In this article, we present our laser-scanning–based geometric analysis of the Franciscan Church of Szeged-Alsóváros (HU). The periodisation and building history of the church has been the topic of scientific debate: the chronological order of the construction of the vaults of the nave, apse and sacristy is not yet decided, and the dating of the nave’s vault is highly uncertain. This building is also a great example by which to study the logic behind the designing and raising of such structures in the Gothic era. Based on the exact data we gathered by laser scanning the church, we analyse the layout of the walls, as well as the net (and stellar) vaults of the nave, apse, sacristy and the ground floor of the tower. Knowing the exact geometry, we propose a potential way of constructing the floor plan of the polygonal apse as well as other details. We also address the probable reasons for the plan alteration resulting in a significant difference between the shape of the lower and upper regions of the polygonal apse. Regarding the vaults, we highlight the geometric differences in the connections between the webbings and rib systems, the global geometry of the rib systems and the shaping of the individual ribs. Based on these descriptions, we discuss the probable construction strategies and building methods of the vaults and attempt the theoretical reconstruction of the building processes. The outcome of our research presented in this article is a description of possible methods and applied proportions for drafting medieval structures and a contribution to the periodisation of the Franciscan Church of Szeged-Alsóváros. In addition, the methodology and building archaeology strategies we applied during our work hallmark the new possibilities of non-destructive research methods opened up by laser scanning technology.

[1]  Eszter Jobbik and János Krähling, “Real Net Vault or Pseudo-Ribbed Net Vault? Geometry, Construction and Building Technique of the Vault of the Reformed Church of Nyírbátor and the Nave Vault of the Franciscan Church of Szeged-Alsóváros,” Építés-Építészettudomány 51, no. 3-4 (Sep., 2023): 229-256, https://doi.org/10.1556/096.2023.00100.
[2]  Zsuzsa Lukács, Szeged. Alsóvárosi ferences templom és kolostor [Szeged. The Alsóváros Franciscan church and cloister] (TKM Egyesület, 1999), 3; However, its position is not yet clear, as its remnants may be included in the present nave walls (Sándor Bálint, A Szeged-alsóvárosi templom [The Szeged-Alsóváros church] (Budapest: Pannonia Kiadó, 1966), 26), or could be under the present apse (István Harsányi, “A szeged-alsóvárosi ferences templom gótikus szentélye csillagboltozatának helyreállítása” [Restoration of the stellar vault above the Gothic apse of the Franciscan church of Szeged-Alsóváros], Műemlékvédelem 45, no. 5 (2001): 294-304, 303), east of the apse (Lukács, Szeged, 3), or somewhere in the vicinity of the church (Zsuzsa Lukács, “A Szeged-alsóvárosi középkori ferences kolostoregyüttes” [The Szeged-Alsóváros Franciscan cloister-ensemble], in A középkori Dél-Alföld és Szer, ed. Tibor Kollár (Csongrád Megyei Levéltár, 2000), 143-192, 144).
[3]  Zoltán Nagy, “A ferencesek Szeged-alsóvárosi temploma” [The Church of the Franciscans in Szeged-Alsóváros], Magyar Építőművészet (1944): 89-93, 92; Ferenc Levárdy, Szeged, Alsóvárosi templom [Szeged, Alsóváros church] (TKM Egyesület, 1980), 7; Lukács, Szeged, 3; Harsányi, “A szeged-alsóvárosi,” 297.
[4]  Levárdy, Szeged, 7.
[5]  Lukács, Szeged, 3.
[6]  Zsuzsa Lukács, “Előzetes beszámoló a Szeged-alsóvárosi ferences kolostor kutatásáról” [Preliminary report about the research in the Szeged-Alsóváros Franciscan cloister], in Koldulórendi építészet a középkori Magyarországon. Tanulmányok., ed. Andrea Haris (Országos Műemlékvédelmi Hivatal, 1994), 437-490, 453; Harsányi, “A szeged-alsóvárosi,” 297.
[7]  Lukács, “Előzetes,” 453.
[8]  Harsányi, “A szeged-alsóvárosi,” 303.
[9]  Harsányi, “A szeged-alsóvárosi,” 297.
[10]  Harsányi, “A szeged-alsóvárosi,” 297.
[11] István Harsányi, Szeged Alsóvárosi ferences templom hajó-boltozatának és falfelületeinek kutatása, építészettörténeti vonatkozások föltárása. II. kötet. A hajóboltozat felújítási munkáinak tervezését megelőző építészeti-műemléki kutatás [Research of the nave vault and walls of the Szeged-Alsóváros Franciscan church, exploration of the architectural historic connections. Tome II. Architectural research prior to the nave’s restauration works] (Budapest, 2006), https://docplayer.hu/16384222-Dr-lukacs-zsuzsa-emlekere.html, 27. 
[12]  Harsányi, “A szeged-alsóvárosi,” 301; Harsányi described the nave vault as a barrel vault subsequently decorated with ribs (see below).
[13]  “Supposedly they realised that for the planned stellar vault, the latter, modified polygon is more suitable.” Harsányi, Szeged Alsóvárosi ferences, 25.
[14]  Lukács, Szeged, 12.
[15]  Levárdy, Szeged, 7-8.
[16]  Levárdy, Szeged, 7
[17]  Lukács, Szeged, 14.
[18]  Balázs Szőke, “A Szeged-Alsóvárosi ferences templom hajóboltozata” [Nave vault of the Szeged-Alsóváros Franciscan church], in A ferences lelkiség hatása az újkori Közép-Európa történetére és kultúrájára 2, eds. Sándor Őze and Norbert Medgyesy-Schmikli (PPKE BTK-METEM, 2005), 875-890, 889; Harsányi, “A szeged-alsóvárosi,” 297.
[19]  Two permissions for the destruction of the “vaults” and “roofs” were granted (1624 and 1625), but the permission for the “repair of the church” was rejected (1626) (Lukács, “A szeged-alsóvárosi,” 145).
[20]  Bálint, A Szeged, 17.
[21]  Lukács, “A szeged-alsóvárosi,” 145; Szőke, “A szeged-alsóvárosi,” 876.
[22]  As the use of the terminology differs in the sources, we hereby define that in the present paper, by “real net vault” we mean the vault structure where the rib system is antecedent to the webbing, and the webs are built on the ribs (either with or without formwork), and by “pseudo-ribbed net vault” we mean the structure where the ribs are mounted subsequently (however, not necessarily in a different building period) on a barrel vault.
[23]  Nagy, “A ferencesek,” 93; Bálint A Szeged, 26; Levárdy, Szeged, 8; Lukács, Szeged, 14; Harsányi, “A szeged-alsóvárosi,” 302; Harsányi, Szeged Alsóvárosi ferences, 14.
[24]  Szőke, “A szeged-alsóvárosi,” 890; Balázs Szőke, “Boltozat-rekonstrukciók és boltozatok számítógépes elemzése” [Vault-reconstructions and computer analysis of vaults], in Reneszánsz látványtár. Virtuális utazás a múltba, eds. Gergely Buzás et al. (Magyar Nemzeti Múzeum, 2009), 443-462, 449.
[25]  Jobbik and Krähling, “Real”.
[26]  Lukács, “A szeged-alsóvárosi,” 147.
[27]  Levárdy, Szeged, 10.
[28]  Since the nineteenth century, numerous scholars, including Eugène Viollet-le-Duc, have sought to elucidate the logic of Gothic constructions. However, ongoing debate surrounds much of the initial research, as the drawings from that era are frequently contrived and diverge significantly from the actual buildings.
[29]  E.g. at Wells Cathedral and York Minster (J. H. Harvey, “The Tracing Floor of York Minster,” in Studies in the History of Civil Engineering Volume 1: The Engineering of Medieval Cathedrals, ed. L. T. Courtenay (Ashgate Publishing, 1997), 81-86; David Wendland and Frédéric Degenève, “How to order fitting components for looping ribs: Design procedures for the stone members of complex late gothic vaults,” in Building Histories: The Proceedings of the Fourth Conference of the Construction History Society, eds. J.W.P. Campbell et al. (Queens’ College, 2017), 159-170, 164.
[30]  Arnold Pacey, Medieval architectural drawing, English craftsmen's methods and their later persistence (c.1200 - 1700) (Tempus Publishing, 2007), 62.
[31]  Carl F. Barnes, The Portfolio of Villard de Honnecourt. A New Critical Edition and Color Facsimile (Routledge, 2009), folio 20.
[32]  Robert Bork, The Geometry of Creation, Architectural Drawing and the Dynamics of Gothic Design (Ashgate, 2011)
[33]  This empiric visualisation method was used by among others e.g. Rave in 1955, as quoted by David Wendland, “Traditional vault construction without formwork: Masonry pattern and vault shape in the historical technical literature and in experimental studies,” International Journal of Architectural Heritage: Conservation, Analysis, and Restauration 1, no. 4 (2007): 311-365, 345, https://doi.org/10.1080/1558305070137 3803; Clemens Voigts, “Spätgotische figurierte Gewölbe in Bayern: Konstruktion und Herstellungsweise,” in Koldewey-Gesellschaft Veereinigung für Baugeschichte Forschung e.v. Bericht über die 48. Tagung für Ausgrabungswissenschaft und Bauforschung vom 28. Mai bis 1. Juni 2014 in Erfurt (Thelem, 2014): 245-252, 247; Clemens Voigts, “Vaults, centring, and formwork of the late gothic period in Southern Germany,” in History of Construction Cultures, eds. João Mascarenhas-Mateus and Ana Paula Pires (CRC Press, 2021), 78-83, 81.
[34]  This nature was generally accepted in the case of the nave vault of the church (as mentioned above), and in the case of the masonry ribbed vaults of South-Transylvania. E.g. Victor Roth, Geschichte der deutschen Baukunst in Siebenbürgen (Heitz&Mündel, 1905), 36.
[35]  Wendland, “Traditional,” 342.
[36]  Manfred Schuller, “Bautechnik,” in Der Dom zu Regensburg 7/3, eds. Achim Hubel and Manfred Schuller (Pustet, 2016), 434-503, 474.
[37]  Eugene Viollet-le-Duc, Dictionnaire raisonné de l’architecture française de XIe au XVIe siècle (Bance-Morel, 1854-68), fig. 58; Georg Gottlob Ungewitter, Lehrbuch der gotischen Konstruktionen. Neue bearbeitet von K. Mohrmann (Chr. Herm. Tauchnitz, 1901), 117.
[38]  Johann Claudius von Lassaulx, “Beschreibung des Verfahrens bei Anfertigung leichter Gewölbe über Kirchen und änliche Räumen,” Journal für die Baukunst 1 (1829): 317-30, 325.
[39]  Voigts, “Spätgotische,” 248; It is to be noted that Voigts proved that the combination of these methods in the same vault occasionally occurred as well (Voigts, “Spätgotische,” 250; Voigts, “Vaults,” 80-81).
[40]  Bartel Ranisch, Beschreibung aller Kirchengebäude der Stadt Dantzig… (Raths und Gymnasii Buchdruckern, 1695); Friedrich Hoffstadt, Gothisches ABC-Buch: Vorlegeblätter zum gothischen A-B-C-Buche… (Siegmund Schmerber, 1840); Otto Warth, “Die Konstruktionen in Stein. Band I,” in Allgemeine Baukonstruktionslehre mit besonderer Beziehung auf das Hochbauwesen…, ed. A. G. Breymann (J. M. Gebhardt, 1896); Ungewitter, “Lehrbuch”.
[41]  Eszter Jobbik and János Krähling, “Late Mediaeval Net Vault Construction Method Rediscovered by Geometric Analysis. A Case Study of the Fortified Church of Băgaciu (Bogeschdorf),” Brukenthal. Acta Musei 17, no. 2 (2022): 179-202; Eszter Jobbik and János Krähling, “The Geometric System of the Nave Vault of the Church on the Hill of Sighișoara,” Studia Universitatis Babeș-Bolyai. Historia Artium, 68 (2023): 7-43, https://doi.org/10.24193/subbhistart.2023.01.
[42]  Taking into account the building time of these systems, we look for construction methods, which require steps that are quite simple to mark out in real scale (parallel or perpendicular lines, circles, divisions into halves or thirds etc.) (see above).
[43]  E.g. the vertical dimension (height) of the junctions depends on their position on the plan view, if the latter is projected to a cylindrical surface – as presumed in the nineteenth-century literature (see above). However, the dimensions are independent if an underlying construction idea (e.g. construction in a quadrate net) can be identified both on the plan and the cross-section of the vault, as we have found in the case of the church of Nyírbátor (Jobbik and Krähling, “Real”).
[44]  Jobbik and Krähling, “Late”; Jobbik and Krähling, “The Geometric”.
[45]  Krisztina Fehér and Balázs Halmos, “Remarks on the Proportions and Dimensions Used in the Design of the Medieval Church of Zsámbék,” Periodica Polytechnica Architecture 50, no. 2 (2019): 110.
[46]  Ranisch, Beschreibung; Hoffstadt, Gotisches; Carl Anton Meckel, “Figurierte Gewölbe der deutschen Spätgotik,” Architectura: Jahrbuch für Geschichte der Baukunst 1 (1933): 107-121; Werner Müller, Grundlagen gotischer Bautechnik. Ars sine sciencia nihil (Deutscher Kunstverlag, 1990); Jos Tomlow, “Versuch einer (zeichnerischen) Rekonstruktion des Gewölbes im spätgotischen Kreutzgang des Klosters Hirschau,” in Hirsau St. Peter und Paul 1091-1991, ed. K. Schreiner (Kommissionsverlag Konrad Theiss, 1991).
[47]  E.g. Lassaulx in 1835, as quoted by David Wendland, Johann Claudius von Lassaulx, “Gewölbe >aus freier Hand< - Die Wiedererfindung der gotischen Architektur und die Entwicklung der technischen Literatur,” in Bautechnik des Historismus. Von den Theorien über gotische Konstruktionen bis zu den Baustellen des 19. Jahrhunderts, eds. Hassler Uta and Rauhut Christoph (Hirmer, 2012), 93-117, 106; David Wendland, “Zum Bau figurierte Gewölbe - eine Anleitung im Werkmeisterbuch des Rodrigo Gil de Hontagñon,” in Werkmeister der Spätgotik: Personen, Amt und Image, eds. Stefan Bürger et al. (Wissenschaftliche Buchgesellschaft, 2010), 244-272.
[48]  Jobbik and Krähling, “Late”; It is to be noted that measuring rib curvatures, especially in the case of shorter ribs, is a difficult task, as a small change in the arch height results in a great change in the value of the radius of the curvature. However, this applies not only to the measurements but to the initial fabrication of the ribs as well. Thus, if such a variation is acceptable as inaccuracy during the building process, it must be accepted as measurement inaccuracy as well.
[49]  Ranisch, Beschreibung; Elena Pliego, “The germ of the Prinzipalbogen concept in Bartel Ranisch,” Nexus Network Journal 19 (2017): 405-25, 407.
[50]  François Bucher, “Medieval architectural design methods, 800-1560,” Gesta 11, no.2 (1972): 37-51, 47.
[51]  Hoffstadt Gothisches, XIV.A/5; Ungewitter Lehrbuch, 67-68; Meckel, “Figurierte,” 108.
[52]  The church, according to Harsányi, was built using Transylvanian Fathoms (TF). 1 TF equals 1.752m according to him (Harsányi, “Szeged Alsóvárosi,” 13). We use this unit to describe the building; however, other units are also possible to have been used. 
[53]  Jobbik and Krähling, “Real”.
[54]  Harsányi, “A szeged-alsóvárosi,” 296.
[55]  It is worth mentioning that closer to the crown – where the section lines show a more visible curvature – the tangent of the vault surface gets closer to the horizontal direction. Thus, the newly built courses are less supported by the previous ones than in the case of those closer to the imposts. Having a more significant curvature means that the rows work as individual arches regarding the load-bearing characteristics. We find this a probable explanation for the phenomenon described.
[56]  Interpreting the measurements, it must be kept in mind that measuring the rib curvatures is a difficult task, as a small change in the arch height results in a great change in the radius of the curvature. However, this applies not only to the measurements but to the initial fabrication of the ribs as well. Thus, if such a variation is acceptable as inaccuracy during the building process, it must be accepted as measurement inaccuracy as well. Based on experiences of our formal works (Eszter Jobbik and János Krähling, “A Self-contained Stellar Vault Construction Method. The Vault of the Matthias Oratorio in the Inner City Parish Church of Budapest,” Periodica Polytechnica Architecture 54, no. 1 (2023): 73–85. https:// doi.org/10.3311/PPar.21454; Jobbik and Krähling, “Real”), and even the sacristy of the present church (see below), we found that even with these uncertainties, the ‘Prinzipalbogen’ can be detected. However, in this case, the lower surfaces of the ribs proved to be quite irregular, making the judgement of the builders’ original intentions even more difficult.
[57]  The detailed geometric description of the nave vault and the deductive reasoning for the reconstructed building methods are given in the article Jobbik and Krähling, “Real”. In this article we only cite the details necessary for understanding.
[58]  The detailed proof for this hypothesis can be found in Jobbik and Krähling, “Real”.
[59]  László Császár, “A Szeged-alsóvárosi ferences templom boltozatairól” [About the vaults of the Szeged-Alsóváros Franciscan church], in Détshy Mihály nyolcvanadik születésnapjára. Tanulmányok, eds. István Bardoly and Andrea Haris (Kulturális Örökségvédelmi Hivatal, 2002), 155-160, 159.
[60]  Szőke, “A szeged-alsóvárosi,” 879.
[61]  Szőke, “A szeged-alsóvárosi,” 887.
[62]  Nonetheless, this does not necessarily mean a different building period, it may have occurred due to the basic geometric differences of the outlines of the spaces that were vaulted.
[63]  Even though during our former research we found examples, where constructing the plan view was not the starting point of building a net vault, in those cases the plan views’ geometries were not orderly.
[64]  Harsányi, “A szeged-alsóvárosi,” 301.
[65]  Jobbik and Krähling, “Real”.
[66]  Jobbik and Krähling, “Real”.

Figure 1. The plan of the Franciscan Church of Szeged-Alsóváros. The Author’s work.

Figure 2abc. The vaults of the nave, apse and sacristy of the Franciscan Church of Szeged-Alsóváros. The Authors’ photos.

Figure 3. The vault of the town’s ground floor in the Franciscan Church of Szeged-Alsóváros. The Authors’ photo.

Figure 4. Theoretic method of ‘mapping’ a vault, presented on the example of the apse vault. The Authors’ work.

Figure 5. Theoretic outcomes of ‘mapping’ a vault. a: barrel vaults and decorative ribs; b: ‘real’ net vault, webs built with formworks; c: ‘real’ net vault, webs built without formwork. The Authors’ work.

Figure 6. Theoretic Cartesian coordinate system for the interpretation of the global geometry of the vault’s rib system, presented on the example of the apse vault. The Authors’ work.

Figure 7. Method 1: 90-degree grid applied to the plan of the apse. The grid is made of squares with side lengths of 0.5 Transylvanian Fathoms. The Authors’ work.

Figure 8. Method 2: Rotating the width of the apse to the southern wall, then rotating the diagonal made this way to the northern wall, and again, the new diagonal to the southern wall. The Authors’ work.

Figure 9. Method 3: 60-degree grid applied to the plan of the apse. The grid is made of triangles with side lengths of 5.33 metres or about 3 Transylvanian Fathoms. The Authors’ work.

Figure 10. Method 2 applied to the apse and nave. The Authors’ work.

Figure 11. Method 3 applied to the apse and nave. The Authors’ work.

Figure 12. Example of a highly distorted rib in the apse’s rib system, frontal view from the point cloud and photo. The Authors’ work.

Figure 13. ‘Mapping’ of the apse’s vault. The Authors’ work.

Figure 14ab. Probable construction methods of the plan of the apse’s rib system. a: construction with lines; b: construction with circles (‘x’ refers to the ‘x’ value defined in the text). The Authors’ work.

Figure 15abc. Reconstructed construction principles on the longitudinal and cross-sections of the apse’s rib system. a: longitudinal section looking to the north; b: cross-section looking to the east; c: longitudinal section looking to the south. The Authors’ work.

Figure 16. ‘Mapping’ of the sacristy’s vault. The Authors’ work.

Figure 17abcd. Reconstructed construction principles on the plan, longitudinal and cross-sections of the sacristy’s rib system. a: a: longitudinal section looking to the north; b: cross-section looking to the east; c: longitudinal section looking to the south; d: plan. The Authors’ work.

Figure 18ab. a: Situation of non-uniformly curved ribs on the sacristy’s plan. b: Situation of ribs with curvatures greatly deviating from the average value. The Authors’ work.

Figure 19. ‘Mapping’ of the vault on the tower’s ground floor. The Authors’ work.

Figure 20ab. Reconstructed construction principles of the groin system on the plan and cross-sections of the vault on the tower’s ground floor. a: cross-section of the vault looking to the north; b: plan of the vault. The Authors’ work.

Figure 21. 60-degree grid applied on the apse and nave, the main corners of these spaces marked.  The Authors’ work.

Figure 22. The lower hexagonal and higher roughly octagonal layout projected on each other. The west endpoints of the hexagonal walls are further west, and the east endpoints are further east than those of the octagonal walls. The Authors’ work.

Figure 23. The octagonal layout of the higher apse walls projected onto the grid of the lower walls. This layout shows no connection to the grid. The Authors’ work.

Figure 24abc. Theoretic reconstruction of the construction and building process of the apse’s and sacristy’s vaults, presented on the example of the sacristy’s vault. The Authors’ work.

Table 1. Errors of each corner from their respective grid points and from the nearest points of their constructing circles. The numbers marked with ‘*’ are the errors if the grid was flipped along the axis of the nave. The Authors’ work.