An Urban Grammar for Portuguese Colonial New Towns In the 18th Century, n Anais do XIII Congresso SIGraDi 2009 sp Do Moderno ao Digital: Desafios de uma Transição, 346-349.

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his study describes the morphological urban order underlying Portuguese treatises and Portuguese urban cartographic representation produced from 16th century to 18th century. The historical documentation suggests that Pythagorean-Euclidian geometry
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  SIGraDi 2009 sp An urban grammar for Portuguese colonialnew towns in the 18th century Alexandra Paio DAU - Departamento de Arquitectura e Urbanismo, ISCTE-IUL Lisbon University Institute, Portugal alexandra.paio@iscte.pt  Benamy Turkienicz SimmLab - Laboratory for the Simulation and Modeling in Architecture and Urbanism, Universidade Federal do Rio Grande do Sul, Brazil –benamy.turkienicz@gmail.com  Abstract  . This study describes the morphological urban order underlying Portuguese treatises and Portuguese urban cartographic representation produced from 16th century to 18th century. The historical documentation suggests that Pythagorean-Euclidian geometry appears to be a crucial ingredient for the understanding of Portuguese urban design- thinking and urban design-making. To unveil the genesis of the morphological urban order present in the Portuguese colonial plans of the eighteenth century, a descriptive method, Shape Grammar has been adopted. Shape Grammar, as method, supports the analysis of the form-making logic and has proved to be powerful in shape analysis, description,interpretation, classification, evaluation and generation of a design language. Keywords  . Urban Design; Knowledge-Based Model; Shape Grammars; Generative Systems. Introduction Shape grammars have, over the past decades, been shown to be apowerful means of analyzing and generating languages of designs (Stinyand Gips, 1972). This paper focuses a generative parametric urbangrammar computational model designed to produce derivations ofPortuguese colonial new towns of the 18th century. The computationalmodel is based in geometric principles embedding Portuguese treatisesand practice at the time. During the model development, particularattention has been given to the similarities between the urban layoutdesigned by Portuguese urban makers, up to the eighteenth century, andthe actual process of urbanization. The depiction of similarities anddifferences has considered iconographic comparisons produced byseveral scholars in the last decade as a reference for this paper’s finaldiscussion. The research behind this paper is part of a larger ongoingproject to develop a generative urban grammar for Portuguese colonialurban design from the 16th to 18th century.The urban grammar proposed in this paper seeks to offer a newagenda addressed to the teaching of geometry and urban design inschools of architecture and urban design. First, by producingevidence that geometry is a fundamental cognitive tool for urbandesigners. Second, by describing some fundamental relationsbetween geometry and urban elements (streets, urban blocks, mainbuildings an squares) and the relations between these elements.This paper has four sections. The first, confronts traditional viewsbased in iconographic evidence and historical data to a new andpossible approach based in syntactical and non visualcharacteristics. The second section describes the Portuguese colonialurban design according to geometric and genetic principles. Thethird, introduces an urban grammar model capable of generatingurban planimetric proportionate and symmetrical systems. The finalsection discusses the partial results of the research in relation to theexistent body of knowledge concerning Portuguese colonial towns. Knowledge-based Portuguese urban design Scholars, mainly from Portugal and Brazil, have been trying todemonstrate that urban layouts of colonial towns evolved fromstructured thinking and urban maker’s knowledge of geometry(Correia, 1997; Araujo, 1992, 2000; Menezes, 1998; Bueno, 2003).This knowledge is clearly present in the training lessons of skilledprofessionals and well documented in treatises, manuals,dissertations, cartographical and iconographical works produced inthe eighteen century (Bueno, 2003; Paio, 2007). As Rossa puts it“Being able to colonise several parts of the world and code it indrawings was one of the major scientific accomplishments ofPortuguese urban planners, and the acquisition of such knowledgedemanded a unique ability for abstraction which could not havesimply emerged out of nothing” (Rossa, 2001). Euclidian geometry,translated to simple and complex geometric constructs present in allthe 30 analyzed treaties, played a fundamental role in the Portugueseurban planning design process (Pereira, 1999; Menezes, 2001).This paper explores the descriptive potential of shape grammars toexplain abstract underlying rules behind similarities and differencesbetween cartographic representations of 75 Portuguese new towns.The methodology is described in table 1. Table 1. Theoretical framework.  PAN Panorama347 The development of the urban grammar computational model forthe selected corpus has involved the analysis of 75 Portugueseurban plans and their reference to different treatises; the descriptionof basic generative (geometric and urban) principles; the inferenceof shape rules and the specifications for the computational modelcapable to automatically generate planimetric proportionate andsymmetrical urban designs according to Portuguese colonialprinciples. The Portuguese urban design genesis:geometric and generative principles. Through the analytical decoding of the sample’s grammar, it waspossible to progressively depict geometric and topologicalattributes and to establish two sets of categories and classes(Mitchell, 1998). These were geometric-configurational andtopological-functional (Table 2.). Each category was divided infour classes. The geometric-configurational category is stronglyEuclidean knowledge-based and constituted by 5 differentelements: Position, Direction, Limit, Diagonal and proportion andsymmetry (Paio and Turkienicz, 2009). The topological-functionalcategory is related to urban elements: Streets; Urban Blocks;Main Buildings and Squares (Table 2). The two categories arerelated in that it is possible to associate the category’s fourclasses one to another.Classes of the geometric-configurational category were used togenerate symmetrical and proportional lay out where the diagonalhas been deployed to generate streets and urban blocks. Thedefinition of the point (geometric center), the direction (vertical andhorizontal axis), allowed operations such as rotation and, further on,the positioning of the church and town hall (or military buildings)and the location of one or more than one squares (Figure 2.). An Urban grammar for Portuguese colonial newtowns: defining the basis for a computationalmodel to generate urban planimetricproportionate and symmetrical systems. Urban grammars have been developed in the past, (Teeling, 1996,Beirão and Duarte, 2005, Duarte et al, 2007) using the shapegrammar formalism to define languages of urban design.In this study, the proposed urban grammar is a parametric shapegrammar defined in the algebras U12 V12 W12. The U algebrarepresents generic shapes, points, lines, planes. The V algebrarepresents labeled shapes, and W algebra represents the weightshapes. The generation of an urban derivation develops over fourstages, two to generate the planimetric proportionate andsymmetrical system and two to generate a planimetric urban system(Table 2.): (1) define position, direction and limit; (2) define the rulesof proportion and symmetry; (3) define streets and urban blocks; (4)insert main buildings and squares. Each stage has a specific set ofshape-rule schemata. These stages are sequential, using a step-by-step process to generate a colonial Portuguese urban plan.Transitions between sequential rules application and stages arecontrolled by the descriptive conventions of Shape-Grammar Meta-Language (SGMT) by Haldane Liew. SGMT’s established analternative method to write grammars for design introducing sevendescriptors for shape grammar language. These explicitly determinethe sequence through which a set of rules is applied, do restrict ruleapplication through a filtering process and use context as to guidethe rule matching process (Liew, 2004). The descriptors modify theconditions (rule selection, drawing state, matching conditions andapplication method) surrounding the process of applying a rule inshape grammar. Due to length restrictions, it will not be possible todescribe in detail all rules of the proposed urban grammar. Stages of the Urban Grammar developing process The Urban grammar presented here is still limited in that it onlypartially describes the universe of Portuguese colonial urban plans.Specifically, it produces urban planimetric proportionate andsymmetrical systems, orthogonal streets, urban blocks, main buildings(church, town hall, priest's house, governor's house, director’s houseand military buildings) and squares. Other elements such lots, housesand topographical features have been omitted. Since the grammar isdesigned as a sequence of stages, the omitted elements can befurther inserted into the grammar as an additional stage. In order todemonstrate the urban grammar developed so far, an example of aBrazilian derivation process is illustrated (Figure 2.) and described. Initial Shape The initial shape for the Portuguese urban grammar is a point with apar coordinates (0,0). Stage 1: Define position, direction and limit. In the first stage of the urban grammar, the user defines the basicgeometric generative principles of the planimetric proportionate andsymmetrical system. This stage is composed of eight rules (Figure1.). From the initial shape, a geometric center, the user has to definethe direction, the geometric axis (x, y) to symmetry and proportion;the limit, a circle, which will be dived in equal parts defining thegenerative shape (Figure 2.). The equilateral triangle, the square andthe pentagon are the three primary plane shape shapes which haveit owns archetypal behavour in terms of itself and in the finalstructure of the planimetric systems. Stage 2: Proportion and symmetry In the second stage of the urban grammar, the user operates rulesto create a symmetric and proportionate structure, based on agenerative shape selected in the stage 1. The sequential stepsemulate the similitude to the operation with the compass and thestraightedge. In order to clarify the following steps, (Figure 1.) is Table 2. Geometric-configurational and topological-functional.  SIGraDi 2009 sp Figure 1. Shape-rulesfor generatingplanimetric urban  PAN Panorama349 ––––––––––––––––––––––––––––––––––––––References  Andaroodi, E; Andres, F.; Einifar, A.; Lebigre, P. Kando, N.:2006, Ontology-basedshape-grammar schema for classification of caravanserais: a specific corpus ofIranian Safavid and Ghajar open, on-route samples, Journal of Cultural Heritage, 7,pp. 312–328.Duarte, J.P., Ducla-Soares, G., Caldas, L. G. and Rocha, J.,:2006, An UrbanGrammar and for the Medina Marrakech, Design Computing and Cognition ‘06,Springer, Netherlands, pp. 483-502. Araujo, R.: 1992, As Cidades da Amazónia no século XVIII. Belém, Macapá eMazagão, FAUP, Porto.Bueno, B.:2003, Desenho e desígnio: O Brasil dos engenheiros militares (1500-1822), Faculdade de Arquitectura e Urbanismo da Universidade de São Paulo, SãoPaulo.Correia, J. H.: 1997, Vila Real de Santo António. Urbanismo e Poder na PolíticaPombalina, FAUP, Porto.Delson, R.: 1979, New towns for Colonial Brazil. Spatial and Social Planning of theEighteenth century, Department of Geography Syracuse University, Michigan. xDuarte, J. P. and Beirão, J. N.: 2007, Urban design with patterns and shape rules,Proceedings of the 2nd International Seminar on New Town Simulation, New TownInstitute, Almere, pp. 1-11.Liew, H.:2004, SGML: A Meta-Language for Shape Grammar, MIT, Massachusetts.Mitchell, W. J.:1998, The logic of architecture, The MIT Press, CambridgeMassachusetts.Oxman, R.: 1997, Design by re-representation: a model of visual reasoning indesign, Design Studies, 18, pp. 329-347.Paio, A.:2007, Knowledge of geometrical design and composition in a Portugueseapproach to urban layout, ISUF XIV International Seminar on Urban Form, XIV, 212 -232.Paio, A. and Turkienicz, B.: 2009, A generative urban grammar for Portuguesecolonial cities, during the sixteenth to eighteenth centuries. Towards a tool forurban design. Proceedings of the 27th Conference on eCAADe, p.585 - 592.Pereira, J.:1999, A cultura Artística Portuguesa (Sistema Clássico), Lisboa.Stiny, G. and Gips, J.: 1972, Shape grammars and the generative specification ofpainting and sculpture, Information Processing, pp. 1460-1465.Stiny, G.: 1978, Algorithmic aesthetics. Computer Models for Criticism and Designin Arts, University of California Press, Berkley.Stiny, G.:1980, Introduction to shape and shape grammars, Environment andPlanning B: Planning and Design, 7, pp. 343-351.Walter, R; ARAUJO, R.; CARITA, R (cood.): 1998, Actas do ColóquioInternacional.Universo Urbanístico Português 1415-1822, Comissão Nacional paraas Comemorações dos Descobrimentos Portugueses, Lisboa. Figure 2. The derivation of the urban design Sample. showed an example of a set operations (steps) that can bemanipulated by the user: Step 1. Define the four axis ofsymmetry; Step 2. Decide the square-based proportions neededto work. The example has shown that the user rotated squaresbased on geometric progressions or arithmetic division in a nine-unit grid. Define the limit of application of the progression or therepetition of the squares (Figure 1.); Step 3. The regulating squareis defined by lines srcinated from the square-based proportion andresults in a particular grid whereby (Figure 1.) streets, blocks andbuildings will emerge in the following stage. The result is aconsistent geometric structure which regulates the planning of thePortuguese urban plans at many scales (Figure 2.). Stage 3: Streets and urban blocks In the third stage, urban generative elements emerge accordingto set-rules as follows: Step 1. Define first structure streets; Step2. Define the final structure of streets, dimensions and hierarchy;Step 3. Define urban blocks; Step 4. Erase the streets structureand geometric structure no longer necessary. This final step willhighlight the urban blocks grid and the main axis, a fundamentalstep towards the final stage of the grammar (Figure 2.). Stage 4: Main buildings and squares The user has, again, set-rules options to locate the main buildings(church, town hall, governor's house, priest’s house and militarybuildings) and set-rules to locate the squares with various formalshapes. All set of shape rules transmit the relation between themain axis and the main buildings and these with the squares. Inthis final stage the user has to define main axis to insert the mainbuildings (Figure 2.). The derivation shows one way to insert thechurch and after the associated square. This grammar allows theuser to locate one, two or three squares, and one of them can begenerated without being related to a main building, as we can seein the derivation. The final step of the stage and the grammar is theerase of the main axis. Discussion and Conclusions This paper showed the application of shape grammar techniques tourban design history. This structural and structured knowledge-basedresearch was essential to develop a generative parametric urbangrammar for Portuguese colonial new towns in the 18th century,because structures are rarely explicitly represented in Portugueseselected corpus. The fundamental motivation of this research was torecover the elements of genetic foundation and represent these asconstituents of visual reasoning processes. Since the major part of pre-design stages in urban design are devoted to the study of precedentsas strategy to produce new design the experience may offer a newincentive to improve the teaching of geometry and urban designprecedents in the schools of architecture and urbanism.The results showed that shape grammars can constitute a valuablebasis for the understanding of the colonial Portuguese urban designprocess. The resulting planimetric system ends up by corresponding toa basic compositional procedure supporting the implementation ofdesigns and working as a scale. Once established the planimetricsystem, the urban plan absorb proportions and symmetry withsurprising balance.From the results obtained, it can be said that is possible to create ausefully tool to be used in the learning process of historical urbandesign. The descriptive and generative character of this tool will allowthe user simultaneously to both interpret and simulate new designsbased on theoretical knowledge, as well as to manipulate and generatevarious Portuguese colonial parametric urban design solutions.
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