3-D Digital Modeling and Giuliano da Sangallo’s Designs for Santa Maria delle Carceri in

sabine frommel École Pratique des Hautes Études, Paris Sciences & Lettres marco gaiani Alma Mater Studiorum, Università di Bologna simone garagnani Alma Mater Studiorum, Università di Bologna

iuliano da Sangallo (ca. 1445–1516) was an archi- tect capable of managing the entire architectural G process, from conception through realization. The pilgrimage church of Santa Maria delle Carceri in Prato (be- gun 1485), a milestone in debates around Greek cross-shaped churches, reveals both Sangallo’s com- petence in building complex structural elements and his ad- herence to ’s theories (Figure 1). The complexity of Sangallo’sdesignprocessmakesitdifficultto understand many of the architectural issues he tackled in this project, the solutions proposed in his drawings, and the eventual translation of his drawings into brick and stone. In this article, we overcome these difficulties by using three- dimensional models to analyze the church and its design pro- cess (Figure 2). Typically, a digital 3-D model of a building results from the virtual assembly of many architectural com- Figure 1 Giuliano da Sangallo, Santa Maria delle Carceri, Prato, begun ’ ponents. When those individual elements are coded to iden- 1485, current front elevation (authors photo). tify their mutual structural relationships (for example, where columns bear the load of a lintel, or where a cupola distrib- Our decision to use 3-D modeling to examine Santa Maria utes its weight onto a drum), the 3-D model can be described delle Carceri was based not only on the increasing popularity 1 asasemanticdatamodel. and reliability of these digital tools but also on the fact that such modeling bears important similarities to the meth- ods used by Sangallo himself.2 Trained as a woodcutter, Journal of the Society of Architectural Historians 80, no. 1 (March 2021), 30–47, ISSN 0037-9808, electronic ISSN 2150-5926. © 2021 by the Society or legnaiolo, he was a skilled model maker. Three-dimensional of Architectural Historians. All rights reserved. Please direct all requests for models afforded him a powerful way to explain projects to permission to photocopy or reproduce article content through the University of customers and supply accurate instructions to craftsmen; he California Press’s Reprints and Permissions web page, https://www.ucpress .edu/journals/reprints-permissions, or via email: [email protected]. also used them to research new technical and formal solu- 3 DOI: https://doi.org/10.1525/jsah.2021.80.1.30. tions, making sketches to conceive 3-D shapes. An excellent

30 Figure 2 Digital semantic 3-D model of an area of the sanctuary of Santa Maria delle Carceri, Prato, with its 3-D graph (image by the authors).

’ illustration of Sangallo s process is provided by the case of Figure 3 Giuliano da Sangallo, Santa Maria delle Carceri, Prato, begun Santa Maria delle Carceri, where a series of 3-D models cre- 1485, current right-side elevation (authors’ photo). ated by the architect and mentioned in the archives reflect a number of changes requested by the patrons, the operai of the historians Piero Morselli and Gino Corti, the building’scon- church. struction history is well known, and we are able to determine For researchers attempting to answer specific reconstruc- theroleofdrawingsandmodelsintheRenaissancedesign ’ tion questions using incomplete data, today s digital models process with unusual precision.6 Archival documents also pro- offer distinct advantages over the sorts of concrete physical vide valuable information about the influence of the building’s models that Sangallo employed. For one thing, digital 3-D patrons on its design and construction. Architectural histori- models bypass problems of representational scale, as they are ans such as Giuseppe Marchini, Paul Davies, Riccardo Pac- built virtually at 1:1 scale. Conventional scale models allow ciani, and Claudio Cerretelli have examined many different for the study of problems and solutions, but the solutions of- aspects of the building and its history, including the institu- ten are not translatable to larger scales. 3-D models also offer tions involved, its urban setting, its construction and architec- a way to work around the incompleteness of drawings: be- tural details, and the geometric system underlying its design.7 cause of their nonscalar properties, they allow modern schol- In his 2016 study of centralized Renaissance churches, Jens ars to reconstruct historic buildings using the same rules the Niebaum considers the place of Santa Maria delle Carceri architects did (in this case, as described by Giuliano da San- within the typology of the pilgrimage church, linking it to gallo in his Taccuino senese, a sketchbook in the collections of religious symbolism and the revival of classical antiquity.8 4 the Biblioteca Comunale degli Intronati in Siena). Such stud- The current investigation builds on these previous studies by ies may provide scholars with opportunities to understand offering a precise analysis of Sangallo’s modular design system. more fully the processes and intentions of individual archi- Centralized structures with clear geometric patterns— tects. Parametric modeling allows for exceedingly specific circles, squares, octagons, polygons—fascinated Renaissance analysis, while digital systems facilitate the collection and ar- humanist patrons and architects. Soon after construction be- rangement of data necessary for describing the geometry of all gan at Santa Maria delle Carceri, , perhaps 5 elements in a work of architecture. In this article, we propose influenced by , developed a now-famous a new hypothesis regarding the design of Santa Maria delle series of drawings (Manuscript B held in the Institut de Carceri based on our research using 3-D modeling; we also France, Paris) showing many variations on the church’s cen- ’ offer new perspectives concerning Sangallo s design system. tralized plan.9 Centralized layouts, however, often failed to meet the needs of the liturgical functions of the Christian church, whose large congregations and complex, dynamic The Church of Santa Maria delle Carceri modes of worship required longitudinal naves. Monuments Santa Maria delle Carceri in Prato holds a significant place in such as the Florence Baptistery, the Basilica of Our Lady in the history of architectural typologies because of its centralized Loreto, and Alberti’s San Sebastiano in Mantua represented plan (Figures 3 and 4). Thanks to the work of architectural grandiose yet practical adaptations of the central plan to

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 31 Figure 4 Giuliano da Sangallo, Santa Maria delle Carceri, Prato, begun 1485, aerial view with the castle of Frederick II of Hohenstaufen in foreground (image from Microsoft Bing Maps, 2017, edited and customized by the authors).

Christian liturgical requirements.10 Functionally speaking, church’s placement. At this point, Lorenzo became person- the central plan was particularly well suited for oratories, ally involved in the project, which coincided with the con- sanctuaries, and mausoleums; notable examples include Filip- struction of his famous villa at Poggio a Caiano by his po Brunelleschi’s Santa Maria degli Angeli in Florence and architect Sangallo, who synthesized local tradition with clas- Giuliano da Sangallo’s Santa Maria dell’Umiltà in Pistoia. sical models. In September 1485, Lorenzo read chapters of Pilgrimage churches dedicated to the Virgin Mary featured Alberti’streatiseDe re aedificatoria and also ordered a survey centralized plans with some frequency. Since the early sev- or a model of Alberti’s centralized Greek cross design for San enth century, the Pantheon in Rome had been dedicated to Sebastiano to be delivered personally to Lorenzo in Florence Santa Maria della Rotonda, or Santa Maria ad Martyres, be- by Luca Fancelli, the architect charged with the execution of ginning a tradition of centralized buildings used to express Alberti’s buildings in Mantua.16 devotion to the Virgin Mary; later examples included Brunel- However, it seems another Tuscan pilgrimage church, the leschi’s Santa Maria degli Angeli in Florence and Gian Lo- Madonna della Pietà at Bibbona, where a similar apparition renzo Bernini’s Santa Maria Assunta in Ariccia.11 In Prato, of the Virgin occurred some years earlier, inspired the cen- the miraculous apparition of the Virgin Mary to eight-year- tralized plan selected for Prato.17 Here, Vittorio Ghiberti, the old Jacopino d’Antonio in July 1484 led to the inauguration son of the famous sculptor Lorenzo Ghiberti, also con- of Santa Maria delle Carceri.12 structed a church according to a Greek cross plan, but on a One year later, in 1485, the municipal authorities of Prato much smaller scale. This form was in fact more suitable for chose a design for the church by the Florentine architect expressing the hierarchy between the center and the subordi- Giuliano da Maiano.13 As Paul Davies has noted, the size and nated spaces and, in the case of Prato, for affirming the signif- shape of da Maiano’s proposed design, recalling the Florence icance of the church as both a religious and a civic symbol. Baptistery, cannot be reconciled with the existing building’s The dimensions of Santa Maria delle Carceri, with a central footprint.14 In addition, this design would have transgressed square measuring 20 braccia per side (11.72 meters) and arms the restriction imposed by the Dieci di Balìa, the Florentine half that length (10 braccia, or 5.84 meters), try to conciliate magistracy in charge of military affairs, stipulating that the with the dimensions of the nearby fortress in the surrounding new church had to stand at a distance of at least 24 braccia urban landscape.18 Sangallo’s use of clear geometric forms, from the nearby castle of Frederick II of Hohenstaufen.15 In placing a dome above a cube, not only emphasized the mid- any event, da Maiano’s proposal reveals the important evolu- point of the structure but also contributed to its urban signi- tion of such typologies with its inclusion of a large portico ficance. Like the dome of Brunelleschi’s Sacrestia Vecchia, surrounding the church, where pilgrims could gather and the dome of Santa Maria delle Carceri is covered by a sloping have indirect access to liturgical functions through the win- roof and thus not visible on the exterior. The design of the dows. Lorenzo de’ Medici, who followed the project closely, Sacrestia Vecchia also evidently inspired Sangallo’s decorative was not convinced by this choice and halted construction pilaster order on the interior. soon after the foundations were erected. Prato was under the When Sangallo left the building site in 1499, the façades control of the Republic of Florence at the time, and therefore were not completed, and the upper exterior order was the Dieci di Balìa strongly supervised the dimensions of the completely missing. The construction of the upper section of

32 JSAH | 80.1 | MARCH 2021 the southwest façade, including its Ionic pilasters and pedi- ment, occurred in the period 1884–87. As we will see, this nineteenth-century design is not entirely consistent with Sangallo’s design principles.

Analyzing Santa Maria delle Carceri Using New Technology The only authentic graphic source regarding Santa Maria delle Carceri, probably from Sangallo’s own hand, is a plan in the Taccuino senese (Figure 5). The parchment sheet represents the building in different forms and thus is of an uncertain date, but details like the niches in the inner walls, the apse, and the pilasters flanking the doorways, later eliminated by the architect, suggest it predates the construction of the church. The freestanding volume reflects an idealized design that ignores the preexisting prisons to the north. Neverthe- less, the plan approximates the final solution in which San- gallo accommodated local restrictions (preserving the existing prisons, one of which contained a miraculous painted image) while maintaining the distance from the nearby castle as required by the Dieci di Balìa.19 On the other hand, on the upper part of the same page in the Taccuino senese there is also a plan of the Chapel of Sant’Aquilino at the Early Christian Basilica of San Lorenzo in Milan, believed to have been drawn by Sangallo during his stay in Milan in 1492, suggest- ing that the plan of Santa Maria delle Carceri can be dated to the same year. We know nothing about Sangallo’s Wander- Figure 5 Giuliano da Sangallo, plan of Santa Maria delle Carceri, Prato, jahre, and he may have previously visited the capital of date unknown (Taccuino senese, fol. 19r, ms. S. IV. 8, Biblioteca Lombardy, where his Florentine colleagues Leonardo da Comunale degli Intronati, Siena). Vinci and Bramante conceived and realized innovative archi- tectural projects. However, it is not easy to understand why Sangallo, or a later copyist, would have produced an obsolete undertaking this survey were to analyze the relationships be- design, given that a new version of the plan was already under tween the existing monument and Sangallo’s plan, to better construction. Did the architect wish to document ideas he understand the drawing’s graphic construction, and to recon- had developed before, either for his own use or for his struct possible solutions and variants beyond those indicated bottega? Surprisingly, this may be the case, given that some in the drawing itself. Our study does not address problems re- options (i.e., the rhythm and the harmony of the architectural lated to site limitations at Santa Maria delle Carceri, such as order of pilasters) in the actual building are more convincing the preexisting fortress and prisons to the north (discussed by and better reflect the evolution of Sangallo’s architectural Cerretelli), or Sangallo’s sources for the church’s architec- language. tural order and decorative elements (investigation of these The verso of the same sheet, which includes a plan of the would require further examination of Sangallo’sdrawingcor- , likewise reveals details of an earlier pus, including the Codex Barberini and the Taccuino senese).22 project.20 Unfortunately, we are still unable to determine a The centralized plan found in the Taccuino senese, precise chronology, as technical analysis of the parchment conceived according to braccia fiorentine, is inscribed within sheet has not resolved the dating issues. Even if the drawing a square like the built pilgrimage church itself, following in the Taccuino senese cannot be considered an original proportions derived from Alberti’s De re aedificatoria.23 scheme, some details shed light on other ideas formulated by Consequently, the arms, spanned by barrel vaults, measure the architect early in the design process. By comparing this half the width of the square in the center crowned by the drawing with a recent survey of the pilgrimage church pro- cupola. The wall mass, drawn at a dimension insufficient to duced using laser technology, we are able to reconstruct and support the weight of the drum and the cupola, was later verify those preliminary ideas.21 Our primary purposes in thickened and reinforced.

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 33 Figure 6 Two hypothetical reconstructions of the sanctuary of Santa Maria delle Carceri, Prato: the regular Greek cross plan (left) and the same plan with the addition of a segmental apse (right) (images by the authors).

The drawing shows two schemes. The first is a regular The reconstruction proposed here is intended to enable a Greek cross with four identical façades (Figure 6). The sec- fuller understanding of these early phases of the design, in- ond includes a semicircular apse at the rear of the building. As cluding the ideas of Lorenzo de’ Medici, who probably de- Davies has demonstrated, the proposed apse interfered with sired a coherent organism based on Alberti’s canon of the ruins of the prison and the miracle-working image lo- harmonious proportions and a perfect structural correspon- cated there.24 Given that Prato’s civic council required the dence between the inner and exterior orders.27 We also dis- preservation of both these preexisting elements, it is unlikely cuss below how the digital model clarifies Sangallo’suseof this scheme would have been accepted. a modular system and his attention to architectural details The use of semicircular niches carved into the thickness such as the design of the internal entablature, with its three of the walls recalled ancient Roman architectural motifs.25 constituent components each measuring 1 braccio in height. Sangallo also employed niches in his earlier design for Pa- Such a study enables us to better understand the design pro- lazzo Scala in Florence, but they were of a shallower profile cess behind , where most projects than the semicircular recessed niches of the Taccuino senese corresponded to ideal proportional systems, although often drawing. The façade design shown in the sketch differs from compromised by physical and functional exigencies. The the actual building, with two additional pilasters placed on ei- model presented here can also help us to reconstruct the ar- ther side of the door at the center of the three main façades, chitect’s design methodology and the construction practice. both inside and out. The portals also do not appear as they Masons often relied on local building traditions, thereby in- were actually executed.26 These details in the drawing intro- troducing further variations to architects’ designs. However, duced a greater vertical emphasis that would have signifi- the virtual reconstruction of Santa Maria delle Carceri reveals cantly modified the exterior appearance of the church. As an astonishing correspondence with the Taccuino senese draw- executed, the façade surface extends unobstructed between ing, indicating that Sangallo managed to maintain excep- the reinforced corners, suggesting a more mature design tional control over the construction process. For this solution. reason, the structure holds an outstanding place in the history The reconstruction of the upper order of the façades of late quattrocento architecture. poses further challenges, as here we have absolutely no indi- Thanks to the level of detail afforded by the virtual model, cation of Sangallo’s intentions. According to both Renais- we can also gain a better understanding of the gradual devel- sance principles and Vitruvian rules, which require a opment of solutions and alternatives proposed for Santa Ma- structural relationship between roof and gable, the pediment ria delle Carceri. Some details, like the design of the apse as executed is too high. It is unclear whether Sangallo meant windows and the order of the exterior upper story, must re- to use Ionic pilasters or whether he intended to adorn the main hypothetical. In such cases the virtual model integrates second level with a more abstract attic order. Regardless, the contemporary architectural motifs to generate a coherent de- virtual reconstruction reveals the symmetry and homogeneity sign. The sophistication of this complex new technology of the architectural framework developed by Sangallo and his opens up new areas for research and has the potential to adviser Lorenzo de’ Medici to introduce pilgrims and be- deepen our formal and technical understanding of Renais- lievers to the miracle. sance architecture.

34 JSAH | 80.1 | MARCH 2021 3-D Model Construction and Data Analysis adjustments are automatic, so that any given modification is To d a y ’s architects and architectural historians are familiar reflected across a model in real time. Our process involved four ideal steps: (1) BIM-based, with the use of 3-D models as a means to reconstruct missing knowledge-based modeling; (2) data capture and as-built elements in existing buildings or to construct unbuilt struc- model construction; (3) ideal and as-built model integration; tures virtually. Until now, practitioners and scholars have and (4) multidimensional analysis (Figure 7). Through largely used this technology, which has been in development knowledge-based modeling, the geometric relationships be- for more than twenty years, to translate measurements into tween architectural components specified in architectural photorealistic images, either to verify proposed design solu- treatises and other theoretical sources can be integrated into tions or to visualize the overall appearance of particular build- a BIM system. The resulting BIM provides a template that ings. Used for these purposes, even if 3-D renderings offer collects and orders surveyed data. Unlike traditional com- new ways to animate or quantify architectural spaces, they do puter-aided design, or CAD, systems, which require intensive not provide much information beyond that already available drawing, BIM manipulates the existing survey data by con- in 2-D drawings. trolling parameters. Despite many recent experiments, few 3-D models have The data-capture approach integrates both range-based been created using the appropriate semantics for the archi- and image-based modeling. Single capture techniques do tecture under analysis. While the association of semantics and not provide satisfactory results for all situations (e.g., when architectural shapes may facilitate a building’sexaminationas there is a need for high geometric accuracy, portability, au- a cognitive system, the potential mismatch between seman- tomation, photorealism, low cost, flexibility, or efficiency). tics and these same architectural shapes may also make it By combining image and range data, the BIM system can more difficult to distinguish the architect’s original intentions fully exploit the intrinsic potential of both approaches. for the project from later modifications.28 Terrestrial laser scanning, or TLS, can be integrated with To investigate Sangallo’s design process for Santa Maria automatic photogrammetry to obtain the extremely accu- delle Carceri, we employed a method that involved generat- rate images essential to 3-D modeling (Figure 8).31 Photo- ing a digital representation of the building as it currently grammetric-based 3-D model construction, a completely stands and then superimposing deficiencies, irregularities, automated preprocessing procedure, provides a robust modifications, additions, deletions, and restorations as these level of image matching that uses both raw image files and occurred over time. We also compared what we found with color photographs (Figure 9). ’ data generated through critical investigation of Sangallo s Following the integration of the ideal model generated drawings as well as other Sangallo buildings, buildings by from the parametric library and the as-built model obtained ’ Sangallo s contemporaries, and surviving visual and textual from the captured data, any deviations are evaluated to deter- ’ references, including Alberti s De re aedificatoria. One of our mine if feature extraction from point clouds may improve the key goals was to determine whether the Taccuino senese plan accuracy of the as-built BIM. Full automation from point and its embedded proportional system carried into the de- clouds to the as-built BIM is not yet possible using existing ’ sign s subsequent development. software, but in most situations it is not necessary to docu- The technique we used relies on a specific semantic 3-D- ment all the as-built data, such as irregular shapes, with BIM. based information system to build a knowledge framework The process, which we applied to analysis of the interior en- that can organize surveyed data; verify measurements, pro- tablature of Santa Maria delle Carceri, comprises the steps portions, shapes, and constructive solutions; and develop described below (Figure 10). photorealistic reconstructions to test alternative proposals. Adjustment of BIM objects to point clouds: Knowledge-based Drawing upon recent digital innovations, the workflow uses modeling provides a parametric template that can be inte- both building information modeling, or BIM, and knowl- grated with data sourced from the as-built condition. The edge-based modeling to translate semantic compositions and BIM building elements from the parametric libraries are 29 their relationships into 3-D models. We developed specific adapted to the point clouds. If the building element family al- semantics based on elements drawn from two key Sangallo ready exists in an object library, a new type is created through sources: the Codex Barberini and the Taccuino senese.30 the adaptation of the parameters of the existing family to the Developing these 3-D models involved translating be- point clouds; if not, a new building element family is created tween two systems of knowledge. Sangallo’s descriptions of and added to the parametric library for future use. In practice, tangible elements can be used to generate BIM components the average dimensions of the BIM elements are obtained and parametric models using constraints based on Sangallo’s from the captured 3-D data. Data generated by the compari- module. Instead of drawing specific shapes, we can replace di- son of these measurements in turn allow for the parameteri- mensions with variables and set formulas. All dimension zation of the object based on relationships.

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 35 Figure 7 Four-step sequence of the semantic 3-D- based information system used to examine Santa Maria delle Carceri, Prato (images by the authors).

Figure 8 Data capture using terrestrial laser scanner: Santa Maria delle Carceri, Prato, plan view and dense point cloud of the front elevation (images by the authors).

Evaluation of deviation: Existing building components are prone to irregularities because of damage, deterioration, and deformation over the course of their life cycles. Although the BIM objects are mapped on the captured point clouds, the graphic primitives in BIM may not be sufficiently precise when the deviation reaches a certain threshold. Consequently, we used a tool to automatically evaluate such deviations and identify objects that failed to meet the demanded accuracy. Such objects were instead modeled using the extracted fea- tures of captured point clouds. Figure 9 Data capture using photogrammetry: Santa Maria delle Carceri, Feature extraction: Various approaches may be used to to- Prato, Doric base (images by the authors). pologically bridge the gap between point clouds and BIM. For example, cross-sectioning is an effective method for ex- tracting features from point clouds to BIM, since the overall and saved in BIM as reusable profile families nested in other design and proportions of classical architecture are closely re- families. lated to the shapes and proportions of individual moldings. Finally, multidimensional analysis facilitates the extraction Most of Sangallo’s architectural elements can be modeled of many insights from produced outputs and simulations. through the sweeping of certain profiles along straight lines BIM-based 3-D modeling allows multiple outputs that can or curves. This is not merely a coincidence; rather, it reflects exploit multidimensional and multisensory analysis techni- the Renaissance craftsman’s technique of using a template to ques, including not only simple renderings and computer make a profile on a block of stone before cutting away the ex- graphic photorealistic animations but also physical models cess. Cross sections can be transformed into 2-D drawings generated using 3-D printing technology and virtual-reality

36 JSAH | 80.1 | MARCH 2021 Figure 11 Different levels of interpretation/uncertainty regarding reconstruction of Santa Maria delle Carceri, Prato, visualized through a pseudo color code (image by the authors).

Figure 10 Ideal and as-built model integration: Santa Maria delle Carceri, Prato, interior entablature (images by Carlo Bergonzini, edited and modified by the authors). visualizations that make use of perceptive cues as well as false color visualizations highlighting those aspects that might Figure 12 Multidimensional analysis using 3-D models: assessing otherwise escape notice. The aim is to show not just the com- construction solutions at Santa Maria delle Carceri, Prato, through digital plete interpretational process but also the reliability of its fabrication (image by the authors). different components. The solution involves eight levels of reconstruction, char- buildings belonging to the same typology; level 6 (LV6) refers acterized by a progressively increasing uncertainty visualized to architectural elements sketched by other contemporary ar- through a pseudo color code that divides the rendered objects chitects; and level 7 (LV7) includes conjectural elements into a small number of color bands corresponding to a hierar- without specific references. chy based on level of interpretation or uncertainty Finally, 3-D models generated using 3-D printing techni- (Figure 11). Thus level 0 (LV0) includes elements from the ques allow for further multidimensional analysis (Figure 12). as-built church; level 1 (LV1) extends actual details of Santa The process involves qualitative and quantitative methods for Maria delle Carceri to other parts of the building; level 2 evaluating and testing the design process and the resulting (LV2) includes building portions inferred from the Taccuino model. In addition, 3-D parametric descriptions and rules senese drawings; level 3 (LV3) represents elements following concerning materials and material assembly provide a new other details from the Taccuino senese sketches; level 4 (LV4) construction grammar. These construction rules do not just corresponds to solutions found in other Sangallo works; level determine the visual appearance of building components, 5 (LV5) describes elements inspired by other contemporary they also define the components’ assemblage in 3-D space,

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 37 providing further structural and functional information about measurement scale. With this as our unit of measurement, we the building. analyzed the ground plan of Santa Maria delle Carceri and found that it reveals interesting details.33 To b e g i n , t h e t o p right side of the small sheet of brown-inked paper features a Reconstructing Santa Maria delle Carceri set of reference points, subdivided into twenty parts. As the in- As noted, our investigation of Sangallo’s design for Santa ternal square of the church measures approximately 20 braccia Maria delle Carceri, including both built and unbuilt compo- fiorentine (11.72 meters), it follows that each subdivision equals nents, involved a multiscale, dual-source process based on an precisely 1 braccio. A further linear division generates five exact analysis of the Taccuino senese drawings and their relationship submultiples, each with a distance equal to 1 braccio.Thismet- to the church as it stands today, as well as a new, accurate sur- ric scale allowed us to understand the relationships governing vey of the existing structure. Sangallo’s various architectural components. Transferring these reference lines to the Sangallo plan revealed how he or- dered and proportioned the wall profiles and interior spaces Investigating the Taccuino senese for BIM-Based, (Figure 14). Knowledge-Based Modeling Sangallo’s design highlights simple layouts, privileging We began our investigation with an analysis of Sangallo’s proportional relationships between squares and circles of note-taking process as well as an analysis of the measurements 1:1 and 1:2. Such modules govern every aspect of the plan. By used to generate the Taccuino plan. Sangallo’s notebook in- taking this square as a base module of M (M = 5,836 meters, cludes numerous combinations of textual and numerical sym- for which the general side is equal to 10 braccia fiorentine), we bols, following architectural conventions still used today, with can trace all the measurements back to the module. In plan, dimensions presented as text alongside annotation lines to the diameter of the dome is identical to the width of the lat- generate a measurable communicative system. Starting with eral wings and double their depth. (As previously noted, the Sangallo’s most legible annotations, we first verified these boundary wall thickness is roughly a quarter of M, or 1.459 symbols against their corresponding lengths in the real do- meters.) The proportions we discovered inside the pilgrim- main and then used them to check the other dimensions lack- age church also regulate its exterior; thus, the lateral façades ing corresponding measurements in Sangallo’sdrawings.We of the wings follow the M modularity, distinguished by a were able to do this by identifying the largest element with a 1/4M separation from the frontal façade (Figure 15). simple symbol, assigning it a value from the measured survey We created a semantic data model built as a cognitive BIM of the existing church in Prato, and then scaling the drawing system using braccia, soldi,anddenari as units. This in turn al- using computer-aided drafting software (given that at this lowed us to systematically verify the local and global propor- stage the units of measurement were unknown, we initially tions of the building. adopted a relative scale). Finally, we measured and checked Constructing an As-Built Model to Compare with Existing the values of other annotations against the measured real Surveys and the Taccuino senese value, while acknowledging the inevitable variations and Surveying the actual building, both inside and out, repre- inaccuracies resulting from a hand-drawn rendering as sented a critical phase of the project, as it allowed us to com- well from a sheet that was perhaps not perfectly planar pare elements inferred from the general plan view in the (Figure 13). Taccuino senese with the building’s constructed dimensions. Comparison of the measurements of the drawings in the Further comparison with existing drawings also generated Taccuino to the built architectural spaces confirmed that as a many novel insights. unit of measurement Sangallo employed the braccio fiorentino Tocomplete the survey of the building, inside and out, we 32 (one braccio =0.5836meters). Further study of the design conducted twenty-six laser scans. Using Faro Scene 5.0 soft- details revealed that he also made frequent use of submulti- ware, we created a general reference point cloud relating to ples of the soldo (0.0292 meters) and the denaro (0.0024 Santa Maria delle Carceri, processing color raw files collected meters). with a Focus3D Cam2 phase shift laser scanner (this device Assuming that Sangallo followed this dimensioning features a 3-D point accuracy of up to 2 millimeters; working scheme, we tested eight order elements represented on folio distance = 0.6–150.0 meters). The ground sample distance, or 12v of the Taccuino and found deviations of, at most, 13 percent GSD (the true distance between the sampled points), could (in one case). Most of the verified comparisons stood within vary between 4 and 15 millimeters, depending on whether the threshold of 8 percent, thus confirming our hypothesis the captured data referred to the whole church or only to cer- that Sangallo used the braccio fiorentino as a standard unit of tain parts of the building. measure. Following this method, we assimilated the individual The photogrammetric 3-D model was assembled from design components of the Taccuino senese to generate a real 230 images taken with a Canon EOS 1000D SLR camera.34

38 JSAH | 80.1 | MARCH 2021 Figure 13 Santa Maria delle Carceri, Prato, analysis of measurements using folio 12v of the Taccuino senese (ms. S. IV. 8, Biblioteca Comunale degli Intronati, Siena).

Figure 14 Santa Maria delle Carceri, Prato, analysis of plan proportions using folio 19r of the Taccuino senese (ms. S. IV. 8, Biblioteca Comunale degli Intronati, Siena).

Selected images were characterized by their distance from measurements for the width of the church varied by only an object included at a range of 4 to 16 meters, taken with a a few centimeters. Major deviations emerged, however, 35-millimeter focal length. The GSD could vary between when we compared vertical sections, such as the overall 0.5 and 2.0 millimeters, allowing for a more accurate docu- height of the building (the sphere of the lantern is, in ef- mentation of architectural details than that offered by the la- fect, lower by approximately 0.40 meters, while the vault’s ser scanner survey. base is higher by approximately 0.50 meters). This is a par- This process enabled us to generate a faithful measured ticularly important point, since our survey revealed some reproduction of the existing structure. By analyzing this evi- key differences regarding certain features recorded in dence, we could better evaluate the potential dissimilarities 1982. As demonstrated by our recent laser scans, the dome from the drawing, mainly regarding the building’supper and the lateral vault present sections with different pro- parts. Measurements registered within an accuracy of 1 cen- files. Neither of the profiles is circular, as was indicated in timeter for the entire building, reaching submillimeter accu- the 1982 survey. Instead, the profiles are more elongated racy for architectural details, ensuring consistency in further ovals (Figure 16). multidimensional analysis. Next, we compared this survey to the measured draw- ings by Morselli and Corti, who performed a manual survey Integrating Ideal and As-Built Models based on total station, or TS, reference data in 1982.35 We compared and superimposed point clouds and elements While our survey resembled Morselli and Corti’sdraw- collected during the survey onto the plan from the Taccuino ings, especially in the lower parts of the building, there senese to verify and adjust the proportions of individual ele- were discrepancies in height estimates, especially concern- ments and their integration with each other. In this way we ing the positioning of the cornice of the dome’sexterior.In produced an ideal parametric 3-D model. The later survey of plan, these differences were minimal: for example, our the existing building proved our findings to be accurate (for

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 39 Figure 15 Santa Maria delle Carceri, Prato, analysis of elevation proportions derived from the integration of ideal and measured 3-D models (image by the authors). example, the surrounding pavement from which the church rises is generated by a shape mostly equal to one-half of the base module M). We used the same module and method to verify that San- gallo adopted the same proportions for the exterior as for the interior. The architect seemed to favor similar dimensions for the vertical development of the church: the height between the floor and the entablature is equal to two base modules, or two M, the distance between the springer and the top of the barrel vault is equal to one M, the dome is one M high, and Figure 16 Santa Maria delle Carceri, Prato, plan and elevation generated the walkway is half an M (see Figure 15). by 3-D survey superimposed on Morselli and Corti’s 2-D survey of 1982 Our analysis verified that the harmonious proportions of (Piero Morselli and Gino Corti, La chiesa di Santa Maria delle Carceri in the interior correspond to those of the external preserved fa- Prato: Contributo di Lorenzo de’ Medici e Giuliano da Sangallo alla 36 çade, as observed by Maurizio Filiaggi. The height of the progettazione [Florence: EDAM, 1982]; images by the authors). entablature’s upper ends, both internal and external, which corresponds to two M, confirms a logical consistency be- tween the interior and the exterior. circular windows, above. This system determined the posi- In addition to identifying the modular proportions linking tioning and heights of the two central entablatures and the interior to exterior, our analysis verified that Sangallo made various heights of the portal elements in the façade. use of the golden ratio to locate various elements, such as the The entire design logic of the building is driven by the base of the drum and the upper limits of the twelve oculi, or proportions of the square pilasters placed at its corners, each

40 JSAH | 80.1 | MARCH 2021 measuring 1.5 braccia fiorentine wide and 16 braccia high (or 1:10.333). These proportions are more elongated than the canonical 1:7 or 1:8 ratio of the Doric order. Sangallo’sdraw- ing on folio 31v of the Taccuino senese explains this customized grammar, subdividing columns into twenty or thirteen parts (Figure 17). This logic is also evident in the actual building. For example, the height of each square pilaster’s base is one-twentieth of the column’s height, while the capitals are one-thirtieth the height of their columns (measured from the top of the column to the top of the collar). The two central bands and the various heights of the portal elements also con- form to this principle. All three elements of the entablature— architrave, frieze, and cornice—are the same height, each precisely 1 braccio (Figure 18). A section generated from our point cloud facilitated com- parison between internal and external pilaster shafts, even if overall dimensions reveal substantial differences. Sangallo ad- hered to the principle of dividing the height of each pilaster into twenty parts, as a rule that determined both the height of its base (1/20) and the height of its capital (2/20). The heights of the pedestals are less consistent: the pedestal bases in the interior are lower than those on the exterior. While the capital and overall entablature height reflect a clear correspondence between interior and exterior, the various elements do not always correspond exactly. For instance, while both the inner and the outer entablature are equally divided into three parts, the inner entablature extends to a slightly greater height to support the spring line of the barrel vaults. Overall, the flexible framework of the braccio fiorentino fa- Figure 17 Giuliano da Sangallo, column proportions, date unknown cilitated Sangallo’s dimensioning of partitions and placement (Taccuino senese, fol. 31v, ms. S. IV. 8, Biblioteca Comunale degli of decorative features. Throughout the project, from the gen- Intronati, Siena). eral scheme to the design of individual elements, Sangallo employed a clear and consistent design methodology.37

Hypothetical Reconstruction Derived from Proportions In our reconstruction of the existing, incomplete church, we relied on the Taccuino senese plan to complete the upper portions of the exterior and to analyze interior variations. We created a semantic data model that retained original elements and removed subsequent alterations and additions, such as the internal balustrade in front of the altar and the aediculae adjacent to the nave. Comparing the drawings in the Taccuino senese to the actual structure helps to illuminate many subsequent modifications. Figure 18 Santa Maria delle Carceri, Prato, entablature proportions as generated through the integration of ideal and measured 3-D models The proportions and measurements that we documented in (image by the authors). Prato suggested some hypothetical answers to questions re- garding Sangallo’s intentions for the façades and the interior. For example, as noted earlier, Sangallo’splanintheTaccuino Our digital models for Santa Maria delle Carceri addressed shows additional external pilasters flanking the main portals the exterior and interior separately. For the outer elements, and a semicircular apse on the northern façade. we first retraced the plan of the Taccuino senese as a vector

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 41 digital drawing. We then prepared a preliminary boundary by extruding walls from the vector drawing, integrating distances and alignments. We modeled the first architectural order in elevation, taking into account the previously conducted survey (to ensure consistency with the heights of the actual building), and then applied moldings, profiles, and decorations to repli- cate the exterior surface ornament, including the double pilasters placed at the corners. The dimensions of the pilasters flanking the portals as shown in the Ta c c u i n o duplicate those of the existing pilasters at the corners, while their spacing corre- sponds to the original drawing. In fact, in the Taccuino senese,Sangalloprovidedacom- parison of architectural orders, following a well-defined proportional scale. Those elements in turn offered a cue for the second architectural order. Drawing upon the evi- dence from the survey, we proposed a hypothetical second order, modifying its proportions to fit with the existing Doric composition.38 The reconstructed pediments follow the Vitruvian recom- mendation that these must coincide with the height of the roof.39 Our design took as an example the tympanum San- gallo placed above the portico at the Villa Medici at Poggio a Caiano (despite its uncertain dating).40 The existing façade provided the model for the remaining missing façades, consistent with the symmetry of the central- ized plan. The extruded drum corresponds to the hatched tracing in the Taccuino drawing, from the elevation recorded in the survey to the circular vault with its twelve oculi. Finally, the design of the lantern corresponds to its actual form as Figure 19 Santa Maria delle Carceri, Prato, development of the built, as confirmed by a photogrammetry-based survey we semicircular apse solution for the northern façade (derived from Taccuino conducted from the adjacent fortress of Frederick II. senese, fol. 19r, ms. S. IV. 8, Biblioteca Comunale degli Intronati, Siena; images by the authors). As Sangallo provided an alternative solution in the plan in the Taccuino senese, we also added a semicircular apse to the northern façade of the digital model. In accordance with San- Other changes included modification of the interior deco- gallo’s traced perimeter, we proposed three hypothetical rations above the main portals in accordance with the new di- openings to illuminate the apse, corresponding to the existing mensions and extension of the existing white-and-blue proportional system. Both the design of the openings and the decorative frieze on the entablature by Andrea della Robbia external order replicate those elsewhere on the church, main- into the new circular apse (Figure 21). All later additions were taining a consistent architectural language. Pilasters subdi- removed (the balustrade in front of the altar, the two aedicu- vide the exterior of the apse into three identical bays, lae adjacent to the nave, and floor finishes). The classicizing corresponding to the pilasters ornamenting the exterior walls semicircular niches shown in the Ta cc u i n o plan correspond to as shown in the Taccuino plan (Figure 19). those on the interior walls, with a governing radius of 1 braccio As for the interior, we found that the wall profiles and fiorentino. The head of each semicircular niche rests on a structural grids of the plan shown in the Ta cc u i n o also dove- stringcourse that runs behind the main order of the interior tailed with the design of the existing church. Our detailed walls, following the design of the Cappella Pazzi in Florence. survey allowed us to accurately model the existing pilasters, This is perhaps one of our most approximate solutions.41 the supporting barrel vaults, and the dome. The dimensions The vertical proportions of the niches conform to the pro- of the pilasters at the corners correspond to those of the exist- portions of the church’s upper windows, their framing corre- ing design, documented using an accurate photogrammetric sponds to the framing of the entrance portal, and their modeling process. These same pilasters, added later by San- heights were documented by the survey. gallo, provided the prototype for our new set of pilasters In terms of procedure, the parametric approach ensures flanking the portals (Figure 20). that the proportions of the model correspond to Sangallo’s

42 JSAH | 80.1 | MARCH 2021 Figure 20 Santa Maria delle Carceri, Prato, pilasters flanking entrance portals (derived from Taccuino senese, fol. 19r, ms. S. IV. 8, Biblioteca Comunale degli Intronati, Siena; image by the authors). design logic, as revealed by both the drawing in the Taccuino decorations and spaces. The successful application of this senese and the existing building. At the same time, this ap- technology demonstrates its value for these reconstructive proach provides new evidence that allows us to update previ- investigations. ous solutions, and it also facilitates continuous editing and We extracted elements of Sangallo’s architectural gram- adaptation of new updates. We assembled these digital ob- mar from details sketched in the Taccuino, generating a library jects using Autodesk Revit, a BIM software technology that of parametric elements to support the final digital assembly. expresses the intrinsic parametric nature of architectural Given the many possible variables that could have affected components. the design for the church elevations, we tested several As noted, Sangallo’s measurements provided us with di- hypotheses before making a final selection of the most mensional rules that then guided the behavior of our param- plausible elements. Again, architectural proportions drove eters: braccia fiorentine, soldi,anddenari offered numerical the decisions governing our digital model, as evident, for constraints that could be adjusted until their proportions, example, in interior elevations featuring semicircular niches driven by parametric geometry, replicated those of the actual (see Figure 21).

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 43 Figure 21 Santa Maria delle Carceri, Prato, development of semicircular niche arrangements for interior façades (derived from Taccuino senese, fol. 19r, ms. S. IV. 8, Biblioteca Comunale degli Intronati, Siena; images by the authors).

Figure 22 Santa Maria delle Carceri, Prato, photorealistic renderings of the reconstructed interior (images by the authors). Figure 23 Santa Maria delle Carceri, Prato, photorealistic renderings of the reconstructed exterior (images by the authors).

The use of BIM technology made it possible for us to test scanning technology in the field of architectural heritage and ar- different hypotheses about the original design of Santa Maria chaeology and has also developed photogrammetry-related and delle Carceri as well as to gain new knowledge about Sangallo’s digital color-related technologies. [email protected] design process. Our synthetic global reconstruction integrated Simone Garagnani, PhD, is an Italian engineer and scholar the proportions used by Sangallo in his drawings and writings whose research focuses on architectural representation, build- ing information modeling, and virtual representation of historic with evidence from the built form of the church itself, generat- buildings for cultural heritage and archaeological studies. simone ing several models that shed new light on the connections [email protected] between the Taccuino senese plan and the existing structure. The complexity of this building analysis is even more impressive when we consider the extraordinary level of detail required to Notes reproduce the elaborate moldings, pilasters, capitals, and 1. In the digital field, the term semantics refers to the meanings of concepts, frames ornamenting both the interior and the exterior of San- ’ properties, and relationships that formally represent real-world entities, gallo s architecture (Figures 22 and 23). Through the creation events, and scenes in a logical underpinning, such as a description logic. The of these 3-D semantic data models, we gain not only more meanings of description logic concepts and roles are defined by their model- precise knowledge of Giuliano da Sangallo’s architectural theoretic semantics, which are based on interpretations. Building a digital se- work but also a better understanding of the close connection mantic 3-D model entails the use of a general concept in software engineering between theory and practice in the Sangallo workshop. for which a conceptual data model includes semantic information. This means that the model describes the meanings of its instances. Such a semantic data model is an abstraction that defines how the stored symbols (the instance Sabine Frommel is chair of the Renaissance Art History Depart- data) relate to the real world. Specifically, in architecture, digital semantic ment at the École Pratique des Hautes Études, Paris Sciences & 3-D models encode not only the geometry (the usual requirement for 3-D Lettres. Her research covers a wide range of transverse themes, in- model construction) but also the identities of a building’s key components, cluding great architects of the Italian Renaissance, the evolution of such as walls, floors, and ceilings, with their locations and geometric shapes. architectural typologies and languages in the fifteenth and six- Digital semantic 3-D models embed a series of structured objects using a teenth centuries, processes of migration in Europe, the representa- specific architectural lexicon, with the final goal of creating representations tion of architecture in painting, the fortune of Renaissance up to not simply for visualization purposes but for the clarification of architectural information, such as a building’s shape (spatial extension), its structures (entity the nineteenth century, and the birth and development of the dis- collections and part–whole relationships), its quality attributes (colors, cipline of architectural history. [email protected] textures, and the like), and its interaction with its time period. Digital models Marco Gaiani is a professor of architectural representation and a have multiple uses for historical analysis and reconstruction related to a specialist in 3-D and 2-D computer imaging, modeling, and visu- building’s current state, its morphology interpretation, and its transforma- alization for the study of architectural heritage, archaeology, and tions over time. On this topic, see Mathieu Koehl and Pierre Grussenmeyer, industrial design. He was one the first developers/users of laser “Semantic Aspects for 3D Modeling,” International Archives of Photogrammetry

3-D DIGITAL MODELING ANDGIULIANODASANGALLO’ S DESIGNS FOR SANTA MARIA DELLE CARCERI IN PRATO 45 and Remote Sensing 33, pt. B4 (2000), 507–14; Livio De Luca, “3D Modelling Prato,” in Santa Maria delle Carceri a Prato: Miracoli e devozione in un santuario and Semantic Enrichment in Cultural Heritage,” in Photogrammetric Week toscano del Rinascimento, ed. Anna Benvenuti (Florence: Mandragora, 2005), ’13, ed. Dieter Fritsch (Berlin: Wichmann/VDE Verlag, 2013), 323–34. For 45–95; Sabine Frommel, Giuliano da Sangallo (Florence: Edifir, 2014), specific discussion of digital semantic 3-D models as applied to Giuliano da 49–69; Sabine Frommel, “Le sanctuaire de Santa Maria delle Carceri à Prato: Sangallo’s architecture, see Sabine Frommel, Marco Gaiani, and Simone Un lieu dédié à la Vierge miraculeuse,” in Art Sacré 32 (2016), 122–35; Paul Garagnani, “Progettare e costruire durante il Rinascimento: Un metodo per Davies, “Giuliano da Sangallo e decorum negli edifici a pianta centrale: Santa lo studio di Giuliano da Sangallo,” Disegnare idee immagini 56 (2018), 20–31. Maria delle Carceri e la sagrestia di Santo Spirito,” in Giuliano da Sangallo,ed. 2. Caroline Bruzelius, “Digital Technologies and New Evidence in Architec- Amedeo Belluzzi, Caroline Elam, and Francesco Paolo Fiore (Milan: Officina tural History,” JSAH 76, no. 4 (Dec. 2017), 436–39. Libraria, 2017), 304–18; Hemsoll, “L’idea dell’architettura di Giuliano 3. Sabine Frommel, “Les maquettes de Giuliano da Sangallo,” in Les da Sangallo, 1485–1492,” in Belluzzi et al., Giuliano da Sangallo,121–32; maquettes d’architecture: Fonction et évolution d’un instrument de conception Frommel, “Le architetture del Taccuino senese.” For more biographical details, et de réalisation, ed. Sabine Frommel (Rome: Campisano Editore, 2015), see Frommel, Giuliano da Sangallo, as well as the German edition, Sabine 75–86. Frommel, Giuliano da Sangallo. Architekt der Renaissance. Leben und Werk, 4. Giuliano da Sangallo, “Progetto in pianta per la chiesa di Santa Maria delle Birkhäuser, Basel, 2020); see also Belluzzi et al., Giuliano da Sangallo. Carceri,” Taccuino senese, fol. 19r, ms. S. IV. 8, Biblioteca Comunale degli 8. Jens Niebaum, Der kirchliche Zentralbau der Renaissance in Italien: Studien Intronati, Siena. The Taccuino senese comprises fifty-two small sheets of parch- zur Karriere eines Baugedankens in Quattro-und frühen Cinquecento (Munich: ment (each 179–81 by 119–25 millimeters) with representations of architec- Hirmer, 2016), 1:184–205, 2:472–86. ture, antiquities, mechanics, and ornamentation carefully made in brown 9. Leonardo da Vinci, 1487–1490, Manuscript B, Bibliothèque de Institut de ink, often with preparatory drawings. The folios extend over a wide chrono- France, Paris, cited in Jean Guillaume, “Léonard et l’architecture,” in Léonard logical field, ranging from the eighties of the quattrocento to the end of the de Vinci: Ingénieur et architecte, ed. Pierre Théberge (Montreal: Musée des second decade of the sixteenth century; however, the collection is mostly rep- Beaux-Arts de Montréal, 1987), 224–41. resentative of the years of Sangallo’s Florentine phase and slightly beyond, 10. On the Cathedral of Our Lady of Loreto, see Christoph L. Frommel, from 1480 to 1500, before his Roman period. It is particularly distinguished L’architettura del santuario e del palazzo apostolico di Loreto da Paolo II a Paolo III from the architect’s other collection, the Codex Barberini, by the large number (Loreto: Edizioni Tecnostampa, 2018). of representations of projects made in the late fifteenth century, including the 11. Richard Krautheimer, “Introduction to an ‘Iconography of Medieval church of Santa Maria delle Carceri in Prato. See Sabine Frommel, “Le archi- Architecture,’ ” Journal of the Courtald and Warburg Institutes 5 (1942), 1–33, tetture del Taccuino senese: La Sapienza di Siena, la villa di Poggio a Caiano, reprinted in Studies in Early Christian, Medieval, and Renaissance Art, ed. James Santa Maria delle Carceri a Prato, disegni per Santo Spirito e San Lorenzo,” Sloss Ackerman et al. (New York: New York University Press, 1969). in Giuliano da Sangallo: Disegni degli Uffizi, ed. Dario Donetti, Marzia Faietti, 12. See Niebaum, Der kirchliche Zentralbau der Renaissance in Italien,1:185. and Sabine Frommel (Florence: Giunti Editore, 2017), 32–49. See also Chloé 13. It is uncertain whether two ground plans for an octagonal building Demonet, “Théorie et pratique du relevé d’architecture au XVe siècle et au (1606A and 1607A, Gabinetto Disegni e Stampe degli Uffizi) have ties to this début du XVIIe: Giuliano da Sangallo et ses contemporains” (PhD thesis, project. See the following note. École Pratique des Hautes Études, Paris Sciences & Lettres, forthcoming). 14. Paul Davies, “The Early History of S. Maria delle Carceri in Prato,” 5. The term parametric originates from mathematics (parametric equation) and JSAH 54, no. 3 (Sept. 1995), 329–33. See also Frommel, “Le architetture del refers to the use of certain parameters or variables that can be edited to manip- Taccuino senese,” 39–40, 48–49. The attribution of this design to Giuliano da ulate or alter the result of an equation or system. Parametric modeling is based Maiano has been contested by some scholars. However, after comparing the on algorithmic thinking that enables a series of preprogrammed rules or algo- details of the drawings and the previous buildings, Niebaum concluded that rithms (known as parameters) that together define, encode, and clarify the re- the plans constitute Giuliano da Maiano’s early projects for the sanctuary. lationship between design intent and design response. That is, the model (or Niebaum, Der kirchliche Zentralbau der Renaissance in Italien, 1:189. Never- elements of it) is generated automatically by internal logic arguments rather theless, the annotations are not in da Maiano’s handwriting, meaning the than through manipulation. Typically, parametric rules create relationships be- drawings were made by someone in his bottega (shop) or by a copyist. tween different elements of the design. A major example of parametric design 15. See Davies, “Early History of S. Maria delle Carceri,” 329–33. The Dieci is classical order, where, from a known column half diameter, one can recon- di Balìa was a temporary magistracy whose members were summoned when struct all other elements using simple algorithms based in proportions. The unforeseen events endangered Florence. same algorithm used to establish an object’s shape might be used throughout 16. Thanks to Lorenzo’s patronage, Alberti’s treatise was published in 1485. a model, so that if an element or rule is changed, it changes throughout. In 17. See Pacciani, “Santa Maria della Pietà a Bibbona.” effect the model is a representation of all the rules that the user has defined. 18. Niebaum, Der kirchliche Zentralbau der Renaissance in Italien,1:197. 6. Piero Morselli and Gino Corti, La chiesa di Santa Maria delle Carceri in 19. In April 1485 the city council issued regulations intended to preserve Prato: Contributo di Lorenzo de’ Medici e Giuliano da Sangallo alla progettazione the ancient prisons on the north side, where the miraculous painting had (Florence: EDAM, 1982). appeared following the apparition of the Virgin Mary. 7. For examples of the rich scientific literature in this regard, see Giuseppe 20. On this page, the portico of the church’s ground floor shows columns Marchini, Giuliano da Sangallo (Florence: Sansoni, 1942), 20–26, 87; Silvestro instead of pilasters. See Frommel, “Le architetture del Taccuino senese.” Bardazzi, Eugenio Castellani, and Francesco Gurrieri, Santa Maria delle 21. The virtual reconstructions presented here were developed as a result of a Carceri a Prato (Florence: Grafiche Senatori, 1979); Stefano Borsi, Giuliano da collaboration between the Renaissance Art History Department at the École Sangallo: I disegni di architettura e dell’antico (Rome: Officina Edizioni, 1985), Pratique des Hautes Études, Paris Sciences & Lettres, and the Department of 417–20; Riccardo Pacciani, “Santa Maria della Pietà a Bibbona e Santa Maria Architecture at the University of Bologna, a collaboration founded on an ideal delle Carceri a Prato,” in La chiesa a pianta centrale: Tempio civico del Rinasci- of cooperation between the disciplines of the history of architecture and mento, ed. Bruno Adorni (Milan: Electa, 2002), 81–95; Paul Davies, “The design, and specializing in virtual models. A detailed report of the survey Madonna delle Carceri in Prato and Italian Renaissance Pilgrimage Architec- appears in the next section of this article. ture,” Architectural History 36 (1993), 1–18; Claudio Cerretelli, “Da oscura 22. On the fortress and prisons, see Cerretelli, “Da oscura prigione a prigione a tempio di luce: La costruzione di Santa Maria delle Carceri a tempio di luce,” 50, figs. 48, 60, 61. On Sangallo’s sources, see Davies,

46 JSAH | 80.1 | MARCH 2021 “Giuliano da Sangallo e decorum negli edifici a pianta centrale,” 304–18; 31. TLS is a ground-based, active imaging method that rapidly acquires Frommel, Giuliano da Sangallo,66. accurate, dense 3-D point clouds of object surfaces through laser range 23. Regarding the drawing in the Taccuino senese, see Cerretelli, “Da oscura finding. prigione a tempio di luce”;Niebaum,Der kirchliche Zentralbau der Renaissance 32. Regarding measurement units, see Gloria Nobili, “‘Delle misure in Italien,1:184–205, 2:472–86; Frommel, “Le architetture del Taccuino d’ogni genere antiche e moderne’: Un inventario delle unità di misura pre- senese,” 38. On the plan’s proportions, see Morselli and Corti, La chiesa di metriche,” in Atti del XVII Congresso Nazionale di Storia della Fisica e dell’As- Santa Maria delle Carceri in Prato,38–53. tronomia, ed. Pasquale Tucci (Milan: Istituto di Fisica Generale Applicata, 24. Davies, “Early History of S. Maria delle Carceri,” 326–35. 1997). 25. The niches were initially previewed for the lateral walls of the arms 33. These details were noted previously in Frommel, “Le architetture del and were then also added to both sides of the doorway. Niebaum, Der Taccuino senese,” 41. kirchliche Zentralbau der Renaissance in Italien,1:198.Itseemsthatsome 34. 22.2 × 14.8 millimeters APS-C CMOS sensor, 3,888 × 2,592 pixels, with evidence of a niche was found during restoration work. See Marchini, 35 millimeters of nominal focal length. Giuliano da Sangallo, 87. 35. Morselli and Corti, La chiesa di Santa Maria delle Carceri in Prato,55–186. 26. Cerretelli, “Da oscura prigione a tempio di luce,” 81. A total station is an electronic/optical instrument used for surveying. It is an 27. The pilasters of the ground plan of the Taccuino senese clearly show such a cor- electronic transit theodolite integrated with electronic distance measurement respondence, which remains obvious today in the section where the Doric order (EDM) to measure both vertical and horizontal angles and the slope distance entablature and façade reach the level of the Corinthian order of the inner space. from the instrument to a particular point; it includes an onboard computer 28. Livio De Luca, “Methods, Formalisms and Tools for the Semantic-Based to collect data and perform triangulation calculations. A TS can be used to Surveying and Representation of Architectural Heritage,” Applied Geomatics 6, record absolute locations to integrate manual measurements. no. 2 (June 2014), 115–39. 36. Maurizio Filiaggi, in Morselli and Corti, 38–53. 29. Building information modeling is a process supported by various tools and 37. For support for this argument, see Davies, “Giuliano da Sangallo e technologies involving the generation and management of digital representa- decorum negli edifici a pianta centrale.” tions of physical and functional characteristics of places. BIMs, or building infor- 38. Giuliano da Sangallo, order proportions, Taccuino senese, fol. 31v, ms. S. IV. mation models, are files that can be extracted, exchanged, or shared to support 8, Biblioteca Comunale degli Intronati, Siena. decision making regarding a built asset. BIMs involve representing designs as 39. Marcus Vitruvius Pollio, De architectura, ed. Pierre Gros (Turin: Giulio combinations of “objects,” usually consisting of solid-shape primitives. For dis- Einaudi Editore, 1997), 4.5.6 (387–92). cussion of recent digital innovations, see Fabrizio Ivan Apollonio, Marco Gaiani, 40. It is possible that the pediment was created by Piero de’ Medici be- and Zheng Sun, “3D Modeling and Data Enrichment in Digital Reconstruction tween the death of Lorenzo and the exile of the dynasty in 1494, or even of Architectural Heritage,” International Archives of the Photogrammetry, Remote after the return of the family and the election of Leo X, Lorenzo’sson,in Sensing and Spatial Information Sciences 40-5/W2 (2013), 43–48. 1513. 30. The folios of the Codex Barberini measure approximately 455 by 390 milli- 41. The Cappella Pazzi’s niches are actually blind. The niches in the model meters; those of the Taccuino senese are approximately 120 by 180 millimeters follow a consistent shape that draws upon other buildings and projects from in size. Giuliano da Sangallo, Codex Barberini, ms. Barb. Lat. 4424, Biblioteca the same historical period. Digital semantic 3-D modeling will facilitate new Apostolica Vaticana. research on this topic.

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