keystone width is in each case equal to these modules, and the front width of the columns three-fifths of “a” (3/5 a). Heights are related to the semicircular arc 5 … los arcos de las arquerías primitivas, si por una parte están muy dentro de la tradición hispanovisigoda, por otra parte son de estructura tan sencilla que casi no admite evoluciones, y así se repiten sustancialmente inalterados en sus repeticiones posteriores… (Camps-Cazorla 1953: 28, our Eng. trans.). 3 Rafael de la Hoz-Arderius, PhD Architect was born in Madrid on October 9th, 1924, he graduated in 1951 and died in the same city on June 13th, 2000. President of the International Union of Architects (UIA) from 1981 to 1985, he was also Fellow Member of the San Fernando Royal Academy of Fine Arts of Madrid since 1990. Besides a relevant work on architecture which he started to produce in Cordoba, his adopted homeland, he explained the so-called Proporción cordobesa theory (Gentil-Baldrich 2021: 896-897). 4 Antonio Fernández-Puertas, PhD in History of Art, was born in Granada on August 2nd, 1950, and died in London on August 21st 2016. In 1981 he became Professor of Islamic Art History at the University of Granada and Director-Curator of the National Museum of the Alhambra from 1978 to 1992 (Gentil-Baldrich 2021: 651). 151 Proportions andDeformations intheMosque‑Cathedral of… diameter (5b) so that, taking as a reference the floor level, the total height is three times the latter (15b); between the imposts of the two levels of arches, just once (5b); and half of the total height up to the impost of the horseshoe arches (15/2 b). Theory byRafael de la Hoz‑Arderius [Hoz] This author’s theory, raised in 1973 under the name of proporción cordobesa, considers of special interest the rectangle with relation � 1+ √ 2∕2≈ 1.307 , derived from the ratio between the side and circumradius of the octagon. Hoz claims that this pattern is present not only in the Mosque-Cathedral of Cordoba, but also in other contrasting buildings such as the Aqueduct of Segovia, Puerta de Alcala in Fig. 4 Graphic transcription of the theory by Camps 152 J.Cantizani-Oliva et al. Madrid, the Pantheon of Agrippa in Rome, the Egyptian pyramid, or the Pyramid of the Moon in Teotihuacan, Mexico (Doblado-González 2008; Hoz-Arderius 1991). Hoz represents the diagrams of proportions by “…two systems of tilted lines, perpendicular to each other symbolizing the diagonals of both families of rectangles…”,6 that is, vertically and horizontally. He refers to the arches of the Mosque-Cathedral in a general way without mentioning the study area: “… the arches also rise following an identical grid”7 (Hoz-Arderius 1991). Their drawings reveal inaccuracy in their relations, as the lines represented do not exactly coincide with the nodes’ centers (see Fig.5). There is consistency between relations 1-2-3 and 4-5-15-6. Notwithstanding, it should be noted Fig. 5 Graphic transcription of the theory by Hoz 6 …dos sistemas de rectas inclinadas, perpendiculares entre sí y correspondientes a las diagonales de ambas familias de rectángulos… (Hoz-Arderius 1991, our Eng. trans.). 7 … las arquerías también se alzan dentro de una trama idéntica (Hoz-Arderius 1991, our Eng. trans.). 153 Proportions andDeformations intheMosque‑Cathedral of… that the floor level was modified in the restorations conducted in the 20th century and, furthermore, the relation between the horseshoe arch radius and stilt is not considered. It seems that there is a possible excess of relations, so that the satisfaction of some of them restricts others. Theory byAntonio Fernández‑Puertas [Fernández] Fernández has accomplished numerous studies on proportions. In the case of the Mosque general floor plan, he considers “… the system of proportions under the whole Mosque of Cordoba was conceived and traced, it is the Pythagorean model of Ancient Greek and Rome classical era, which reached the Umayyad emirate in the 8th and 9th centuries, and then the Caliphate art, prevailing in the taifas, Almoravid, Almohad and Nasrid dynasties”8 (Fernández-Puertas 2000). This system would be characterized by the use of set squares with 45º and 90º angles and with 30º, 60º, and 90º angles. Starting from the square, it is very simple to obtain a rectangle with a longer side equal to its diagonal, with a dimension √ 2 (≈ 1.414 ) . By successively repeating this operation it results in relations of √ 3 (≈ 1.732 ) , √ 4 (= 2 ) , √ 5 (≈ 2.236 ) , etc. According to Fernández the floor plan in the area of Abd al-Rahman I extension in the Mosque comprises two squares. Its central nave is defined by the intersection of two arches with radii of the same length of that of the side of the square, and the aisles dividing the rest in five equal parts. The rectangular grid, supporting the column axes, is traced either through divisions in five parts or creating a grid drawn using rhombuses with a 60-degree set square (Fernández-Puertas 2008a). The extension floor plan commissioned by Al-Hakam II also shows a Pythagorean layout using a 30-degree set square (Fernández-Puertas 2000). Fernández considers that the arcade follows the same system of proportions as the one applied to the floor plan (Fernández-Puertas 2008a), with a square resting on the floor level, with a side equal to that of the intercolumn (see Fig.6). The height of the capital, which may vary, is obtained by drawing an arc with a radius half the diagonal (R1) and then by the vertical folding of the midpoint (R2). To define the impost line and stilt, an arc is placed on the latter, centered on the middle of the lower side of the square (R3) and the middle of the length of the diagonal (R4), respectively. The interior of the horseshoe arch and the exterior of the rounded arch are determined by drawing two equilateral triangles with reversed vertices forming a rectangle with side √3 and diagonal √4 . The height of the ceiling correlates to the intersection of two lines at 45°, whose height equals half the distance between the axes. 8 Fernández-Puertas considers that …el sistema de proporciones con el que la mezquita de Córdoba entera fue concebida y trazada, y que es el pitagórico heredado de la Antigüedad Clásica grecorromana que llegó al emirato omeya de Córdoba de los siglos VIII y IX, y luego pasó al arte del califato, y pervivió bajo los taifas, almorávides, almohades y nazaríes (Fernández Puertas 2000: 217, our Eng. trans.). 160 J.Cantizani-Oliva et al. two levels of arches (between 241 and 250cm). It presents deformations of up to 6.5cm in E12, which indicates a relation with the intercolumn width between 1.252 and 1.314; and as such six arches exceed 1.300, resulting in 1.294 as the mean value. Fig. 9 Analysis and quantification of deformations 161 Proportions andDeformations intheMosque‑Cathedral of… Conclusions To analyze the dimensions of the arcades in the central nave central of Al-Hakam II expansion at the Mosque-Cathedral of Cordoba, this research accomplished its own digital geometric model from the point cloud obtained with a 3D laser scanner. Subsequently, a meticulous graphic transcription of the three major theories on arcades proportions was conducted to compare them through their superimposition over the rigorous model of the survey in its current state. This first approach has proved that the graphic results of these three theories show different patterns between them, and they also differ from reality. The highest point of both the floor and the ceiling display major differences in Camps and Fernández. It must be noted here that both elements have suffered major transformations; in the 18th century plaster vaults and skylights were added, later dismantled in restorations carried out in the 20th century, when floorings were also modified. In other respects, the average stilt of the horseshoe arches, 1/3 according to Camps, does not correspond with the one obtained in the theories of Hoz and Fernández. The same occurs in the relation between the distance of the intercolumn and the height of the imposts line in the two levels of arches, whose mean value is 1.294, thus being almost square in Camps (6/5 = 1.200), and greater in Hoz and Fernández (1.405 and 1.443 respectively). All this indicates that the theories on proportions regarding the area commissioned by Abd al-Rahman I do not apply to the Al-Hakam II’s Mosque extension. Furthermore, the digital model allowed the major and current deformations of the analyzed arcades to be quantified. It can be affirmed that the average diameter and distance between columns is 44 and 315 cm, respectively, and not 66 and 270 as indicated in the aforementioned publications. Furthermore, the significant differences in the altimetric level of the cymatia, 4.5cm above the value and 5.0cm below it, are quite revealing. The major deformation corresponds to the intercolumns in the south end, where the radius of the upper semicircular arch is reduced 19.0 and 12.5cm in the east and west arcade, respectively, in their intersection with the perpendicular row of arches. Another key fact, not considered so far in the scientific literature on the Mosque-Cathedral, is the slope of 0.4% between both ends of the arcade, with a total difference in height of 8.0 cm in the sections analyzed, decreasing southwards. Finally, from the analysis of the theories of proportions and the rigorous survey carried out, there is evidence to suggest the existence of a relation of 1.3 between the width of the intercolumn and the height between the impost lines of the two levels of arches. This relation is the one displaying the greatest compositional and constructive importance found so far (referred to as “main proportion” in to Fig.10) since it does not depend on the transformations or restorations of the floor elevation and ceiling height. Its dimensional analysis reveals a mean value of this relation of 1.294, though 6 of the 13 surpass the relation of 1.300. It is currently unknown why the arch designers would have used this relation related to the classical or Pythagorean proportions discussed by Fernández (Fig. 11a) and the theories of 162 J.Cantizani-Oliva et al. proportions based on the number 1.307 which Hoz called proporción cordobesa. In the first case, Fernández applies this relation to obtain the capital height from a square and the tracing of two arcs (R1 and R2); and in the second (Fig. 11b), Hoz derives it from the ratio between the circumradius and side length of a regular octagon. However, there is another simple method (Fig.11c) based on the tracing of an arc (R0) with the center to ¼ of the side, from which an approximate relation of 1.309 is obtained. Fig. 10 Relations in the arcades of the central nave, Al-Hakam II extension Fig. 11 Outlines showing proportions close to 1.3. a Fernández (1.307), b Hoz (1.307), c another simple method (1.309) 163 Proportions andDeformations intheMosque‑Cathedral of… Another relation affected by the grade of slope of the floor, and the hypothesis that part of the columns is buried, is the height of the spring line of the horseshoe arch. Its ratio with the intercolumn width has a mean value of 1.231, though five arches slightly surpass this relation and could reach the 1.300 proportion when considering the architectonic transformations already mentioned. Finally, after superimposing and comparing the theories of Camps, Hoz, and Fernández with the digital model created for this study and quantifying the deformations which were not previously considered in the related scientific literature, it is apparent that not all the arcades are identical. No metric pattern is repeated in their different areas and thus no general theory on architectural proportions can be deduced for the arcades of this singular monument. This research foresees carrying out new surveys in the Abd al-Rahman I zone, and in the extensions built by Abd al-Rahman II and Almanzor to further analyse the theories of proportions mentioned, as well as studying the metrology and measurement units at the construction level to enable a better understanding of the geometry and proportions of the Mosque-Cathedral of Córdoba. Acknowledgements This research has been made possible thanks to the collaboration of the Cabildo de la Catedral de Córdoba. The authors are also grateful for the support from the research group ‘HUM- 976. Expregrafica. Lugar Arquitectura y Dibujo’; Programa de Doctorado en Arquitectura, Instituto Universitario de Arquitectura y Ciencias de la Construcción from the University of Seville; the research group ‘TEP-164. Ingeniería Cartográfica’ from the University of Jaén; the Survey and Modelling Laboratory (SMlab) from the University of Granada; and Internationalisation grants to the Instituto Universitario de Arquitectura y Ciencias de la Construcción (IUACC) of the VIII Plan Propio de Investigación y Transferencia in the University of Seville. All images are by the authors. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. References Almagro-Gorbea, Antonio, ed. 2015. El Legado de Al-Ándalus. Las Antigüedades Árabes en los dibujos de la Academia. Madrid: Real Academia de Bellas Artes de San Fernando, Fundación Mapfre. Chueca-Goitia, Fernando. 1965. Historia de la arquitectura española: Edad Antigua y Edad Media. Madrid: Editorial Dossat. Camps-Cazorla, Emilio. 1953. Módulo, proporciones y composición en la arquitectura califal cordobesa. Madrid: CSIC, Instituto Diego Velázquez. Doblado-González, Marina. 2008. La proporción cordobesa en la arquitectura. In: Segundo Congreso Internacional de Matemáticas en la Ingeniería y la Arquitectura. Madrid: Universidad Politécnica de Madrid, 359–362. 164 J.Cantizani-Oliva et al. Fernández Puertas, A. 1999. Uno de los dos trazados proporcionales de la Bab al-Uzara. Miscelánea de Estudios Árabes y Hebraicos. Sección Árabe-Islam, 48, 59–104. Fernández Puertas, Antonio. 2000. I. Mezquita de Córdoba. Trazado proporcional de su planta general (siglos VIII-X). Archivo Español de Arte. https://doi.org/https:// doi. org/ 10. 3989/ aearte. 2000. v73. i291. 829. Fernández Puertas, Antonio. 2008a. II. Mezquita de Córdoba. ‘Abd al-Raḥmān I (169/785-786). El trazado proporcional de la planta y alzado de las arquerías del oratorio. La qibla y el miḥrāb del siglo VIII. Archivo Español de Arte. https://doi.org/https:// doi. org/ 10. 3989/ aearte. 2008. v81. i324. 127. Fernández Puertas, Antonio. 2008b. Otro trazado de la Bab al-Uzara. Miscelánea de Estudios Árabes y Hebraicos. Sección Árabe-Islam, 57: 75–121. Fernández-Puertas, Antonio. 2009. III. Mezquita de Córdoba. El trazado de la portada interior de la Bāb al-Wuzarā’. La Puerta de los Deanes (s. VIII), su trazado interior y exterior,” Archivo Español de Arte. https://doi.org/https:// doi. org/ 10. 3989/ aearte. 2009. v82. i326. 146. Fuentes-González, Paula. 2019. The Islamic Crossed-Arch Vaults in the Mosque of Córdoba. Nexus Network Journal. https://doi.org/https:// doi. org/ 10. 1007/ s00004- 018- 0403-y. Gámiz-Gordo, Antonio. 2019. La Mezquita-Catedral de Córdoba. Fuentes gráficas hasta 1850. Al Qantara Revista de Estudios Árabes. https:// doi. org/ 10. 3989/ alqan tara. 2019. 005. Gámiz-Gordo, Antonio, Juan Cantizani-Oliva and Juan Francisco Reinoso-Gordo. 2021. The Mosque- Cathedral of Cordoba: Graphic Analysis of Interior Perspectives by Girault de Prangey around 1839. ISPRS International Journal of Geo-Information. https://doi.org/https:// doi. org/ 10. 3390/ ijgi1 00301 81. Gentil-Baldrich, José María. 2021. Bibliotheca Geométrica: Bibliografía histórica para la Geometría Descriptiva y el Dibujo Arquitectónico hasta 2001. Sevilla: Universidad de Sevilla. HUM976. Expregráfica. Lugar, Arquitectura y Dibujo. [Available online: https:// hdl. handle. net/ 11441/ 128665 (accessed 29 December 2021). Herrero-Romero, Sebastián. 2016. Teoría y práctica de la restauración de la Mezquita-Catedral de Córdoba durante el siglo XX. Ph.D. Thesis. Universidad Politécnica de Madrid. Available online: http:// oa. upm. es/ 39987/1/ SEBAS TIAN_ HERRE RO_ ROMERO. pdf (accessed on 29 december 2021). Hoz-Arderius, Rafael de la. 1973. La proporción cordobesa. Córdoba: Colegio Oficial de Arquitectos de Córdoba, 2002. Hoz-Arderius, Rafael de la. 1991. La proporción cordobesa. Varia espacial. Madrid: Real Academia de Bellas Artes de San Fernando. Messina, Barbara. 2017. La memoria nel disegno. Le trasformazioni della moschea di Cordova attraverso la lettura grafica dello spazio. Salerno: Università degli Studi di Salerno. Moneo-Vallés, Rafael. 1985. La vida de los edificios. Las ampliaciones de la Mezquita de Córdoba, Arquitectura 256: 26-36. Nieto-Cumplido, Manuel. 2001. La catedral de Córdoba. Córdoba: Caja Sur. Nieto-Cumplido, Manuel and Carlos Luca-de-Tena. 1992. La Mezquita de Córdoba: planos y dibujos. Córdoba: Colegio Oficial de Arquitectos de Andalucía Occidental. Ruiz-Cabrero, Gabriel. 2009. Dibujos de la Catedral de Córdoba: Visiones de la Mezquita. Barcelona: This Side Up. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Juan Cantizani‑Oliva Architect (1988), Master in Projects Architectural (Fundación Antonio Camuñas, 1992), Degree in Electrical Engineering (2014) and Master in Industrial Engineering (2016). Profesor Sustituto Interino in Department of Engineering Electrical and Automatic (University of Córdoba, Spain). Since 2019 member of the research group ‘HUM976 Expregráfica. Lugar, Arquitectura y Dibujo’. Thesis in progress (University of Seville) on geometry and light in the Mosque-Cathedral of Córdoba. Juan Francisco Reinoso‑Gordo PhD in Geodesy and Cartography (2008) and Profesor Titular at Department of Graphic Expression Architectural and Engineering (University of Granada, Spain). He is a 165 Proportions andDeformations intheMosque‑Cathedral of… member of the research group “TEP164. Ingeniería Cartográfica”. He has authored about 70 publications (articles, book chapters and conferences proceedings) related to cartography, architecture, heritage, photogrammetry and laser scanner. Antonio Gámiz‑Gordo PhD in Architecture and Profesor Titular at the Architectural Graphic Expression Department (University of Seville, Spain). Since 2015 he has led the research group ‘HUM976 Expregráfica. Lugar, Arquitectura y Dibujo’. He has authored about a hundred publications (books, articles, congresses and conferences proceedings) on drawing, architecture, heritage, city, landscape, and its graphic sources images throughout history.