parametric design: theoretical development and algorithmic ... · generative design as the...

Parametric Design: Theoretical Developmentand Algorithmic Foundation for DesignGeneration in Architecture

Ning Gu, Rongrong Yu, and Peiman Amini Behbahani

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Generative Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Common Characteristics of Generative Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Main Generative Design Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Parametric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Historical Review of Parametric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Parametric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Reshaping Architectural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Impact on Architectural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Limitations of Parametric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Abstract

This chapter presents the theoretical foundation of parametric design for designgeneration in architecture. Parametric design has been increasingly applied toarchitectural design in recent years. It is essentially a digital design method,which can be characterized by rule-algorithmic design and multiple-solutiongeneration. Parametric design originates from generative design, which is atypical computational design approach based on rules or algorithms (e.g., ingenerative grammars or evolutionary systems). This chapter starts with a critical

N. Gu (�) · P. A. BehbahaniSchool of Art, Architecture and Design, University of South Australia, Adelaide, Australiae-mail: [email protected]; [email protected]

R. YuSchool of Engineering and Built Environment, Griffith University, Southport, Australiae-mail: [email protected]

© Springer International Publishing AG, part of Springer Nature 2018B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences,https://doi.org/10.1007/978-3-319-70658-0_8-1

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review of generative design, followed by the background, history, and theory ofparametric design, including various fundamental concepts and applications thatunderpin parametric design, and concludes with a discussion of the impact ofparametric design on architecture.

KeywordsParametric design · Architectural design · Generative design · Mathematics ·Algorithm

Introduction

Generative design is a general term commonly used to describe a number of com-putational methods that aim to automate the whole, or a part, of the design process.Their main purpose has been to assist human designers to explore the design spacewith computational means (Herr and Kvan 2007). This is usually realized throughrapid prototyping, powered by computers (Chien 1998). Furthermore, because theconceptual frameworks and design opportunities they offer are very distinct fromthe traditional approaches to design, it is arguable that generative systems have alsocreated new paradigms or tools for design thinking (Oxman 2006). Shape grammaris one of the typical generative design methods (see chapter � “Shape Grammars: AKey Generative Design Algorithm”). As discussed in that chapter, shape grammars,their generative nature, as well as formal approaches to design representationand generation, have influenced the emergence and development of contemporarycomputational design methods and tools, including parametric design, which is thefocus of this chapter. Deriving from generative design principles, parametric designhas distinctive features and has been widely adopted in leading architectural designpractices.

This chapter is structured into three main sections. The first section summarizesgenerative design as the theoretical background for parametric design; the sectionintroduces generic features of generative systems and reviews key examples ofgenerative design methods. The next section “Parametric Design” focuses on para-metric design including its historical development as well as its main components,applications, and implementation. The section “Reshaping Architectural Design”discusses the impact of parametric design and how parametric design has reshapedarchitecture and is followed by a concise conclusion.

Generative Design

As defined above, generative design refers to a collection of computational methodsor algorithms used to explore the design space for generating solutions. Forthis purpose, algorithmic procedures are formally defined and applied to producenumerous design alternatives, of which the most suitable would be selected (Herrand Kvan 2007). This definition has been systematically used since the 1990s in the

http://link.springer.com/``Shape Grammars: A Key Generative Design Algorithm''

Parametric Design: Theoretical Development and Algorithmic Foundation. . . 3

computational design domains, although most generative design systems (such asshape grammars) had been developed decades earlier.

The term generative appeared much earlier in the relevant fields of design andvisual art, at least since 1965, as reported by Boden and Edmonds (2007). It hasgradually evolved to shift or extend its meaning from a description of designmechanics (as computer-generated design) to a more specific reference to designparadigms capable of supporting design thinking (Eckert et al. 1999).

Tracing back to its origin, generative design initially emerged in the 1950s–1960s, inspired by natural phenomena. For example, evolutionary systems orgenetic algorithms were inspired by the processes of biological evolution (Holland1975), cellular automata were modeled based on biological growth (von Neumann1951), and design grammars had synergies with the formulation of natural languages(Stiny and Gips 1972).

Common Characteristics of Generative Design

Although developed for a variety of purposes, generative design methods share somecommon characteristics. As noted, generative design systems rely on formal algo-rithms to describe and generate designs and are mostly associated with computation.This chapter defines three common characteristics of generative design: algorithm,ideation (for numerous design alternatives), and computation.

Algorithms in most generative methods, are realized as a collection of generativerules, an interpretation made by Oxman (1990) and Boden and Edmonds (2007).Others describe similar concepts as build commands (Hornby and Pollack 2001),transformation rules (Gero and Kazakov 1996), and so on. Generative rules areresponsible for changing the whole or a part of the design to a new one. Rulesdiffer by the mechanisms of generation they adopt, which refer to the different waysrules alter the design. For example, in shape grammars the generative mechanismin a shape rule can be used for either replacement or modification (Knight 2003).Replacement is the substitution of the design or its part(s) with another; it can alsoinclude addition (replacing void with an element) and subtraction (replacing anelement with void). On the other hand, modification is used to change the scale,orientation and direction, or other numerical properties (e.g., in parametric shapegrammars) of the design. Through the application of the rules, design generation isthen arranged in sequence (Herr and Kvan 2007). This sequential and recursiveprocess selects a combination of rules to process the design generation in astructured manner, from an initial state of the design to the final outcome. Designalternatives emerge when different combinations of rules are selected and applied.These sequences are not always explicitly defined and may emerge during theirapplications. For example, in shape grammars, rule sequencing is made possiblein real time by the recursive matching of existing shapes from the design withthe left-hand side (LHS) shapes of the rule set (Maher 1990). Another moreadvanced type of sequencing is through the cyclic reproduction of design (Eckertet al. 1999). In this case, rules that have directed the generation of the previous

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stage will undergo further round(s) of application, but only applied to the highestpotential designs and alternatives identified during the process. Such a qualityis quintessential to evolutionary design, which will be introduced in the section“Evolutionary Systems.”

Ideation (for numerous alternatives), or design divergence, refers to the capabilityof generative design methods to create multiple instances that satisfy the designrequirements; usually this is enabled by the selection of multiple rules and theirdifferent sequencing for application during design generation. For example, in shapegrammars, the decidability of LHS shapes (e.g., multiple possibilities in recognizingand matching LHS shapes) can contribute to the divergence of the design results(Knight 2003). Other factors can also play a role in enabling design divergence. Forexample, in parametric shape grammars, the range of parameters may allow multipledefinitions of design by adjusting the values of those parameters (Knight 2003).

The computational characteristic refers to the fact that generative design has aformal structure comprising visual or mathematical properties for design generationin a systematic way. Because of the increasing complexity and intensity of thedesign and the generation processes, research has extended the notion of “computa-tion” to the use of computers as well (Boden and Edmonds 2007). In some domains,for example, “computer art” and “generative art” have been used interchangeablyderiving from this context.

Main Generative Design Systems

Generative design systems have been developed since the 1960s. Many of themshare common origins or features, which are useful for categorizing different sys-tems. For example, Fischer and Herr (2001) characterized generative systems intofour general types: emergent systems (e.g., cellular automata), generative grammars,algorithmic generation (e.g., parametric design), and algorithmic reproduction (e.g.,genetic algorithms). While such categorization makes sense in abstracting anddistinguishing common generative features, the terminologies themselves may notbe very precise. For example, “algorithmic generation” can be a very broad termand arguably applicable to all generative systems. The term “emergent systems”suggests support for design emergence and is also applicable to a number ofsystems. A different approach (Singh and Gu 2011) does not explicitly developmore general categorizations, but acknowledges that different generative systemscan have both differences and overlaps between each other. This section reviews fourcategories, by considering both their differences and similarities and therefore doesnot mutually exclude one from another. These categories are: generative grammars,evolutionary systems, self-organized emergent systems, and associative generation.

Generative GrammarsAs discussed in chapter � “Shape Grammars: A Key Generative Design Algorithm”,generative grammars are based on transformational rules which can be appliedrecursively to develop the final shape. This notion was originated from linguistics



but has evolved into different forms for different unique purposes. For example,visual grammars such as shape grammars were inspired by Chomsky’s idea ofgenerative grammars (Stiny and Gips 1972), meanwhile graph grammars wereinitially developed in computer science and are especially suitable for computerimplementations (Chakrabarti et al. 2011), and L-systems were based on anotherlinguistic concept – string grammars – developed in the 1950s (Singh and Gu 2011).In recent years research has combined these approaches to enhance generativecapabilities, for example, the combinations of shape grammars and graph grammars(Grasl and Economou 2013; Lee et al. 2016) have been demonstrated to address bothvisuospatial and syntactic issues in architecture. Generative grammars are one of theearliest generative design systems to be used in architectural design, for example,the shape grammar of Palladian villas by Stiny and Mitchell (1978). On the otherhand, graph grammars and L-systems were applied to architectural design muchlater, having been in use since the 2000s (e.g., Parish and Müller 2001).

The original generative mechanisms of rules in grammars are mostly for replace-ment not modification (Knight 2003). Nevertheless, modifications later becamepossible in grammars and significantly enhanced their generative power, especiallywith the emergence of parametric shapes and parametric shape grammars.

Generative grammars are sequential due to the nature of rule application. Thesequencing of rules for application is determined by matching different existingelements of the design against LHS shapes of the rule set for rule selection(Stiny and Gips 1972). The divergent generation of design alternatives could befulfilled by different possibilities in such rule selection and application. Whileall grammars are computational, only graph grammars and L-systems have beenrealized as computer implementations to a greater extent. As discussed in chapter� “Shape Grammars: A Key Generative Design Algorithm”, during shape detection,shape grammars allow designers to freely decompose and recompose shapes. Thisfeature is called shape emergence, which regards shapes as not being predefined butemerged. To appropriately handle shape emergence has been difficult in computerimplementations because of the finite representations of design being restricted bythe computer memory (Krish 2011; Tching et al. 2016), and therefore it has becomean ongoing challenge for visual grammars such as shape grammars.

Evolutionary SystemsAs the term suggests, evolutionary systems in design were derived from evolu-tionary biology, especially with the simplified notion of “survival of the fittest”(Holland 1975). In summary, an evolutionary system defines a recursive processof design reproduction, in which each organism reproduces (slightly) divergentoffspring. Only the “fittest” among them would survive to trigger reiteration of thereproduction and selection cycle (Fasoulaki 2007). In an evolutionary system, the“fitness” of the generated design instances is evaluated using certain fitness criteriato select the most appropriate ones to continue the generation and selection cycle,until a satisfactory outcome is achieved. Because of such a basis in evolutionarybiology, these generative design systems are also called genetic algorithms (GA).


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Unlike most other generative design systems, there are no inherent generativerules in evolutionary systems. Design alternatives can be produced by differentmeans, including other generative methods (e.g., shape grammars, L-systems, etc.).The sequential characteristic of generation reflects the cycle of generation andselection, rather than the order of specific rule selection and application. Divergencein evolutionary design is also supported by the generation and selection cycle,and the evolutionary process is usually sizable in terms of both depth (numberof stages in design generation) and breadth (number of alternatives per stage). Inmost existing evolutionary design systems, computers have been used to assist inmanaging the generation and selection cycle. However, in cases where the selectioncriteria are more subjective (e.g., aesthetics), human designers in particular havebeen used for intervention.

Generative design systems or genetic algorithms have emerged from the verybeginning of computational design (Holland 1968). However, their explicit applica-tions in architecture only began in the 1990s (Jo and Gero 1998). A possible reasonmay be the complications of formulating fitness criteria that address rather complexarchitectural design issues or considerations and the challenges for formulating themusing abstract computer representations.

The concepts of generation and selection, or synthesis and evaluation, havealways been an important part of design theories and methodologies, and they arealso the fundamental basis of evolutionary design systems.

Emergent and Self-Organized SystemsThe concept of emergence here is defined as the explicit outcome of implicitrepresentation (Gero 1996). Therefore, emergent systems refer to generative designsystems whose outcome emerges out of self-organized components. A commonapproach to this emergence is a collection of self-organizing agents, who shapethe final form by interacting with each other and with their surroundings. Cellularautomata and swarm intelligence are the two typical examples of emergent and self-organized systems (Singh and Gu 2011).

Cellular automata systems were inspired by biology through an interest insimulating biological growth (von Neumann 1951). With its formal establishmentin the 1980s (Wolfram 1986), it attracted the attention of designers. In practice, acellular automata system is made of a grid (or structured geometry) whose cells canhave different properties or states (Sarkar 2000). A rule or set of rules, inherent tothe cells, can direct the alteration of states responding to their neighboring cells ortime intervals (Batty 1997b). As time passes, the cells automatically change theirproperties or states, and the corresponding design combinations emerge on the gridas the outcome. Because of this automation process of the cells, the term cellularautomata is therefore used for such generative design systems.

Considering the rather abstract nature of the cells, the generative rules (i.e.,for state alteration) can have both replacement and modification as the generativemechanism. The automation process is sequential as state alteration proceeds andspreads cell by cell. Design divergence in cellular automata can be achieved either


by recording the collective states of cells at different times or enabling parametersand variations that can affect the automation rules (Batty 1997a).

Swarm intelligence concerns the design of complex and intelligent systemsbased on collective behaviors of simple individual agents who work collaboratively(Blum and Li 2008). Similar to the cells in cellular automata, agents in swarmintelligence behave collectively based on their inherent rules, as well as interactionswith each other and their surroundings. However unlike cellular automata, theirdesign outcomes are not bound to the defined grid (Singh and Gu 2011), thereforetheir behaviors can be more complex than those of the alteration of states incellular automata. Swarm intelligence originated in the study and simulation ofinsect swarms, and later has been extended to other animals and humans who canundertake more complex cognitive activities (Garnier et al. 2007).

Similar to cellular automata, the agents in swarm intelligence usually operatebased on time intervals, which define the sequential characteristic of designgeneration using swarm intelligence. The divergence of the design outcomes maybe realized by various means such as varying (or even randomizing) the numbersand types of agents, their surroundings, time intervals, etc.

Associative GenerationIn this type of generative system, the design and its alternatives are generated byfirstly defining the association between different components that will make upthe design, and then by assigning and alternating the values of different propertiesbetween each other. Unlike grammars, the design components are not explicitlytransformed, but any changes made to their properties will subsequently lead to thegeneration of new design instances by adjusting other properties due to the definedassociation.

Parametric design is one of the most typical generative systems and the latestdevelopment based on associative generation or associative geometry. Parametricdesign is the focus of this chapter and will be more extensively introduced in thesecond half of the chapter. Parametric, as a term or method, originated from themathematical notion of parametric equations, with its design application initiallyseen in the works by Italian architect Luigi Moretti in the 1940s (Frazer 2016).The essential idea of parametric design is that the values of different variableschange, usually associatively, based on different input parameters. The conceptof parametric design has also been adopted to enhance other generative designsystems, for example, parametric shape grammars. In theory, parameters andvariables can be of any types or values, including those related to visual qualities,while in practice they are usually numerical, which make them ideal for computerimplementation. Divergence may be supported by either adjusting the parametersand variables, or modifying and redefining the association between them. Thesequential characteristic here is largely reflected in iteration or rapid prototyping,where a large number of design alternatives can be very efficiently produced bythe abovementioned adjustment, modification, or redefinition, which can then beexplored and reviewed (often with the intervention of human designers) to perfectthe design generation.

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Parametric Design

As described above, the concept of parametric design originated from generativedesign. Deriving from those core generative design principles, parametric designhas since evolved into one of the most widely applied generative design systems inpractice and in education. This section firstly introduces the historical backgroundand development of parametric design. The main content of the section describesthe theoretical foundation of parametric design, including various fundamentalconcepts, as well as their application and implementation.

Historical Review of Parametric Design

Origin of Parametric DesignAs noted, parametric design is a specific type of system for generative design. Thegenerative process of parametric design focuses on the control of variations andconstraints. The variation control of geometry can be traced back to the Churchof Colònia Güell designed by Antonio Gaudi. He created a model in which theceiling shape could be altered by adjusting the position of the weight or the lengthof the string. This association of the ceiling shape with the position of the weightand the length of the string in the system, demonstrates the fundamental conceptof parametric design and is the initial application of it in architecture, althoughwithout explicit computational techniques. Based on this concept, Hillyard andBraid (1978) proposed a system for computer-aided mechanical design that allowedthe specification of geometric constraints, restricted within a certain range. Thissystem represents one of the first attempts to theorize variations and constraintsin computational design systems. A few years later, Light and Gossard (1982)furthered the development and presented what was called variation geometry orvariation design. Their work provided geometrical representations with enhancedmathematical and geometrical modeling tools to support the design process. Theseparametric modeling tools were then utilized widely in aerospace, ship construction,and product design industries. From the late 1980s, Frank Gehry, a leading figure incontemporary architecture, used CATIA as the main platform for the documentationof his building designs. As a component of this platform, a parametric package (formodeling NURBs surfacing) formally entered commercial architectural practices.Though most of Gehry’s designs only used parametric techniques in the documen-tation stage, at around that time his style suggested new architectonic possibilitiesand triggered intellectual debates about the style and the role of the computer.Without parametric tools, these dynamic, open-ended, and complex designs wouldhave been difficult to achieve. Later, the consulting firm Gehry Technologies (GT),standardized this parametric approach into Digital Project (DP) to specificallyhandle complex architectural designs. Today GT has expanded their services to awide range of computational design areas.


Development of Parametric DesignFrom the mid-1990s, the number of architectural practices and academic orga-nizations that explored and adopted parametric design in architecture increasedsignificantly. During that period, software such as GenerativeComponents™ (GC),Grasshopper, and Processing were developed and evolved rapidly with enhancedfeatures. By the year 2000, the applications of parametric techniques in buildingdesign had matured, and a growing number of landmark buildings using parametricdesign were proposed and constructed. The leading practices using parametricdesign in the architecture industry at the time included Foster+Partners, Zaha HadidArchitects, UNStudio, KPF, AA Emtech, and SPAN. Designers were able to usedifferent parametric design tools to produce and control free-form architecture. Thiswas a major breakthrough for many of the leading architectural practices shiftinginto designing through parametric modeling.

In research and education, AA in London, LAAC in Spain, and Hyperbody atDelft University of Technology, MIT, and Columbia University have since becomecradles for the next generation of parametric designers. Meanwhile, internationalcomputational design conferences including ACADIA, ASCAAD, CAADRIA,eCAADe, SIGraDi, and CAAD Futures have an increasing number of publicationson parametric design, an important topic that has since been established in theseresearch forums. In more recent times, there have been many other conferences andworkshops that continue the effort in promoting parametric design.

ParametricismOver the past 20 years, parametric design has gradually played an increasinglyimportant role in architectural design, especially among leading design practices.Some scholars have argued that it has become a design style or movement that isreplacing Modernism (Schumacher 2009). In the 2008 Venice biennial exhibition ofarchitecture and titled “Out There: Architecture Beyond Building,” the term para-metricism was first raised by Patrik Schumacher and later more comprehensivelydescribed as a combination of design concepts that provide a new and complexorder based on key principles of differentiation and correlation (Schumacher 2009).During the 2011 ACADIA conference, the term then became the main conferencetheme.

The overarching implications of parametricism and its related concepts arestill largely underexplored in a broader industry context, and the approaches toapply parametricism can also vary. For example, architects can maintain modernistaesthetics in buildings but only use parametric modeling to address differentlevels of complexity or to optimize the overall design. Such approaches can beseen in projects like Soho Shang Du in Beijing. It is considered to be a finelydesigned building achieved through parametric tools, but with a rather conventionalappearance.

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Parametric Design

Key Concepts and TerminologiesParametric design. Parametric design focuses on the representation and control ofthe relationships between objects in a computational design model. It supports thecreation, management, and organization of complex designs (Woodbury et al. 2007).Using parametric design tools, designers can create rules according to the aestheticsand functional or performance-related requirements of a design. A parameter is avalue or measurement of a variable that can be altered or changed. Each object ina parametric system may have certain rules embedded, and when one parameterchanges, other parameters will adapt automatically (Ostwald 2012). By changingvarious parameters, particular instances can be created from a potentially infiniterange of possibilities (Kolarevic 2003).

From the notions above, parametric design can be understood to have thefollowing characteristics. Firstly, these systems are structured based on designparameters. Eastman (2008) suggests that in parametric design, key variables areoften defined by parameters (Eastman 2008). While most parameters are relatedto geometrical modeling, others can be connected to functional or performance-related requirements. Secondly, there are relationships between design variables.As Cárdenas (2007) noted, parametric design establishes the relationships betweenmodeling components defined by constraints, while Abdelsalam (2009) claims thatthe relationships are maintained by variations. In most cases, both constraints andvariations in combination help to define the relationships between the modelingcomponents. The entire parametric system will update when certain variables arechanged, because the defined relationships between them will lead to changes inother variables. However, a parametric system may become “over-constrained” ifthere is no effective control over the defined relationships (Burry 2003). Thirdly,the rule-based algorithms ensure that the parametric design process is flexible butcontrollable. By making rules, designers can produce variations that result in “fullyorganized controllable building forms” (Abdelsalam 2009). Fourthly, parametricdesign provides a formal process from which multiple design solutions can bedeveloped simultaneously and efficiently. Both Hernandez (2006) and Karle andKelly (2011) emphasize that to develop parallel ideas is one of the main advantagesin parametric design.

In summary, parametric design is a dynamic, rule-based design process con-trolled by variations and constraints, in which multiple design solutions can bedeveloped in parallel. It is especially effective in generating complex forms andoptimizing multiple design solutions. As a result, parametric design is usuallyutilized in complex building form generation and fabrication, structural and energyoptimization, and other design iteration and prototyping tasks. As a new digitaldesign method, parametric design is quite different from traditional CAD/CAMbecause of these rule-based algorithmic characteristics.

Parametric variations. In a parametric design system, variations are controlledby changing the values of parameters and constraints without necessarily altering


Fig. 1 Simplified examples of parametric variations generated in the same system

the original structure of the model (see Fig. 1 for different variations of a primitivegeometry generated by the same system). Variations can be single or multiple,independent from or interrelated with each other. Karle and Kelly (2011) arguethat as a new design method, parametric design does not push designers intogenerating the right design solution but, rather, into asking the right question,which can then be answered with multiple solutions. As a result, the selectionprocess of the generated variations is an important step in parametric design. Priorto selecting the appropriate variation(s), a typical workflow in parametric designalso involves identifying the design problem(s) and developing a series of rule setswith associative design variables, which can support a dynamic and flexible designprocess enabling the emergence of variations.

Design constraints have a significant role in directing the entire parametricprocess. They can be used by designers to describe and generate a range ofvariations and to define and control the unique characteristics of each. Constraintsset limits on parameters and control the possibilities for the range of variations.In parametric design, constraint satisfaction is important in the decision-makingprocess, connecting individual factors with the overall design outcomes. Thereare two basic forms of constraint – geometric and dimensional (Monedero 2000).Geometric constraints are properties that control how geometrical entities relate toeach other. Dimensional constraints are properties that can be assigned to a singularvalue, relating the geometry to a numerical value that fixes its behavior until itis changed or removed. An optimal parametric design process often requires thecomputational model to be well balanced, which is neither under-constrained norover-constrained (Monedero 2000).

Parametric modeling. Parametric modeling refers to specific techniques that“create design spaces and geometric dependencies within a model” (Gane andHaymaker 2009). It provides a formal descriptive and generative design framework(through parameters and their associative relationships), by which designers are ableto change the input values to generate and optimize the design with variations.The most significant advantage of parametric modeling is that it allows changesto be made to the parameters at any stage of the design process (Monedero 2000).Different parametric modeling techniques have been developed for visual purposes(i.e., form finding), as well as for other functional or performance-related purposes.Figure 2 demonstrates some typical parametric modeling techniques for formfinding, for example, repetition (Fig. 2, left) and subdivision (Fig. 2, right); othersimilar types of techniques can include tiling, recursion, weaving, etc.

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Fig. 2 Examples of parametric modeling techniques for form finding: repetition (left) andsubdivision (right)

Research further synthesizes and formalizes essential parametric modelingtechniques into “design patterns” (Woodbury et al. 2007). With these patterns, morestandardized approaches can be adopted in parametric design to address particularproblems. The advantage of these general patterns in parametric design is that“[p]atterns are a way to identify successful general strategies that exemplify a keyconcept in a memorable fashion that can easily be taught” (Woodbury et al. 2007, p.229). Parametric design patterns have since been proposed as abstract and reusabletools in parametric design. It is suggested that by using and learning these generalpatterns, architects and students alike are able to master parametric design moreefficiently and skillfully (Woodbury 2010) through abstraction and standardization.

ApplicationParametric design and form finding – Parametric design tools can capture andexplore critical relationships between design intentions and geometries. Designersinteract with the tools through rule algorithms to capture and manipulate theserelationships, as well as relationships among different design elements. For thepurpose of form finding, parametric design can be especially useful to facilitate themodeling process for complex geometries, and the integration of parametric toolsin design can also enhance flexibility and control during the process (Fischer et al.2003). To explore form finding in parametric design, some studies have focused ongeometrical modeling methods. For example, Hnizda (2009) suggested that therecan be at least two different geometrical modeling methods in parametric design –object extraction and transformation – each of which can be used to explore therelationships between formal aesthetics and functional properties. Others, such asBaerlecken et al. (2010), explored the issues through problem definition in theearly conceptual stage. To a large extent, the latter form-finding approach throughproblem definition is dependent on variation settings (Baerlecken et al. 2010),and through parametric variations they have explored functional and structuralproperties resulting from sunshading and to derive the final design form.

One of the most significant form-finding exercises using parametric design is the“Sagrada Familia” project. Gaudi’s Sagrada Familia cathedral is characterized bycurved sculptural surfaces that follow specific sets of principles. These embeddedrules in Gaudi’s design provide perfect opportunities for further design and analysis


Fig. 3 Selected examples of new garden plans generated using a parametric design system (Yuet al. 2015b)

using parametric tools (Roberto and Hernandez 2004). These rather simple geomet-ric rules and procedures can produce a rich formal language. Since the early 2000s,Professor Mark Burry (2003) and his team have developed and applied parametricsystems for modeling complex geometries in a major case study of Gaudi’s SagradaFamilia. The research later extended to aspects of fabrication and constructionaiming to complete the unfinished masterpiece. Their series of developments hasprovided important evidence of the effectiveness of parametric design for designingand analyzing complex geometries through rule algorithms.

Extending into landscape design, Yu et al. (2015b) applied parametric design toproduce new garden plans that are consistent with the style of Chinese traditionalprivate gardens, replicating selected socio-spatial characteristics of those heritagegardens. The socio-spatial characteristics of the original gardens were analyzedemploying various space syntax techniques, and the resultant mathematical mea-surements were then mapped into parameters and constraints in the system. Throughthe defined rule algorithms, the parametric system can generate new garden planswith similar spatial structures and connectivity values. Figure 3 shows selectedexamples of the newly generated garden plans using the developed system, on threedifferent given sites.

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Parametric design and design performance – As discussed earlier, beyondforms and aesthetics, parametric design tools can also respond to functionalor performance-related requirements. Such applications are mostly for structuralanalysis and building performance optimization (i.e., sustainability).

When using parametric tools for structural design, Maher and Burry (2003)compared parametric structural analysis with traditional approaches in a cross-disciplinary collaboration between architects and structural engineers. The combi-nation of structural analysis and parametric design not only enhanced the designprocess and result but also provided new platforms for collaboration across dis-ciplines. In a similar study linking architectural design to structural optimization,Holzer et al. (2007) investigated geometry generation with structural analysis andoptimization, which shows that parametric systems (supported by parameters, rules,and constraints) are effective for generating a variety of solutions for structuraldesign. Most of these works have been focused on analyzing the volume of structuralmaterials. ETABS is one of the popular structural analysis tools whose data can beimported into parametric design software. For instance, Almusharaf and Elnimeiri(2010) studied structural performance in high-rise building design by utilizingETABS in the parametric environment of Grasshopper. A design scenario waspresented in their study where instant feedback of structural performance couldbe provided during the parametric process to assist decision making and designgeneration.

One of the advantages of a parametric design system is that multiple analysescan be established and conducted in parallel within the same model to supportmore comprehensive optimization. Besides structural analysis, building perfor-mance, especially in terms of sustainability, is another important application ofparametric design. For instance, “multi-parametric façade elements” were proposedand examined by Schlueter and Thesseling (2008). In their study, the performanceanalysis of the façade offers instant assessment (in terms of the solar gain indifferent façade forms) during the design process, so that designers can betterimprove energy performance while generating design forms. In another study, aformal framework that combines parametric modeling with the “performance-baseddesign” (PBD) paradigm was proposed (Bernal 2011), aiming to standardize theparametric applications of building performance and providing real-time feedbackon the building performance index during the design process.

Collaboration in parametric design – With the continuing evolution andgrowing popularity of parametric design, researchers have begun to explore designcollaboration using parametric systems, including cross-disciplinary and distantscenarios. As discussed above, collaboration between disciplines using parametricsystems, for example, in structural design and analysis, can critically optimizesolutions using interdisciplinary knowledge. Cross-disciplinary collaboration isconsidered to be especially beneficial in the early design stage, and the use ofparametric design in the early design stage can effectively assist multidisciplinaryteams in problem finding, which in turn directs the generation and selection ofvariations during the parametric process (Gane and Haymaker 2009).


In terms of distant collaboration, Burry and Holzer (2009) explored the potentialfor sharing parametric models in a version control platform, which could be used bydesign teams located in different geographical locations. Rajus et al. (2010) used theparticipant observation method to study distant collaboration in parametric design.In their study, 18 participants were asked to perform different design tasks using theparametric software GenerativeComponents™ (GC). The study developed differentcontrols in collaboration and applied them in the experiments. The results show thatmoderately controlled collaboration can enhance the team performance and usersatisfaction in parametric design.

Implementation SoftwareTo date, quite a number of software packages have been developed and adoptedfor parametric design in practice. Most software supports free-form modeling, butalso has scripting plug-ins that enable designers to create rule algorithms moredirectly and freely. Some of these software packages are briefly introduced inthis section. Rhino + Grasshopper has been one of the most commonly usedparametric tools, especially in architectural design, while Digital Project (DP)and GenerativeComponents™ (GC) are more tailored for large-scale projects withcomplex parametric and geometric associations.

Computer Aided Three-dimensional Interactive Application (CATIA) was firstdeveloped in 1977 by French aircraft manufacturer Dassault Aviation. Thereafter,it was applied in aerospace, automotive, shipbuilding, and other industries for itscapabilities in controlling and manipulating complex geometries, as well as itssupports for manufacturing accuracy. Multiple versions of CATIA have since beendeveloped to perfect the commercial uses, and at the same time it has graduallyentered the architectural field. Based on CATIA 5.0, Gehry Technologies developedDigital Project (DP), which specifically aimed to service architectural design. DPhas been known as a very powerful parametric software package that can effectivelyhandle complex parametric as well as geometric associations, which makes it idealfor large complex parametric design projects.

In 2005, GenerativeComponents™ (GC) was developed by Robert Aish forBentley Systems. GC implements parametric concepts across the entire designproject life cycle, from the early conceptual phase to the final documentation. Inaddition, GC has been integrated with Building Information Modeling (BIM) aswell as other analysis and simulation platforms for design evaluation and optimiza-tion. Such integration can potentially make parametric design more targeted andrealistic, effectively linking design conceptualization with production, fabrication,and construction.

Rhinoceros (Rhino) is a stand-alone, NURBS-based 3D modeling tool. It wasdeveloped by Robert McNeel and has since been widely applied in a range ofdomains, including architecture, industrial design, jewelry design, automotive, aswell as marine design. Grasshopper, on the other hand, is a rule-algorithm editorwith a graphic interface, which can be integrated into Rhino as a scripting plug-in.It is structured with specific definition files that link to the main parametric modelin Rhino. Usually Grasshopper is used as a generative tool rather than a modifier

16 N. Gu et al.

during the parametric design process. Compared to other parametric software, Rhino+ Grasshopper has been much more widely adopted in both practice and educationat the present time. This is because of its ease of operation as a visual programmingtool (supported by the graphic rule-algorithm editor) as well as its relatively lowcost.

Scripting uses computer programming languages such as Java and Visual Basic(VB) to directly interpret and execute commands. It can establish and controlparameters and translate design intents into codes that are easily identified bya computer. Consequently, designers (with fluent scripting skills) can define andcontrol the logics and rules for parametric design in a way that allows them morefreedom than any other tools. Common scripting languages include Python, VB,and Ruby, while scripting tools include Python Script, RhinoScript, Processing, andCADscript.

There are also several design analysis tools, which are often used togetherwith parametric software. For example, Ecotect is used for analyzing energyperformance, while ETABS is used for structural analysis. These analysis toolsare capable of exporting analysis data into parametric software to direct designgeneration and optimization.

Reshaping Architectural Design

Impact on Architectural Design

Designers’ activities change in a parametric design environment compared to thosein a traditional CAD environment. Firstly, designers design rules and define logicalrelationships of the design rather than only modeling geometries. One of the biggestdifferences between parametric design and traditional computer-aided design isthat rule sets become basic design elements and procedures in parametric design(Abdelsalam 2009). While building parametric models, designers set variations,design data flows, and define and adjust rules as well as the values of parameters.They are not only required to think about a particular building design but also therule sets that generate and underpin the design. Additionally, through the controlof these logical relationships, parametric design ensures many more possibilitiesfor the generated solutions (Hernandez 2006; Karle and Kelly 2011). Secondly,architects can easily trace back through the parametric design process and are freeto make changes in any steps of the process. During parametric design, through thedefined rule algorithms, systems are clearly differentiated and correlated, and designactivities are clearly communicated with each other within the process (Schumacher2009). Therefore, designers are able to go back to any step along the process tochange parameters or revise rules in order to modify the design process for differentpurposes or to trial different variations. This level of flexibility allows architectsto keep the design “open.” Thirdly, a large number of design alternatives can bedeveloped in parallel. Traditionally, designers consider a very small number ofalternatives because of time or memory limitations (Woodbury and Burrow 2006).


Fig. 4 A large number of form variations generated in a parametric design system

Therefore, as Akın (2001) has argued, design solutions are not usually optimal, butonly satisfactory, according to a preset level of aspiration. In parametric design, oncethe rule algorithms are established, a large number of design alternatives may begenerated (see Fig. 4, for instance). This rapid design prototyping can significantlyexpand the design possibilities and widen the designer’s thinking. Further, designersdo not need to predetermine or fixate on any solutions at early stages (Hernandez2006; Holland 2011; Karle and Kelly 2011), which allows the maximum potentialto be maintained in the process, until the final design solution is achieved andevaluated.

Parametric design offers not only a new computational design tool but also a newway of design thinking. Generally, design is an abduction process in which both thefinal artifacts and their behaviors are designed or defined (Dorst 2011). In parametricdesign, Yu et al. (2015a) suggested that designers’ behavioral patterns shift betweentwo levels of activities – the design-knowledge level and the rule-algorithm level(Fig. 5). During a typical parametric design process, there are design activities thatoccur on both levels. At the design-knowledge level, architects make use of theirdesign knowledge, including, for example, how to adapt a building to the site, howto shape the way people use the building, and how to satisfy other requirements oftheir clients. At the rule-algorithm level, designers apply design knowledge throughthe operations of various parametric design features, including defining the rulesand their logical relationships in the design, choosing the parameters suitable fora particular purpose, and importing external data into the system to direct andevaluate the generation. During the parametric design process, designers progressby applying specialist knowledge, and in some parts (namely, at the rule-algorithmlevel), they apply design knowledge indirectly through rule algorithms. As observed

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Fig. 5 Two types of designspaces in a parametric designenvironment

by Yu et al. (2015a), designers often start from the design knowledge level, thenas the design proceeds their activities at the rule algorithm level can rise, whilethose at the design knowledge level can decrease but do not cease. This implies that,although rule algorithms in parametric design are the focus and offer many advan-tages, such as the support for design flexibility (Fischer et al. 2003) and a capacityto deal with design complexity (Leach 2008), nevertheless design knowledge stillappears to be essential during parametric design. These preliminary findings byYu et al. (2015a) have implications for the practice and teaching of parametricdesign in architecture. Although training for programming/scripting skills is ofcourse important, training for design thinking is also vital. As designers substituterule algorithm for design knowledge during parametric design, understanding howdesign knowledge is expressed in rule algorithms in parametric design is important.It has been noted that, in terms of high-level design thinking, designers’ cognitivebehavior does not significantly vary because of the computational tools adopted (Yuet al. 2013).

Limitations of Parametric Design

Parametric design has been widely practiced in recent years, and its characteristics,such as design flexibility and controllability, have rapidly escalated its popularity(Barrios 2005; Fischer et al. 2005; Salim and Burry 2010). However, a numberof limitations have been reported. Firstly, parametric design requires relativelyhigher acquisition and implementation costs. Some large-scale and more complextasks also require additional and specialized computing power. Therefore it can bedifficult for small-scale design firms to adopt parametric design. Secondly, a typicalchallenge of using parametric design is how to select appropriate variations. Peñaand Parshall (2001) have argued that problem finding is the most important part ina design process, and only by defining problems appropriately would problems besolved. In parametric design, defining variations is critical to representing designconcepts. Variations support design flexibility and the possibility to develop ideasin parallel. Designers benefit in having multiple variations, and this only makes


sense when the system can adequately and appropriately capture and represent theproblems. For example, some design factors such as Energy Conservation Index(ECI), budget, architectural building codes, and structural requirements can be quiteeasily quantified and integrated into the parametric system. However, other factorssuch as aesthetics, historical context, and social interaction are difficult to measureand represent in the system. As a result, architects’ critical thinking (by applying therelevant design knowledge) is still important even with the use of parametric designtools. Thirdly, parametric design without careful implementation can sometimeslead to excessive or unnecessary complexity. Over-pursuing forms and appearancescan make some parametric design projects appear to be superficial and lackingcontextualization. After all, for architecture, the complex form should come fromthe complex needs and behaviors of people rather than the pure urge for “bizarre”appearances (Leach 2008).

Conclusion

As one of the most frequently applied computational and generative design systems,parametric design plays an important role, especially in various leading architecturalpractices. This chapter has presented the theoretical development of parametricdesign, discussing its connection to generative design in general, together with ahistorical review and a basic introduction of the key concepts and applications.

Parametric design has significant impact on architecture. Firstly, parametricdesign provides a formal framework and computational means for generating andmanaging complex and dynamic building forms that have never been easily andadequately achieved (by traditional CAD tools). This has opened up intellectualdebates about new aesthetics, styles, and movements in contemporary architecture.Secondly, parametric design promotes collaboration. With parametric design tools,as well as the integration of other specialization tools for performance analysis, wehave witnessed increasing and more integrated teamwork between architects andother experts for design optimization. Thirdly, through defining rule algorithms,parametric design adds and controls rationality in architectural design, which canassist designers in making more informed decisions to achieve more superioroutcomes.

From the designer’s perspective, parametric design tools provide architects withopportunities for designing at both the design knowledge and rule algorithm levels,which opens up many new possibilities, as discussed throughout the chapter. At thesame time, new challenges also emerge. First and foremost, the role of architectsis changing, such that they need to be both architects and programmers/scripters.The fact that architects can directly encode designs as computer languages can beboth efficient and constraining. Constantly switching between activities of designknowledge and rule algorithm during parametric design can also affect an architect’sdesign cognition, which should be carefully considered when designing parametricsystems and facilitating them in practice and in education.

20 N. Gu et al.

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� Shape Grammars: A Key Generative Design Algorithm

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Parametric Design: Theoretical Development and Algorithmic Foundation for Design Generation in ArchitectureContentsIntroductionGenerative DesignCommon Characteristics of Generative DesignMain Generative Design SystemsGenerative GrammarsEvolutionary SystemsEmergent and Self-Organized SystemsAssociative Generation

Parametric DesignHistorical Review of Parametric DesignOrigin of Parametric DesignDevelopment of Parametric DesignParametricism

Parametric DesignKey Concepts and TerminologiesApplicationImplementation Software

Reshaping Architectural DesignImpact on Architectural DesignLimitations of Parametric Design

ConclusionCross-ReferencesReferences

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