Responsive Algorithms: An investigation of computational processes in early stage design

Frano Ba탑alo

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0.1 Acknowledgements I have been extremely fortunate to have all of the support that I have received throughout my Architectural Studies. Firstly, I would like to thank my supervisors, Professor Jules Moloney and Tane Moleta. Their guidance and enthusiasm has allowed me to explore the areas of Architecture I am truly passionate about. This thesis would not have been possible without their expertise and encouragement. I would like to thank my close friends and fellow students who have assisted in getting me through the last five years. Your company and support has kept me sane. A special mention to Chris Welch for his technical expertise, rescuing me whenever the algorithms got the better of me. Finally, endless gratitude to my family, the Gallegoâ€™s and girlfriend Necane. You have ultimately made this whole experience possible with your love and support in pursuit of my dreams. Forever grateful.

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1.0 Algorithmic Architecture

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1.1 Abstract 8 1.2 Computation in Design Practice 10 Potential for Computation in Architecture A Position of Terminologies: From Parametric To Algorithmic

2.0 Research Proposal 2.1 Proposition, Scope and Research Question Research Question

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15 16 16

2.2 Methodology 17 Tools Evaluation Criteria

3.0 Early Stage Design 3.1 Defining Early Stage Design

4.0 The Voronoi Algorithm 4.1 An Introduction to Voronoi 4.2 Voronoi and Contemporary Design

5.0 Architectural Voronoi Precedents

17 18

21 22

25 26 27

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5.1 2D Voronoi Precedents

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5.2 3d Voronoi Precedents

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Water Cube – Beijing Olympic Aquatics Centre Voronois Corrals – DEC.Architecutre Glorieta Juan Carlos I / ESC Studio The Serpentine Sackler Gallery / Zaha Hadid Architects Bubble Skyscraper/M&A Architects UN Memorial / ACME Vertical Village: A Sustainable Way of Village-Style Living

6.0 Exploration Phase 1 - Responsive Network – Urban Application

6.1 6.2 6.3 6.4 6.5

30 31 32 33 34 35 36

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Public Transport 40 Design Problem 41 Design Description 44 Voronoi Zoning 48 Review 52

7.0 Exploration Phase 2 - Southern Transport Hub

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7.1 Brief 56 7.2 Space Planning With Voronoi 59 2D Voronoi 3D Voronoi Algorithmic Voronoi Sectioning Culling Cell Division And Space Articulation

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60 62 63 64 65

7.3 Structural Resolution Panelising Space Frames Voronoi Skeleton

66 66 67 68

7.4 Review 69

8.0 Exploration Phase 3 - Algorithmic Bus Shelters

8.1 8.2 8.3 8.4 8.5

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Aim - Intuitive Logic 90 Brief 91 Cell Culling 92 Iterative Optimisation 93 Circle Packing 94 Metaball

8.6 Space Syntax 8.7 Interpreting Site 8.8 Form Finding

Catenary Mesh Relaxation Stress + Deformation Development

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98 100 101 101 102 103

8.9 Seating 105 8.10 Review 106

9.0 Exploration Phase 4 - Northern Transport Hub

9.1 9.2 9.3 9.4 9.5 9.6

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Brief 122 2D - 3D 124 Internal Voronoi Divisions And Floors 127 Form Optimisation 128 Revisiting 2D-3D Transformation 129 Review 132 Input of the Algorithm - Restating of Design Intention

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10.0 Algorithm Refinement

151

11.0 Final Discussion

185

11.1 Conclusion 186

12.0 Bibliography Works Cited List of Figures List of Animations

13.0 Appendix Appendix A - Transport Canopy Construction Drawings Appendix B - Developed Algorithms

189 190 196 200

203 204 218

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1 1.0

Algorithmic Architecture

1.1

1.1 Abstract An algorithm is a process of addressing a problem in a finite number of steps. It is an articulation of either a strategic plan for solving a known problem or a stochastic search towards possible solutions to a partially known problem (Terzidis, 2006). In the context of architectural design, algorithmic thinking means taking on an interpretive role to understand the results in relation to design criteria, knowing how to modify the code to explore new options, and speculating on further design potentials (Peters, 2013). The majority of applications of algorithms in architecture address the developed design stages, primarily to optimise structure, test environmental performance or to resolve complex construction. This dissertation aims to explore algorithmic tools with a focus on early stage design. This design stage is often developed using traditional processes and is where algorithmic applications have been less successfully executed. This research targets the Voronoi algorithm, as it has become the â€œgolden-meanâ€? of computational architecture (Stefanescu 2010). The objectives are to explore the specific uses and limitations of Voronoi algorithms within early stage architectural design. This includes space planning, programme layout, form finding and form optimisation as defined in the literature reviews. This is the scope in which Voronoi methods are tested, with the ultimate aim of integrating a computational workflow into practice at the early design stage through the simultaneous calculation of a range of algorithms.

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The primary methodology employed is research through design. In order to provide a range of scales and programmatic contexts to test the robustness of algorithms, the sketch design of a public transport proposal for Wellington City is undertaken. The design of the overall transport network, a regional interchange hub, and a medium scale bus shelter enable the development of a range of approaches in which additional algorithmic tools are explored to supplement the use of Voronoi. In order to demonstrate how these sketch designs can be translated, construction drawings are undertaken for the shelter. The three design cases allow the development of a range of techniques that enable a mix of intuition and automation. These techniques are bought together and further refined in a fourth design case, a second transport hub sited in a complex urban context. In conclusion, a working method for employing algorithms that are responsive to the pragmatics of context and the subjectivity of the designer is demonstrated. The designs embed a personal predisposition for curvilinear geometry, but the method can be adapted for other types of geometry. Differentiating between existing algorithmic self-organisation techniques, the approach developed permits subjective input from the designer, allowing outputs to be tweaked and enhanced based on the perspectives and opinions of the creator.

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1.2

1.2 Computation in Design Practice The idea of using computers for form generation and evaluation in the architectural design process was put forward in the early days of computers. However, as opposed to computer aided drafting, the generation of form, its optimization and manufacturing, has not yet been widely accepted and implemented by practitioners (Grobman, Yezioro, & Capeluto, 2009). Computational processes have been largely inducted into architectural practice as a drafting technique to simply digitise preconceived designs, not as a true partner in the process of conception (Picon, 2010). “Architects use the computer as a virtual drafting board making it easier to edit, copy and increase the precision of drawing” (Terzidis, 2006). However in order to reduce the time spent on the transition from the early design stage to more precise stages, increasingly more architects are starting to use CAD programmes in all stages with mixed results. As Aliakseyeu et al observe - “The down side of this practice is that the use of such precise programmes in the early design stage tends to limit the creativity and can encourage poor design” (Aliakseyeu, Martens, & Rauterberg, 2006). A number of influential thinkers have stated that the core of architectural thinking is still totally dependent upon the designer’s intuition (Picon, 2010). Despite this, a review of current literature reveals that increasingly architects are developing computational tools that create opportunities in design process, fabrication and construction (Peters, 2013, p. 10). For the past 10 years, emerging computational tools and techniques have had an increasing impact on architectural design (Agkathidis, 2012). Architects and students of architecture are experimenting with ways to embed digital methods into the design process, exploring new possibilities and challenges. We are moving rapidly from an era of being aspiring expert users, to one of being adept digital toolmakers (Burry M. , 2011, p. 8). Firms such as MOS and Facit Homes have fully integrated computation into practice and the actual design process. In these firms there is no separation between design intent and computational technique. Computation is used in a natural or unconscious way (Peters, 2013, p. 11).

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Many architects in practice still prefer to use paper and pen or scale models during the early design stage (Gross and Yi-Luen Do, 1996; Aliakseyeu, 2003). Use of these forms of media offers the required ﬂexibility, speed and natural (intuitive) interaction (Aliakseyeu, Martens, & Rauterberg, 2006). This way of working, however, has been cited by Aliakseyeu as creating an interruption in the flow of the design process, since the architect has to transfer their design into computer-aided design (CAD) speciﬁcations after the early design stage. (Aliakseyeu, Martens, & Rauterberg, 2006). Potential for Computation in Architecture As computational methods graft themselves into an industry-wide digital workflow, algorithmic and generative techniques have gained traction within practice. An unprecedented volume of research has centred on the methodology behind these emerging design tools with the emergence of the term parametric design as a generic description. Reaction to parametric design ranges from enthusiastic endorsement to open criticism; many are intrigued due to its potential complexities (Shireen) while others are more sceptical (Grobman, Yezioro, & Capeluto, 2009). While theorists and practitioners like Greg Lynn, William Mitchell, Peter Eisenmen or Frank Gehry endorsed the new perspectives opened by digital tools early on, others like Kenneth Frampton or Juhani Pallasmaa have been more reserved about them (Picon, 2010, p. 8). Dr. Elie Haddad of the Lebanese American University states that his scepticism is based on the “general euphoria that has accompanied the digital ‘revolution’ in architectural design, the effects of which have not yet translated into a ‘real’ improvement in the quality and nature of the built environment” (Agkathidis, 2012). In my opinion, the industry’s general scepticism is attributed to a misconception based on the architectural results and even the aesthetic that is now associated with parametric design.

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Leach observes, “many people have misgivings about the term parametric” (Leach & Schumacher, 2012). Peters states much of the industry’s ill-fated impression of parametric design has come from both the increase of availability of these tools, paired with an uneducated understanding of the algorithmic processes behind the “black box” (Peters, 2013). Many critics blacklist “parametrically” designed buildings from the beginning as scripting often veers towards complexity of otherwise quite simple things (Burry M. , 2011, p. 40). A number of influential thinkers have stated that it is clear that computation enables new ways of thinking (Peters, 2013, p. 15) but furthermore, computational accomplishment requires a greater algorithmic, mathematical or even scientific understanding which the current architectural curriculum does not always possess (Legendre, 2011, p. 76). Casey Reas has expressed the need for the education system to start teaching procedural literacy from an early stage. Students would then be able to build on these skills to focus on the context of architecture (Burry M. , 2011, p. 43). Similarly, Robert Aish expresses in an interview with Burry, that what is far more important than the mechanics of scripting is for students to be able to think algorithmically (Burry M. , 2011, p. 44). This necessitates the ability to procedurally decompose a problem into composite elements and formulate a logic to interpret and process the quantified information in order to solve the given problem. While the connotation of an algorithm may be associated with computer science, architectural practice is no stranger to the use of instructions, commands, or rules used to deal with the complexities of architecture. Terzidis states these are in essence algorithms (Terzidis, 2006). To conclude, there are a range of views on the potential for computation to transform architectural design. My position aligns with that of Peters - that computation can assist the architect in the design process, extending the designer’s abilities to deal with highly complex situations (Peters, 2013, p. 10). Ultimately, they could perhaps help change the way architectural design is undertaken 12

in an increasingly complex, data-driven society. The potential lies in the possibility for factual parameters to be incorporated in the design process alongside the designers intuition and formal predisposition: parameters that scientiﬁcally deal with population growth, sustainability, site constraints and regulations, and other issues allowing the exploration of all possible solutions to given problems (Agkathidis, 2012). A Position of Terminologies: From Parametric To Algorithmic The term ‘parametric’ has emerged to describe computational approaches to designing. My observation is that this is an inaccurate label that has become a convenient way to describe a range of activity that is generally not well understood within mainstream practice and architectural critique. Burry, Peters, and Terzidis have stated that all architecture is parametric. These authors note that the practice of Architecture is a physical output resulting from a set of given input parameters. From a purely personal position, I am less concerned with the name, but this general misconception reflects the industry’s current understanding of these design tools. In the context of this thesis I propose that these tools are more accurately denoted as algorithmic design tools:

·

Algorithm - a step-by-step procedure for calculations used for data processing and automated reasoning.

An algorithm is a process of addressing a problem in a finite number of steps. It is an articulation of either a strategic plan for solving a known problem or a stochastic search towards possible solutions to a partially known problem (Terzidis, 2006). Theoretically, as long as a problem can be defined in logical terms, a solution may be produced that will address the problem’s demands (Terzidis, 2006). Algorithmic thinking means taking on an interpretive role to understand the results of the generating code, knowing how to modify the code to explore new options, and speculating on further design potentials (Peters, 2013).

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2 2.0

Research Proposal

2.1

2.1 Proposition, Scope and Research Question This thesis proposes that a computational design workflow provides designers with a greater capacity to explore designed outcomes. It argues a complexity of design issues can be interpreted simultaneously while generating results that otherwise might not have been reached using traditional methods. Algorithmic design tools offer the power of computational iteration, which enables multiple design permutations to be undertaken in a short time span. Moreover, I propose that some of the problems associated with a computational approach to design, in particular the capacity to enable subjective input from the designer, can be addressed. This proposition is captured by the phrase ‘responsive algorithms’. The scope of the thesis is on the early stages of design. The aim is to explore how a combination of algorithms can be used for the simultaneous creation, analysis and optimisation of design ideas. The early design stage includes space planning, programme layout, form finding and form optimisation as defined in the literature reviews by Burry, Peters, Picon, and Terzidis. Additionally the research focuses on the potential uses and limitations of Voronoi algorithms. The Voronoi algorithm has been described as “the ‘golden mean’ of computational architecture” (Stefanescu, 2010) and in my view, offers much potential for the early stages of design. Research Question This research is fundamentally concerned with the relationship of contemporary digital design tools and how they can be used for designing. From the scope outlined above, the specific research question that provides a focus for the thesis is:

·

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How can Voronoi algorithms be used to augment the design workflow within early stages of architectural design?

2.2 Methodology The primary methodology employed is research through design. In order to provide a range of scales and programmatic contexts to test the robustness of algorithms, the sketch design of a public transport proposal for Wellington City is undertaken. The design of the overall transport network, a regional interchange hub, and a medium scale bus shelter enable the development of a range of approaches in which additional algorithmic tools are explored to supplement the use of Voronoi. In order to demonstrate how these sketch designs can be translated, construction drawings are undertaken for the shelter. The three design cases allow the development of a range of techniques that enable a mix of intuition and automation. These techniques are brought together and further refined in a fourth design case, a second transport hub sited in a complex urban context.

2.2

Tools In the present marketplace there are several algorithmic platforms including: Maya, 3DS Max (via plugin), Rhino Script, Processing, Dynamo. Currently Grasshopper® has the largest market share, frequently cited by both practitioners and researchers. Grasshopper permits an algorithmic workflow with direct application to architectural design process. Brady Peters states in the Computational Works edition of AD, “Grasshopper has become a true design tool within the office” (Peters, 2013, p. 93). Grasshopper’s visual programming language has propelled the increased usage of computation in practice (Peters, 2013, p. 10). Based on these criteria I propose it is the most suitable platform for this study. Having over five years of experience with digital design in an academic setting using a wide range of platforms, the decision to use Grasshopper as the primary setting for this thesis is additionally informed by experience.

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Evaluation Criteria The components created in the technical studies will be individually rated on its balance between dynamism vs. function. Each technical study works towards providing the final algorithm with a balance of dynamic programme and form, while working towards complete functionality of the design. This scale will be used to reflect and refine the processes developed throughout the research, working towards a final tool for early stage design. The slider illustrates a balance between dynamism and function. The degree of dark blue displays the components success to each of these criteria. Perfection would be illustrated by a balanced spread of dynamism and function and filled with a broad band of dark blue. Less successful applications will be skewed to one end, and/or a thin band of blue will be present. dynamism

function Thin Band, Equal Balanced

dynamism

function Thin Band, Skewed

dynamism

function Thin Band, Heavily Skewed

dynamism

function Broad Band, Balanced

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To assess the design outcomes of each exploration phases, a matrix has been developed based on the published theoretical positions of Burry, Hillier, Schumacher, Anderson & Tang.

· · · ·

“Spatial Arrangement” This is a term used to define the spatial and volumetric concerns inside the structure (Schumacher, 2009). “Programmatic Arrangement” This is used to define relationships between the functional programmatic aspects of the building (Hillier, Space is the Machine - Space Syntax, 2007). “Formal Composition” This term is used to evaluate the relationship to external volume and siting in the built environment (Burry). “Constructability” Ability to convert design into Developed Design State (Anderson & Tang, 2011).

DESIGN ANALYSIS MATRIX spatial arrangement programmatic arrangement formal composition constructibility

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3 3.0

Early Stage Design

3.1

3.1 Defining Early Stage Design Early stage design is a broad term all designers understand but seem to struggle to quantify unanimously (De Biasse & Seminara) (RIBA) (AIA) (NZIA). For the purpose of this research, I have reviewed several key sources ranging from architectural practitioners to architectural institutions. I have also sampled a range of influential theories to assist in defining early stage design. This will be used to develop a definition of â€œearly stage designâ€? for which future design investigations can be evaluated against.

Research prepared by De Biasse & Seminara, states that the architectural design and delivery process can be simplified into five phases: ConsumerBuild NZ, is an organisation of the

1. Schematic Design 2. Developed Design 3. Construction Documents 4. Bidding 5. Construction Administration

Ministry of Business, Innovation & Employment and Consumer NZ. They present an article aimed at explaining the design process to clients. The design phase is broken into three stages with the first step categorising early stage design (ConsumerBuild NZ, 2010).

1. The initial sketch plans

The Royal Institute of British Architects (RIBA, 2012) defines the design process as:

1. Brief

concept, preliminary or discussion drawings

2. The developed designs 3. The final documentation tender, building consent, construction or working drawings and specifications

2. Concept Design 3. Developed Design 4. Production 5. Installation

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Despite the many possible ways of dividing the design process, this literature review describes a common stage that all processes require: an initial phase of conceptual design. It is this early design phase that Fleming and Woodbury state “specifically addresses architectural programming, schematic layout design, and the generation of a fully three-dimensional configuration of physical building components like structure and enclosure” (Flemming & Woodbury, 1995). “In the schematic design phase the overall characteristics of the building are established. Significant issues are identified, and initial design decisions are made” (Dace & Maxwell Wells, 1996). The significance of early stage design operates as the genus for the design of a building.

1. Schematic Design 2. Design Development 3. Construction Documents

The American Institute of Architects follow a similar structure (AIA).

4. Bid Phase 5. Constructions / Administration

1. The project brief 2. Pre-design 3. Concept design 4. Developed design

The NZIA: Guide to Architects Services provides a lengthier process aimed at a suggested fee structure. This list helps in clarifying some of the broader terms used in the above examples (New Zealand Institute of Architects Incorporated).

5. Planning approval 6. Detailed design 7. Building consent 8. Project procurement 9. Contract administration 10. Project observation 11. Completion 23

Dragonfly Wing

Girrafe Skin

Dried Mud

Human Bone Tissue

Insect Wing

Cow Stomach

7.

.

4 4.0

The Voronoi Algorithm This section describes the capacity of computational design to act as a powerful tool for contemporary design practice. The section identifies a singular aspect within algorithmic design practice that has attracted increasing interest in the research community. I propose that this presents an outstanding opportunity for early stage design.

4.1

4.1 An Introduction to Voronoi The Voronoi diagram is described as the division of a space into contiguous cells (Weisstein, Voronoi Diagram, 2010). Each cell corresponds to a generating “seed” or point which is closer to that site than to any other (Burry & Burry, 2010, p. 226). Each cell is obtained from the intersection of half-spaces creating convex polygons. The segments of the Voronoi diagram are equidistant to the two nearest sites while the Voronoi nodes are equidistant to three (or more) sites. The distribution nature of the points determines the pattern and shape of the cells. This may vary from a random polygon tiling to a highly ordered periodic pattern (fig.1) (Burry & Burry, 2010, p. 112).

Voronoi Grid Variation fig.1

The Voronoi diagram is one of those mathematical peculiarities, like fractals and Fibonacci spirals, that turn up frequently in the natural world (Taylor, 2010). Examples include turtle shells, cow stomachs, leaves, microscopic cell structure and compact bone tissue, dragonfly wings, to even the way mud cracks when it dries up (Stefanescu, 2010). The Voronoi diagram wasn’t however considered mathematically or spatially until 1644 by René Descartes, and further in 1850 by Dirichlet with the investigation of positive quadratic forms (Weisstein, Voronoi Diagram, 2010). Later Georgy Voronoy (1907) extended the investigation of Voronoi diagrams to higher dimensions. They find widespread practical and theoretical applications in areas such as computer graphics, epidemiology, geophysics, and meteorology (Aurenhammer, 1991). A particularly notable application of a Voronoi diagram was the analysis of the 1854 cholera epidemic in London, in which physician John Snow determined a strong correlation of deaths with proximity to a particular (and infected) water pump on Broad Street (Weisstein, Voronoi Diagram, 2010). 26

4.2 Voronoi and Contemporary Design As an area of research, the Voronoi diagram is one of the most over-used, imitated and abused algorithmic design processes within architecture. I can personally confirm it is the go-to tool for many aspiring parametric designers. It has now “become the ‘golden mean’ of computational architecture” (Stefanescu, 2010). Architectural critics have become exasperated to such an extent that the programmers of Grasshopper have now included a pop-up notification for anyone wanting to use the component. Despite the overuse of the Voronoi algorithm, primarily for 2D surface articulation, I believe there is much untapped potential for its application to space planning, programme layout, form finding and form optimisation at the early stages of design.

4.2

Excessive use of Voronoi Diagrams has been associated with: - Creative gland atrophy -Loss of critical thought -Confused or nonsensical speech -An inability to get taken seriously -A marked increase in pyrrhic victories -Temporary euphoria followed by prolonged self-loathing -Vitamin Cleaver efficiency -Blurry artistic vision.

“Ask your supervisor if Voronoi is right for you” Grasshopper Voronoi Notification fig.2

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5.

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Voronoi Precedents You don’t have to look far to find a surplus of architectural precedents employing Voronoi algorithms. In saying that, most Voronoi applications are only skin-deep, serving as an aesthetic computational façade. As opposed to these arbitrary façade patterns, on an urban scale, the cells tend to have a direct relationship with their size, arrangement and programming intentions. Hence, historically, successful Voronoi programming and planning applications are on a much larger scale, for example, Snow’s cholera study (Weisstein, Voronoi Diagram, 2010). This section is used to demonstrate a number of examples that optimise Voronoi for its planning and programming potentials on an architectural scale.

5.1

5.1 2D Voronoi Precedents Water Cube – Beijing Olympic Aquatics Centre The Water Cube, while visually representative of a Voronoi diagram, is more accurately categorised by the Weaire–Phelan structural algorithm (Weaire, 2008). Weaire– Phelan is a complex three-dimensional structure representing idealised foam. While algorithmically different to the Voronoi, it exposed computational methods in architecture to a global audience. The Water Cube strangely erroneously sparked an interest in Voronoi diagrams as designers attempted to replicate or experiment with similar structures (Grasshopper 3D).

Beijing Olympic Aquatics Center fig.3

WATER CUBE

spatial arrangement programmatic arrangement formal composition constructibility

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Voronois Corrals â€“ DEC.Architecutre Voronois Corrals by DEC.Architecutre is a coastal building located on the island of Milos in Greece. The site is protected by the European treaty Natura, which states that buildings must be smaller than 250sqm (ArchDaily, 2012). Due to this restriction, the site was investigated with an aim to expose micro-environments that might yield the most optimal locations for a variety of uses. Considerations for making these assessments took into account the sun trajectories, the prevailing winds, the views, the sound of the sea, the geological morphology and the vernacular flora (ArchDaily, 2012). These locations were the points that were chosen to stimulate the proposition, forming a non-Cartesian grid. This Voronoi grid defined the geometric structure of the designersâ€™ interventions, from the planting schedule, to the space layout, to even the floor pattern. This is one of the more successful and tastefully executed uses of the Voronoi equation. Its success is not in the form but the way various programmes were distributed across the site. This stems from the initial manner in which Voronoi was used for planning and programming in the early design stage.

Voronois Corrals fig.4

Voronois Plan fig.5

VORONIS CORRALS

spatial arrangement programmatic arrangement formal composition constructibility

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Glorieta Juan Carlos I / ESC Studio The Glorieta Juan Carlos I, by ESC Studio, is an interesting use of Voronoi. While Voronoi was exploited for its aesthetic appeal, the designers also harnessed the algorithmâ€™s dynamic capabilities for use in the early design stages. The algorithmic space planning technique subdivided the space into circulations and activity areas. This use of Voronoi was ESCâ€™s initiative to allow the community to be involved in the design process. The algorithm allowed an interactive public consultation process, taking place in Mula in December 2009 (ArchDaily, 2010). It gave the citizens the opportunity to actively participate in the design process by proposing their own design ideas, all of which were facilitated by the Voronoiâ€™s ability to adapt. This unique early stage design phase provides an interesting quality to the proposal.

Glorieta Juan Carlos I - Render - fig.6

GLORI ET A JU AN C ARL O S spatial arrangement programmatic arrangement formal composition constructibility

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Plan fig.7

The Serpentine Sackler Gallery / Zaha Hadid Architects The organic form and layout of the Serpentine Sackler Gallery by Zaha Hadid Architects characterises both Hadid as well as the general forms of digital architecture. With more organic layouts, orthogonal organisation is no longer applicable. The use of Voronoi in The Serpentine Sackler Gallery is both subtle and effective. It wasnâ€™t employed for its aesthetic merits but merely as an effective way of dividing space. The tables, banquets and chairs are designed as a continuous Voronoi pattern, reminiscent of organic cell structures (ArchDaily, 2013). The success of the Voronoi in this example comes from the fluid nature of the table and chair arrangement. Voronoi is based on living entities which in turn are dynamic. This active process is replicated in the way these objects are moved around the space.

Serpintine Sackler fig.8

Plan fig.9

SERPENTI NE S A CK LE R spatial arrangement programmatic arrangement formal composition constructibility

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5.2

5.2 3d Voronoi Precedents Two-dimensional and three-dimensional Voronoi diagrams, while similar in theory, are contrasting in architectural application. The examples thus far have been two-dimensional. Their success has been in the ability to organically divide spaces based on varying parameters. Three-dimensionally, the Voronoi offers extremely interesting conceptual forms but equally awkward and inefficient divisions of space. The core reason for this is that in 2D, the Voronoi is mapped on a perpendicular or on an inhabitable surface. In 3D, the Voronoi division is mapped in all three axies, with algorithmically no intention of an inhabitable space. This results in non-orthogonal spaces, in particular angled “floors.” As a result, 3D Voronoi is often used to generate external form, but its internal partitions, the fundamental process of the algorithm, are often ignored. Bubble Skyscraper/M&A Architects

Section fig.10

Render fig.11

BUBBL E S K YSC RAPER

spatial arrangement programmatic arrangement formal composition constructibility

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The “Bubble Skyscraper” by M&A Architects is an example which epitomises this three dimensional struggle. “After studying bubble constructions, we created a 3D computer model to find the junctions between the bubbles and find out how bubbles could sit beside each other” (ArchDaily, 2010). Despite their reasoning, in the section, you can see they have gone about legitimising the Voronoi cells through a manual process of inserting floors. The Voronoi has provided a shell and general zones, but has required intervention from the designer during the early stage design phase to assist in providing a programmatically feasible proposition. I am not criticising this technique, merely bringing to attention some of issues other designers have had to deal with in attempting to use Voronoi in early stage design.

UN Memorial / ACME A different approach is taken for UN Memorial by ACME where, while it appears to be a “true” 3D Voronoi tessellation from the exterior, in plan we start to understand this is all a façade. After studying the forms, the process becomes evident. By taking 2 x 2D Voronoi extrusions on the x and y axis, and removing overlapping areas, it has allowed ACME to achieve the perception of a complex and intriguing form from the exterior while maintaining orthogonal spaces seen in plan. This was a well thought out method which demonstrates the lengths designers have gone to, to legitimise the use of Voronoi in practical application. This 2.5D example however did not justify the use of a Voronoi tessellation in a purist sense. While it has been utilised to divide programme in section, the orthogonal plan provokes an interesting juxtaposition in the Voronoi argument of misuse for “a computational aesthetic” vs. informed algorithmic space partitioning.

plan - 14th floor

fig.12

section

fig.13

External Render - UN Memorial fig.14

UN MEMOR IA L

spatial arrangement programmatic arrangement formal composition constructibility

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Vertical Village: A Sustainable Way of Village-Style Living Yushang Zhang, Rajiv Sewtahal, Riemer Postma & Qianqian Cai

Vertical Village External Visualisation Render fig.15

Vertical Village, a project out of TU Delft, employs the greatest understanding of 3D Voronoi algorithms. The fact that it is limited to an orthogonal boundary takes away some of my appreciation for it, as it has been restricted to the bounds of the Grasshopper component. However, what is impressive is the designersâ€™ understanding of how the Voronoi algorithm works in three dimensions. Through this deep understanding they have started to control and regulate the divisions in an orthogonal manner more suited to architecture and inhabitation. As the diagram suggests, to achieve a regular perpendicular face in each cell, the generating point must have a corresponding point that is perpendicularly offset in the direction of the desired face (fig. 16). As this neighbouring cell is generated, the shared partition will be perpendicular to the direction of the offset. This method has allowed the designers to somewhat regulate these divisions semi-orthogonally. This method complicates the freedom and the way in which the points generate the structure, however paired with a well coded algorithm it is a fairly successful and â€œtrueâ€? method of dividing three-dimensional space using the Voronoi. It appears to have been a useful technique in the early stage design phase providing a clear framework for development in the sequential stages as the designers work towards resolution.

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Vertical Village: Controlling Voronoi Cells Render fig.16

V E R TI CA L VI L L A G E

spatial arrangement programmatic arrangement formal composition constructibility

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6 6.0

Exploration Phase 1 Responsive Network â€“ Urban Application

Taking into account successful urban Voronoi applications such as John Snowâ€™s cholera study (Weisstein, Voronoi Diagram, 2010), my first application of Voronoi began with a similar urban scale. As public transport was an area I was both challenged with and passionate about, I used it as a broad study to test these digital design tools. This subproject formed the basis for the development and exploration of further architectural briefs to explore Voronoi as a tool for early stage design.

6.1

6.1 Public Transport In 2011, the Chair of the Greater Wellington Regional Council stressed the importance of public transport to economic growth and productivity: an increase in public transport would ease road congestion resulting in better access to jobs and markets and allowing more efficient use of existing networks and infrastructure. In addition, Wilde stated that public transport contributes to social wellbeing through safe and affordable travel. It provides an additional benefit to the protection of the environment through reduction in energy use, as well as air, noise and visual pollution (Wilde, 2011). Despite the outlined benefits, a 2001 global study of public transport use showed New Zealand cities had one of the lowest rates of public transport use in the world, lower even than that of United States cities (Humphris, 2012).

6.2 Design Problem Wellington’s public transport’s foremost issue is its inability to cater for both the specific and varying needs of potential users. Public transport remains an unpopular choice due to the perception that it is an inconvenient, irregular and expensive for Wellington commuters (Armstrong, 2014). Due to the complexities of Wellington city such as rigorous terrain, low density and lack of regular grids, it is not possible for a general, “best-fit” system to meet the needs of the masses as it might in a medium density metropolitan like London, which has the population to support both a vast yet frequent public transport system. Derived from 20th century logic, Wellington’s current public transport service is rigid and unaccommodating. Based on the initial tram layout, today’s system still operates as if attached to tracks, while achieving none of the benefits of a tram. Due to this system, the journey from A to B often involves

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going via C, D and E. Under the current system, 77% of Wellingtonians live within a 10 minutes walk of a public transport stop with service throughout the day (Greater Wellington Regional Council, 2011). However in the words of Fran Wilde (Chair, Greater Wellington Regional Council) our lack of reliance of public transport has stemmed from â€œyears of inconvenience from dilapidated and malfunctioning infrastructureâ€? (Greater Wellington Regional Council, 2011). In response to these issues, the Wellington Regional Public Transport Plan 2011-2021 outlined the following objectives: Objective 1

Simple, easy to understand services that go where people want to go.

Objective 2

An integrated network of services that makes it easy and safe to change between and within modes.

Objective 3

A high quality, reliable public transport system that customers choose to use.

Objective 4

Improved accessibility for communities and groups whose needs are not met by the regular public transport network.

Objective 5

Public transport operations that provide comfortable and safe travel, and minimise adverse environmental effects and improve health outcomes.

Objective 6

A high standard of public transport infrastructure.

Objective 7

A fare schedule that attracts and retains customers and balances user contributions against public funding.

Objective 8

An integrated system of fares and ticketing that enables seamless travel between services and modes.

Objective 9

A consistently branded transport system that is easy to use, offers a consistent customer experience and generates customer loyalty.

Objective 10

An integrated public transport network that provides value for money.

Objective 11

Effective and efficient allocation of public transport funding.

6.2

(Greater Wellington Regional Council, 2011)

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I believe that, in order to achieve these goals, a dynamic system that is customisable by the users is required to provide the incentive and convenience Wellington commuters require. In order to establish a new system that will cater for the forthcoming needs of Wellington, I propose to explore the potential of Voronoi logic to provide the most effective service possible, while using the minimum amount of resources. The logic required, in its simplest form, is to calculate the most efficient route between a starting point and an end point (McNeelEurope, 2011). Efficiency will be based on time, distance, cost and number of patrons. In 1956, Dutch computer scientist Edsger Dijkstra developed the ‘graph search algorithm’ (Dijkstra, 1959). This algorithm can be used to solve the single-source shortest path problem using edge path costs (Dijkstra, 1959). For a given source node (vertex) in the graph, the algorithm finds the path with the lowest cost (i.e. the shortest path) between that node and every other node. All unvisited neighbouring nodes are considered and their tentative distances are calculated. If node W is marked with a distance of 3, and the edge connecting it with a neighbour Y has a length of 4, then the distance from A to Y (through W) will be 3 + 4 = 7 (fig.17).

3

A

Y

7 5

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W

4

X

3 6

Z

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B

Minimal Spanning Tree fig.17

This logic was further developed in 1968 by Peter Hart, Nils Nilsson and Bertram Raphael of Stanford Research Institute. Dubbed ‘A*’, the extension to the path finding algorithm achieves faster calculations by way of assumptions through heuristics (Hart, Nilsson, & Raphael, 1968). A* uses a best-first search. By exploring a graph, it expands the most promising nodes chosen according to specified rules. It finds a least-cost path from a given initial node to the goal node out of one or more possible routes. As A* traverses the graph, it follows a path of the lowest expected total ‘cost’ or distance, keeping a sorted priority queue of alternate path segments along the way. It uses a knowledge-plus-heuristic cost function of node x (denoted f(x)) to determine the order in which the search visits nodes in the tree (Princeton University, 2012). The total cost function is a sum of two functions:

· ·

the past path-cost function; the known distance from the starting node to the current node x (denoted g(x)) a future path-cost function; an admissible “heuristic estimate” of the distance from x to the goal (denoted h(x)).

Like all informed search algorithms, it first scans the routes that appear to be most likely to lead towards the goal. What distinguishes A* is its ability to take into account the distance already travelled.

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6.3 Design Description By treating the Wellington road infrastructure as a graph, this logic can be easily applied for obtaining optimum paths for transport routes. The paths described in the A* algorithm were defined as the existing Wellington road infrastructure. These roads were fed into the logic and treated as paths or edges. Starting points, destinations and “stops” acted as nodes for the algorithm to calculate and navigate a route between. The algorithm took into account each node and assessed the possible paths between “A” and “B” using the existing roads to approximate the most efficient route. If A is the starting point, and B is the destination, U, V and W are “stops” in which the algorithm must pass through. These checkpoint nodes influence how the path between A and B is routed, ensuring specific points are included between the beginning and end destination.

Route Adaption - Working Algorithm fig.18

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Using the logic developed by Dijkstra, there is the ability to express desirable and undesirable routes. A “cost value” is assigned to each path in the graph. Usually this will represent a road’s physical length, but also offers capability of interpreting pragmatic parameters such as road gradient, width, directness, traffic, speed limits, sharp corners, traffic lights and road works. Starting with the initial node, the definition maintains a priority queue of nodes to be traversed. The lower f(x) for a given node x, the higher its priority (where x = length of road and f= added cost value). At each step of the algorithm, the node with the lowest f(x) value is removed from the queue.

6.3

With an algorithmic logic and paths defined, the nodes become the variable in the equation. With the ability to move, add and remove nodes, and its aptitude to recalculate these paths, a whole new dynamic capability and functional potential is introduced to public transport routing and services. This dynamic function has the capability to target the rigid flaws of the current system by providing a flexible, customisable and adaptive route. Similar to that of a GPS navigation system, if you take a path that differs from what was suggested, the GPS quickly updates the best route from that point. This algorithm however would work in reverse, so as a patron registered their desire to commute, the current route would update accordingly to accommodate the new node. Using the path-finding logic, there is the opportunity for commuters to design their own route in conjunction with other commuters at any given time. Present technological developments offer the capability to develop such user driven interface for public transport. For many, smartphones have become an extension of their hands with 60% of New Zealanders currently using these devices (as of May 2013), a figure which had almost doubled since 12 months prior (ONE News, 2013). This study shows the exponential trend of technology, suggesting smart phones are a viable means of interfacing with a public transport system. Real time rerouting introduces a new dynamic to public transport. It is one of complexity; however its potential, paired with technology, offers exciting possibilities. On a scale such as Wellington, it provides personalised routes based on the specific commuters using the system at that time, not on general â€œbest-fitâ€? assumptions made several years earlier.

Route Adaption - Working Algorithm fig.19

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Responsive Network Wellington

Responsive Network Wellington

Wellington Airport Wellington Railway Station

Smart Phone App - Trip Planner Arrive by. fig.20

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Smart Phone App - Trip Planner, Depart by. fig.21

ETA 16:45 (23min)

Pick UP

confirmed 16:22

Collection

Smart Phone App - Purchase Ticket fig.22

Smart Phone App - Map fig.23

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6.4

6.4 Voronoi Zoning A Voronoi tessellation requires a set of points; seeds, sites, or generators that correspond to a resulting region. Using these dynamically established areas, the way in which the routing algorithm interprets the routes and pick-up nodes can be regulated. To initiate the system, the existing bus stops can serve as the central node points for the Voronoi tessellation. As people begin to express their ideal pick-up points, this centre point controlling each cell may adjust. As the grid is completely fluid, if one cell is adjusted, it has a direct effect on its neighbouring cells. As commuters begin to use the service, it will undergo a process of optimisation while the algorithm acquires the metadata to provide a fully informed service.

Orthogonal Grid over Wellington fig.24

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By embedding Boolean statements or rules, certain parameters can be moderated ensuring the route is somewhat consistent. Rules can include standard routes, for example:

· · ·

buses must travel along roads Δ, Π, Σ Buses can deviate (x) amount from a ‘standard route’ Bus must complete route in (y) time.

Voronoi Grid over Wellington fig.25

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By creating zones, average travel times can be moderated and standard nodes or pick up points can be established. Zones are based on the number of people and the ideal pickup and drop off locations of the commuters.

Un-regulated Voronoi Grid over Wellington fig.26

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Using this metadata, Voronoi zones can be established that are representative of the number of people using the system, entitling them closer proximity to desired nodes (pick up points). The Voronoi zones allow the algorithm to read controlled averages based on various factors depending on the target travel time. Architecturally, these average nodes can be used as standard pick up points indicating the efficient and fair, allocation and placement of shelters and infrastructure.

Regulated Voronoi Grid over Wellington fig.27

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6.5 6.5 Review The usefulness of this particular design case study offers a detailed investigation of the Voronoi algorithm across a largely two-dimensional plane. It demonstrates the algorithmic dynamism of Voronoi with its ability to plan, divide space and adapt to the input parameters. This exploration phase has established a framework for the Voronoi algorithms to be tested as a tool for early stage design. A range of parameters were explored which mimics the complexity found in most architectural applications. The use of Voronoi in this situation offers a seamless division of space while optimising a system. Though this early stage design largely differs in scale from architectural application, the process of experimentation at an urban level has surfaced many potential applications to explore on an architectural scale. The parameters outlined in this public transport framework will be used to further explore Voronoi as a tool for early stage architectural design. The exploration phases to follow in this thesis will explore Voronoi and supplementary algorithmic tools for early stage design propositions, with the brief of designing architectural infrastructure to service the dynamics of a responsive public transport network in Wellington.

RESPONSIVE NETWORK spatial arrangement programmatic arrangement formal composition constructibility

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Final Routing Algorithm fig.28

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7 7.0

Exploration Phase 2 Southern Transport Hub

The section explores Voronoi algorithms as a tool for dividing space. It proposes a large transport hub on Cambridge and Kent Terrace and uses algorithmic processes for the development of an early stage design.

7.1

7.1 Brief Under the dynamic routing system proposal, a transfer hub would be required to service the southern suburbs. This transport hub would fundamentally serve as an interchange. To further test the limits of Voronoi as an architectural planning tool, the complexity of architectural programme was diversified. To compliment the transport system, temporary office spaces were included, allowing commuters to hire corporate spaces, encouraging the ease of the transport system. Additionally, a conference centre was included in the scheme to service the Wellington region with direct connections to the airport and northern links. This hybrid programme provided the complexity required to test the limits of Voronoi procedures as an early stage design tool. A conceptual mass was created which spans across two large sites on Kent and Cambridge Terrace in downtown Wellington. The form was derived from several pragmatic requirements. An empty lot on either side of the road provided north and southbound stops while the land areas were used to house the required programme. These two masses were then joined to provide an over bridge access linking the two sites. While I am personally inclined towards free-form architecture, this form provided a challenging interface to test the limitations of Voronoi planning techniques.

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Schematic Route Framework fig.29

Site Massinging and Road Layout fig.30

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Conceptual Mass Iterations fig.31

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7.2 Space Planning With Voronoi Space planning is required in every architectural design process with varying levels of complexity. Quick bubble diagrams are often the method of choice in the preliminary stages (Karlen, 2009). They allow schematic visualisation of the program required while starting to establish adjacencies, relationships, connections and functions.

7.2

Bubble Diagram fig.32

As a way to further interpret these bubble diagrams, Voronoi tessellation logic was explored to test if it could effectively assist in deciphering architectural space in a similar way in which it was useful on an urban scale (fig.32).

Section - Bubble Diagram to Voronoi Space Divisions fig.33

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2D Voronoi This exploration of the Voronoi began in two dimensions. Sectioning the form at four-meter intervals provided the required floor plates. By placing points on the floor plates that represented the required programme, a Voronoi diagram was established and was a fairly successful method of dividing space within a plastic boundary (fig 34).

Plan - Bubble Diagram to Voronoi Divisions fig.34

As this was based on two-dimensional logic, a simple wall extrusion would not cooperate with the organic external form. Another method to translate this logic to three dimensions had to be developed. By applying the seeds to the floor plate above, a second Voronoi diagram that corresponded to four-meters above was generated. By lofting together each resultant cell, dynamic walls, representative of the form, were created (fig 35).

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As a further development of the logic, a culling component was introduced to remove undesired cells in order to create spaces such as atriums and entries. While rather unintuitive, the culling function opens up an interesting area of logic to be further explored. Due to the process requiring multiple steps: sectioning, two voronoi diagrams, then lofting the result, the overall algorithm loses dynamism and does not rate highly on ether side.

Plan + Axo- Lofted Walls fig.35

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3D Voronoi The previous method is similar to that of ACMEâ€™s UN Memorial in that it is 2.5 dimensions, only utilising Voronoi on one plane. In an attempt for a more instinctive logic, the process of a true three-dimensional Voronoi diagram was explored. Representative of the way that bubbles cluster together for optimisation, the structure of each cell is formed based upon the position and size of its neighbouring cells. Where the 3D Voronoi presents its flaws, is through its legibility of architectural space. The irregular dodecahedron-like forms present disobliging spaces, principally due to the lack of horizontal planes, in particular the ground planes.

3D Voronoi fig.36

3D Voronoi fig.37

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Algorithmic Voronoi Sectioning In an effort to target this spatial illegibility, an instinctive logic needed to be developed to architecturally interpret these cells. By scheduling each cell to be sectioned at horizontal intervals, parallel ground planes are generated within the bounds of the Voronoi arrangement. This relatively simple method brings an algorithmic order to this otherwise chaotic mathematical structure. With suspended floor plates in this optimised network of structure, an intriguing architectural quality is established and the space can begin to be read inhabitable.

Algorithmic Voronoi Sectioning - Single Floor per Cell fig.38

Algorithmic Voronoi Sectioning - Multiple Floors per Cell fig.39

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Culling Due to the nature of the logic, a number of undesirable uninhabitable sections of cells remain. As part of this optimisation strategy, a code was written in order to cull any uninhabitable remnants of the previous command. The definition locates and removes floor plates either (y < (x) m2) or any outliers based on their location in relation to other floor plates or available room height.

Voronoi Floors pre-cull fig.40

Algorithmic Floor Culling fig.41

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Cell Division And Space Articulation With the cell logic formed around programme, the subsequent step was to develop navigation logic to articulate these spaces. Following the lines of an intuitive logic that will maintain a consistent language when the parameters are altered, an algorithm was scripted to locate the centre of each cell. Using these nodes in conjunction with the A* (shortest path) algorithm, a path is interpolated through each of these cells. In addition, unique programmatic relationships can be established and included in the path finding algorithm. A rectilinear extrusion is fitted to this path before subtracting the mass from the cells using a Boolean difference. This results in an intertwining hallway space based on the shortest path algorithm. As a continuation, the culling logic is applied post algorithm to remove uninhabitable spaces. As this path intersects each cell, it is possible that small sections of the cell are isolated. An area thresholdÂ (p < (x) m3) can be set in order to remove any spaces deemed unusable if desired.

Interpolated Path fig.42

Extrusion fig.43

Boolean Difference fig.44

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7.3

7.3 Structural Resolution While the research is fundamentally concerned with early stage design, as stated in the methodology, in order to truly assess the design outcomes, a level of resolution must be achieved prior to drawing conclusion on the process. This resolution is required to illustrate potential developments that architectural critics can begin to relate to, and analyse as architecture; not merely as digital matter. The following technical studies aim to utilise algorithmic processes in order to illustrate and explore a level of physical integrity. Panelising

Triangluar Subdivisions fig.45

Rectilinnear Subdivisions fig.46

Offset Rectilinnear Subdivisions fig.47

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One of the major critiques about free-form design is its often lack of constructability presenting a disparity between its digital composition and physical realisation (Hatzellis, 2006). In an attempt to explore the form’s constructability at an early stage, various methods of subdividing the external skin into manageable panels were explored. Computational meshes often favour triangulated subdivisions but are capable of other shapes. Depending on the desired tessellation resolution, the form can lose its fluidity and become rather faceted. Alternatively, a smaller grain can achieve a smoother appearance however can complicate construction and fabrication processes. While a panelised cladding is theoretically a valid method of construction, in practice it opens the doors for significant deviation in tolerances. A similar method saw the construction problems “plaguing” Zaha Hadid’s Guangzhou Opera House in China (O’Dea, 2011).

Space Frames To supplement a panelised cladding, space frames can be an effective structural option. These have gained a formidable reputation in the resolution of free-from computational design. Useful for spanning large areas with minimal interior supports, they can offer a highly desirable structural system. This is enhanced by modular construction often using interlocking struts. As the algorithm demonstrates, space frames have an ability to offer a sense of resolution to these otherwise intangible digital designs.

Parametric Truss System fig.48

With such an irregular fluid form, the exploration of a space frame seemed necessary. Several definitions were developed which explored various structural systems. While offering a sense of structural resolution, it unfortunately raised more questions about its constructability than it resolved.

Parametric Truss System fig.49

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Voronoi Skeleton As Voronoi had been used to partition the internal spaces, it was logical to explore the possibility of using the geometric perimeter framework of these spaces to provide the internal structure for the building, as opposed to an exoskeleton structure, such as the space frame. After experimenting with several definitions, a flexible internal frame was developed in conjunction with the internal floors. By utilising these internal partitions, an extremely expressive internal space was created. The floors seem to suspend from the network of structure, all of which can be inhabited by the occupants.

Internal Voronoi Structure fig.50

Internal Voronoi Structure fig.51

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7.4 Review

7.4

Three-dimensionalising the spacepartitions were a crucial development in the exploration of Voronoi algorithms for early stage design. While less than revolutionary, in my observations of architectural Voronoi precedents, there seems to be a lack of success in translating these awkward areas into inhabitable and efficient spaces. More specifically, there is a lack of success in achieving architectural comprehension, algorithmically. Examples show Voronoi being used to create an external form, but regulated floor plates are retrofitted as seen in M&A Architects Bubble Skyscraper (fig.10 + 11). Others undergo a manual process of regulating cells as seen in the UN Memorial (fig 12) and Vertical Village (fig 15). This workflow completely contradicts the purpose of using an algorithmic process and reduces Voronoi to an arbitrary affiliation with natural phenomena. Success of the first design came in the algorithmic process of sectioning the cells to produce both functional and dynamic spaces. The staggered floor plates could perhaps be viewed as inefficient in a traditional construction sense. They do however offer architecture merit in their ability to define spaces through levels and produce a unique aesthetic.

Internal Voronoi Structure fig.52

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Where the design saw less success was in its ability to adapt. Subtle changes in the external form would result in quick adaption internally. However if the building envelope were completely changed, it would require a relatively lengthy rebuild procedure due to the way the processes were established. While all the algorithms were in place, a change in parameters wouldnâ€™t result in a fully functional early stage design without significant tweaking and debugging. It would require manually altering points and reestablishing programmatic relationships. Overall, the process which defined the architecture was too removed from the programmatic requirements, resulting in a manual and unintuitive algorithmic process. Despite this, I was pleased with many of the experimental results and processes yielded, most importantly the way in which Voronoi could be used to architecturally divide irregular forms. The overall lack of success came from the preconceived form that had little consideration and development towards the programme required. It seemed to defy the purpose of an organic structure as I found myself trying to â€œfillâ€? this conceptual form with programme in an attempt to ground the building. If the obvious architectural design flaws were set aside and the focus was merely on the performance and potential of the Voronoi as a early stage design tool, there are definite merits in the way in which it could dynamically handle both an awkward building envelope in conjunction with complex and ever-changing programme requirements.

S O UT HE RN HUB

spatial arrangement programmatic arrangement formal composition constructibility

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Voronoi Structure within Volume fig.53

Internal Voronoi Structure fig.54

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8 8.0

Exploration Phase 3 Algorithmic Bus Shelters

The previous experiments assessed Voronoi on its ability to divide space. This section explores the potential of Voronoi as a form finding tool in early stage design.

8.1

8.1 Aim - Intuitive Logic While some interesting results and processes were developed in the first exploration phase, the overall process was far too manual and unintuitive. If the parameters were vastly altered, such as the site or the programme, it would require a relatively intensive rebuild. This undermines the reasons for exploring these algorithmic methods for early stage design. David Gerber has stated, â€œWhen the topology of a project changes the parametric model generally needs to be remadeâ€Śâ€? (Gerber, 2007). As opposed to a parametric model, which the second exploration phase characterised, I am more interested in the potentials of an algorithmic model which aims to reduce these traditional parametric limitations through intuitive scripting. Having struggled programmatically with a pre-conceived form in the previous exploration phase, this section explores Voronoi with a form-finding agenda.

Grasshopper Input Parameters fig.55

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8.2 Brief In an extension of the public transport brief, the current project explores the capacity for Voronoi to be implemented in early stage design though a series of transport shelters and small hubs. While the Responsive Network system aims to eliminate many of the frustrations of public transport by getting closer to patrons and providing flexible routes, it does not completely eliminate the need for transport infrastructure such as shelters. Within our communities there are natural points of congregation where buses will frequently stop. In addition, the algorithm undergoes a consistent process of optimisation calculating the necessity and positions of transport shelters. By pairing this metadata with the simple parameters outlined in figure 54, a unique definition for each site is provided which the algorithm is capable of interpreting. By assigning simple rules to possible facilities, the architecture can be defined by these basic parameters. This schedule demonstrates the logic for defining these components. For example, the number of seats provided would be based on the number of passengers per hour vs. the average wait. The goal for this design was to test how effectively Voronoi algorithms could be used to distribute and organise components; ideally a form would be generated representative of this process.

8.2

Algorithmic Rubrics fig.56

Schematic Shelter Examples fig.57

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8.3

8.3 Cell Culling The culling processes explored in the first design were some of the more successful and intriguing ways of controlling and three-dimensionalising Voronoi cells. In the first research design, culling processes were only used to remove sections of individual cells, not necessarily a method of controlling the overall composition. These experiments explore the possibility of using culling procedures to design through process of elimination. In theory, a large Voronoi diagram would include all the cells possibly required. Using culling procedures, any cells that are not required due to programme or site restrictions are subsequently removed leaving an “optimised” form. The main reason for exploring this method is due to the over-dynamisms of the Voronoi. Each cell in a Voronoi is not just a representation of itself but also everything that surrounds it. This means if one cell is modified, the whole diagram is essentially affected. As I wanted to explore modularising the Voronoi, it seemed the most effective way was to standardise the framework and remove what was not required. This would allow cells to remain constant, as they would represent specific programme.

Culling Cells Animation 1

Culling Cells Animation 2

While this was an interesting study, and would suffice for a simplistic brief such as this, it was not a general methodology I would like to employ for early stage design. Culling was too much of a backhanded method of ‘controlling’ the Voronoi for architectural purposes. A further interest lay in exploring dynamic Voronoi applications; more intuitive, and more complimentary to the way the Voronoi algorithms are processed.

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8.4 Iterative Optimisation Interested in its dynamic origins, a further understanding of how Voronoi worked in nature was required.Â Voronoi can represent the predominant force in a living tissue as a uniform pressure exerted on a cell by surrounding cells (Stefanescu, 2010). The phases of cell intuition is rather intriguing in a design sense; â€œProliferation, Specialization, Interaction and Movement.â€? This process represents the intuition and interface required in exploring the Voronoi for early stage design.

8.4

Without any physical parameters assigned to a Voronoi seed, it is extremely hard to control the area of a cell. Initially iterative optimisation was explored using the Grasshopper evolutionary solver Galapagos. By assigning target sizes to each cell (area/2D or volume/3D), through iterations, a best-fit solution could be achieved. This was a relatively successful method of post-optimisation however I wanted to explore possible ways of initially integrating a means of regulating these cells.

Stills from Iterative Optimisation Animation 3

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8.5

8.5 Circle Packing In the first research design, bubble diagrams were used to schematically define spaces. The Voronoi divisions were then based on these roughly defined areas. This allowed for a prediction of how the Voronoi would divide the space.

Sections - Bubble Diagram to Voronoi Divisions fig.58

Using this logic, I looked into circle packing. This is the study of the arrangement of circles on a surface so that no overlapping occurs and the circles are packed as tightly as possible. Packing is referred to as the subdivision of space in which as little space as possible, or none, is left over.

Circle Packing fig.59

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After research into the fundamental logic of circle packing, Grasshopper was reentered with a new agenda. It occurred to me that iterative optimisation might not be the key. As I was looking to replicate a natural phenomenon, the key would be to produce similar conditions using physics simulations. This experimental simulation process began by calculating the arrangement of a group of given circles based on their sizes. Â As the simulation ran, the circles were drawn to an anchor point and arranged themselves based on size and collisions with each other.Â With the particles arranged, a Voronoi division was applied and each Voronoi cell roughly equated to the size of the circle representing it.

G.H. Circle Packing fig. 60

G.H. Voronoi Circle Packing Animation 4

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While this packed the circles as tightly as possible, there was no consideration to a boundary. To achieve this, a pull force was assigned to a target boundary curve, forcing the particles towards the boundary. Â Paired with an outward force, the particles recognised a given boundary and the circles arranged themselves accordingly.

Boundary Recognition - Forces Applied fig.61

While the algorithm was relatively effective in packing the cells, there was little control over how they were arranged. Â

Physics Simulation Animation 5

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Metaball When translating a packed circle or a “bubble diagram” to Voronoi divisions some large discrepancies occur in terms of target cell sizes due to the way in which the Grasshopper component is programmed. As the distances between two points define boundaries, there is no strict relationship between the sizes of the bubbles to the size of the cells other than its nucleus. Furthermore, the component works within the bounds of a rectangle or cube. This seems to contradict the way in which Voronoi should work, alluding to possible deficiencies in using pre-loaded components. To counter this issue in previous experiments I had used culling methods, but with a significantly more dynamic process, metaball algorithms were explored to assist in re-parameterising these cell sizes. Traditionally used in computer graphics, metaballs require “charges.” By reassigning each point of programme a charge representative of the target area, a hybrid Voronoi-metaball diagram produces a significantly more accurate division of space.

Circle Packed Voronoi Diagram Animation 6

Hybrid Metaball Voronoi Diagram Animation 7

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8.6

8.6 Space Syntax The physics simulations were yielding extremely interesting results. However in terms of optimising architectural programme, it had a complete inability to establish and maintain programmatic relationships. This is a key role in early stage design. As far as the algorithm was concerned, the solutions were optimised based on efficient packing, though it was far from optimised in terms of architectural planning. In order for the algorithm to organise architectural programme, it had to recognise relationships, connections and adjacencies between programmes. By studying Space Syntax theories the algorithm took a huge step towards an intuitive, self-organising early stage design tool. Space Syntax is a set of theories and techniques designed to analyse spatial configurations. It was conceived in the late 1970’s by Bill Hillier and Julienne Hanson as a tool to help architects simulate the likely social effects of their designs (Hillier & Vaughan, 2007). Space Syntax’s intended use was an analytical tool (The Bartlett, 2007) but paired with generatively defined algorithms, these theories have the potential to not only perform post analytical assessments but to define and optimise spatial configurations based on adjacency rules. By embedding simple rubrics as with manual space planning, for example,

· · ·

‘a’ has to be connected to ‘b’ ‘b’ to ‘g’ ‘x’ to ‘y’

the algorithm is capable of recognising primary and secondary connections in which it can aim to optimise with the help of the A* shortest path algorithm. Several experiments were conducted testing the instinctual capabilities and limits of these Space Syntax processes. Striving for an intuitive processing language, the algorithm developed a capability to understand simple rules, for example, - a store requires an ATM directly adjacent - seating must be located next to a platform etc.

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In practice and in theory, these simple statements work for orthodox situations, however architecture is usually the contrary with complex programmatic relationships. To help counter this, a review and input stage was encrypted into the process. This permits the designer to make executive decisions that might be unique to the situation, outside of the algorithms programmed understanding. It will then be possible to add or overwrite connections that are predetermined by the algorithm. This is key in allowing the designer to “design” and not the algorithm to determine.

Space Syntax Optimisation Animation 8

After experimenting extensively with “self-organising” structures and following the theories of many influential architectural computational practitioners, by this stage of the design case study I was convinced that algorithms should be used to assist in the process of design, but at some stage the designer requires a subjective level of input.

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8.7

8.7 Interpreting Site Each architectural output is ideally a direct response to the specific site where it is intended to be located. As the bus shelters are to be situated in various sites across Wellington, the algorithm had to be capable of interpreting the terrain, as it is unlikely the site would be level. By adapting the Voronoi sectioning procedure, floor plates can be created that respond directly to the surface below. By projecting each cell seed perpendicularly in a negative z coordinate, the point which intersects the input topography can be located. Using this projection of points, the algorithm is capable of interpreting any given terrain and producing a floor surface which responds to each site.

Topography Interpretation fig.62

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8.8

8.8 Form Finding Catenary Mesh Relaxation An intuitive logic defining the two-dimensional layout of the shelters requires an equally instinctive form-finding procedure. With a focus on optimisation, free-form structures were explored to complement the programmatic procedural conception. In physics and geometry, a catenary is the curve that an idealised hanging chain or cable assumes under its own weight when supported only at its ends (Weisstein, Catenary). This formfinding logic was explored discovering its aesthetic and functional limits. It enables digital form-finding, in the tradition of engineers/architects such as Frei Otto, Antoni Gaudí and Heinz Isler, where the physical response of a model (such as a hanging chain network or soap film) to a set of forces is used to generate an optimal form for resisting the design loads on the actual structure (Piker, 2013).

Antoni Gaudi - Hanging Chain Model Colònia Güell. 1915 fig.63

By replicating the processes based on these classic techniques, it was possible to generate instinctive three-dimensional forms from a mere two-dimensional outline. By establishing anchor points before inflicting forces onto the geometric plan, various forms could be generated based on a range of parameters. The forms self-organised into catenary-like thrust surfaces. Aligned with its structural vectors, it allows for minimal structural depths. The results were structurally optimised forms directly representative of their plan.

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Stress + Deformation Further structural analysis was performed on the mesh post-simulation. The analysis aimed to determine the areas under the most amount of stress. Being a tension based structure; the edges where catenary cables would run were obviously under the most amounts of tension, and also where the panels were significantly deformed or deviated from the standard shape. Most of the stress across the rest of the form was relatively uniform demonstrated by the dominance of green and blue.

Structural Analysis fig.64

Structural Analysis fig.65

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Structural economy is one of the more familiar applications for optimisation processes in architecture, but it is far from being the only one (Burry & Burry, 2010). While these results had some aesthetic merit and were technically structurally optimised, the arch forms were not optimal for human inhabitation. They resulted in significant areas of unusable space due to their arching ceilings and openings. Development By removing some of the anchor points, larger inhabitable spaces could be created. The overarching canopy roof provided more flexible space and striking columns acted as both aesthetic and structural features.

Traditional Catenary Form fig.66

Catenary Form with Added Columns fig.67

Catenary Columns with Trimmed Roof fig.68

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Having too many external edges complicated the arrangement so I moved towards an orthogonal perimeter shape to allow the central columns to speak. The form is then wrapped in a glass curtain wall representative of the metaball outline.

Final Framework for Shelters Animation 9

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8.9 Seating Incorporated into the algorithm is a process that defines seating. The number of people per hour and their average wait defines the length of the seat. The organic nature of the seat includes several profiles that aim to cater for various waiting postures. The profiles are based on 3 positions; leaning, perching and sitting. As the profiles transition, it creates hybrid forms intended for commuters to make use of in their own way. As a standard means of fabrication, the algorithm simultaneously divides the seat into two-dimensional profiles, creates slots, and arranges and labels them for CNC machining.

8.9

Algorithmic Seating fig.69

Algorithmic Seating fig.70

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8.10

8.10

Review

I believe the input of physics simulation into the processes provided several advantages to the computational workflow. It provided the experimentation and free flowing nature required in the early stages of design, while simultaneously revolving around several, strict pragmatic requirements. By using physics simulations to generate form, it permitted both the complete freedom in formal exploration with a focus on parameter optimisation. Space syntax was the crucial link in providing the algorithm planning logic and constraints. By providing these rules, it allowed a certain freedom for the form finding to take place. This resulted in an expressive, but controlled form finding exercise; allowing any situation, any topography, any site boundary, or any number of facilities to yield a tailored result suited to these parameters. One of the key factors to achieve solutions tailored to any site was the ability to narrow down the parameters and possible facilities into simple algorithmic language. The success of this perhaps came from the simplicity in programme allowing for predictable equations and decisions to be made. To really test the competency of this logic, a significantly more complex programme of functions, site and requirements would be required. Equally, this design exercise was programmatically singlelevel (2D). With a focus on testing the applications of Voronoi, its three-dimensional counterpart will need to be explored in order to fully investigate the potential of this logic for early stage design.

ALGORITHMIC SHELTER S spatial arrangement programmatic arrangement formal composition constructibility

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Algorithmic Shelter - Iteration 1 fig.71

Algorithmic Shelter - Iteration 1 fig.72

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Algorithmic Shelter - Iteration 2 fig.73

Algorithmic Shelter - Iteration 2 fig.74

Algorithmic Shelter - Iteration 2 fig.75

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Algorithmic Shelter - Iteration 2 fig.76

Algorithmic Shelter - Iteration 2 fig.77

Algorithmic Shelter - Iteration 2 fig.78

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8.11 Construction Drawings

8.11

Refer to Appendix A

Parametric Transport Canopy

Parametric Transport Canopy

SARC 421: Project 02

Integrated Technologies + Construction

Frano Bazalo 300157293

This design is a parametrically generated series of public transport related shelters and hubs. The strucutures are designed to facilitate the public transport netword across Wellington. The generative logic is designed to optimise these architectural facilities within the Wellington Public Transport Network. The structure is designed to grow and adapt according to the use and demand of commuters. Consequently, the construction methods for the structure had to allow for this shifting architecture. Equally, the logic adapts the structure to suit specific sites. Not one structure is identical. However, it was important to achieve this through a set of modular components that have the ability to mould to the unique site conditions. For this project I have chosen to focus on the construction of the canopy as this is the fundamental part of the design. The central stems of the canopy remain constant on any site while the undulating grid shell is unique and is therefore CNC machined to fit. 4000

It was then important to create a series of components and systems for this central stem as it could be applied to any structure. I have broken this central stem into three sections to detail.

roof height

Top third: Canopy connections relating to the glazing and membrane S2 A2.02

0 ground level

S1 A2.02

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Longitudinal Section 1:100

Centre: Canopy connection relating to tension ring and membrane

Bottom Third: Canopy footing

S1

A2.02

Reference Notes:

P1 A2.01

Floor Plan Including Reflected Ceiling 1:100

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9 9.0

Exploration Phase 4 Northern Transport Hub

The previous sections explored several design experiments with contrasting briefs, scales and algorithmic methodologies. This section aims to use the acquired knowledge and combine a range of algorithmic processes from these experiments to explore and conclude an exploration of Voronoi supplemented algorithms in early stage design.

9.1

9.1 Brief The existing Interislander site on Aotea Quay is the only place in Wellington where the ferries, trains and buses come within close proximity of each other. Yet currently, you cannot transfer between any of these modes of transport. As a result, the Interislander is cut off from the city and a range of transport opportunities are missed. Another potential opportunity is the influx of cruise ships Wellington has seen in recent years. Currently Wellington can host up to two cruise ships along Aotea Quay but facilities are hugely limited. The passengers currently disembark two kilometres out of the city and are greeted by an extremely unattractive side of town. In 2012, cruise-ships injected $39.5 million dollars into the Wellington economy (The Scoop, 2013). By increasing cruise ship-docking capacity, Wellington could see the economic benefits within a couple of years. The Interislander site provides an ideal opportunity to combine all modes of transport, improving facilities from daily commuting to a one-off visit to Wellington. Based on existing infrastructure, routes for each mode of transport based on their individual pragmatic requirements have been schematically resolved. There are several key moments within the scheme that must remain static.

· · · ·

A large portion of the building must remain in close proximity to the water’s edge so that the cruise ships may dock The building mass must not compromise the motorway and must work within the existing infrastructure Both freight trains and vehicles must have uncompromised access to the ferries Interchange between buses and trains must complement each other and encourage transfers.

Due to these strict parameters, the schematic path layout served as the boundary for the structure to arrange around.

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Schematic Route Layout fig.79

As previously discussed, this experiment aims to sample several of the algorithmic processes developed in the preceding explorations. Combining the three-dimensional Voronoi and culling operations of the first research design with the physics simulations and organisational logic of the second, a complex amalgamation was explored using Space Syntax rubrics to tie together the algorithmic processes into a self-organising early stage design tool. Unlike the initial transport hub in the first research design which started with an external form, in this experiment the external form came as a result of the algorithmic processes and therefore the internal programme entirely justifies the form.

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9.2

9.2 2D - 3D Previous self-organisation has been two-dimensional. As an intended tool for early stage architectural design, it is a necessity that self-organisation works on multi-levels. A natural example of Voronoi working in three-dimensions is the highly intriguing interaction of bubbles: forming and optimising. This natural process of organisation and optimisation appears to share many parallels with some of the overarching goals I was hoping to explore in intuitive, algorithmic early stage design.

Bubble Organisation fig.80

2D Space-Syntax Relationships fig.81

Scientists have observed that when bubbles form clusters, their boundaries merge to form a new partition wall perpendicular to the loci of the bubble. This process is replicated in 3D Voronoi diagrams. More interestingly, when two or more bubbles meet, they proceed to adopt a shape which encases the original volume of air while reducing the sum of their surface areas as small as possible. This process of formfinding through preservation and optimisation provided the stimulus to explore these parallels. By drawing inspiration from these natural procedures, a dynamic process of optimisation, ordering and adaption will be combined with an underlying logic of establishing 3D architectural programme and form for early stage design techniques. In the same way that bubbles interact with each other based on intuitive logic, rules needed to be embedded into the programme to allow the logic to optimise the layout interactively and dynamically.

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To translate the data from the two-dimensional space syntax diagrams explored in the second phase of exploration, physics simulation logic was employed to transform a historically two dimensional process of spatial arrangement into an operable three dimensional framework. A target NURB spline acts as a spine for the diagram to be arranged around. A NURB spline can alternatively act as a boundary depending on the forces applied to it. Similar to the two-dimensional algorithm, forces are applied to each node. The space syntax rubrics restrain and provide the programme guidance and maintain the relationships using the established spring lengths as the simulation works to optimise spatial arrangement. The added dimension creates an immediate sense of space that its two-dimensional counterpart lacks.

2D - 3D Space Syntax Transformation During Simulation Animation 10

As the simulation transfers the 2D diagram into a 3D framework, the process works towards a state of optimisation. When the form begins to settle around the NURB spline, the algorithm has deemed all processes and parameters to be optimised under the outlined conditions. This process permits the traditional space syntax diagram to be relayed into three-dimensions, providing a more dynamic framework to arrange space around.

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Each node in a diagram now has a spatial depth which can be used to generate a justified 3D Voronoi framework. A metaball algorithm once again assists in re-parameterising volume specifications using charges. This is demonstrated in the diagrams; however the metaball boundaries are merely a visualisation tool in this stage.

2D - 3D Space Syntax Transformation During Metaball Simulation Animation 11

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9.3 Internal Voronoi Divisions And FloorsÂ Referring back to the second exploration phase, the Voronoi reasoning logic was reemployed to establish floor plates within the volumes defined by the algorithm. This procedure proved to be the key process in legitimising the Voronoi space-partitioning algorithm for legible three-dimensional architectural spaces. The algorithm has been re-parameterised to work simultaneously in the form-finding process. This allows the designer to view the whole simulation process as potential variations, as opposed to applying each algorithm in subsequent chronological order.

9.3

Voronoi Floor Plates During Metaball Simulation Animation 12

Voronoi Floor Plates During Metaball Simulation fig.82

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9.4 Form Optimisation

9.4

Form Resolution fig.83

Form Simulation Animation 13

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In the previous section, the Space Syntax diagrams are translated into three-dimensional space visualised by metaballs. As this algorithm is intended to be a tool for early stage design, I did not want to restrict the form-finding process to a singular shape or aesthetic. It was an important aspect to remain flexible and dynamic in the same way the process is. For this reason, the form can be reparameterised using spheres, cubes, cuboids, metaballs, Voronoi cells, or a combination, depending on the overall desired aesthetic and programme requirements. Each of these reparameterise a singular Voronoi-based cell not the overall form or envelope. To unify this collective geometry, (Bailey & Katzenstein) a â€œshrink wrapâ€? definition was adapted in order to re-skin the algorithmic outcome. This algorithm runs simultaneously with the form finding process, encasing the internal geometry within a unified boundary. As a result, the external form is a direct representation of the programme it contains. This contrasts with the first research design by eliminating any need to cull or remove components as was initially required.

9.5 Revisiting 2D-3D Transformation The initial 2D to 3D translation used a NURB-Spline to attract the programme. While this had its advantages and returned results, producing an initial spine is not always an ideal driver to base programme and early stage design around. The process from graph to spatial arrangement is the vital step to this early stage design technique therefore I felt I had to revisit it after experimenting with the process. As the brief outlined, there were several extremely strict parameters while the rest of the programme was â€œfreeâ€? to be organised according to the parameters set in the equation. This is a common situation in architectural planning so with this in mind, I experimented with an element of manual input to individualise the results. Beginning with the two-dimensional Space Syntax diagram, I experimented with adapting the graph using several anchor points (Fig.115). These anchor points represented programme with specific location requirements. The manual input allowed for the Space Syntax diagram to be tweaked or altered with a simple drag and drop of the mouse. Using the pre-established spring lengths, the graph remained in an optimised form while the overall composition could be altered.

9.5

Space Syntax Adaptation Using Physics Animation 14

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This experimentation produced the logic required to translate this graph more effectively into three dimensions. The brief states that, as with many architectural projects, several elements of the programme required specific locations on the site, due to pragmatic requirements. For example, in this case, the ferry terminal had to be located along the port while the bus stops had to be along the road. With these parameters in mind, I included the ability for target points to be assigned to any programme with strict instructions, ensuring the simulation arranged the programme around these points. Any un-specified programme was free to optimise within the bounds of the Space-Syntax relationships and site. This version provided a workflow pragmatically suited to the way in which early stage design is often undertaken. Alternatively, an attractor spine or boundary, as seen in the first edition, could also be used to influence the spatial arrangement of programme in conjunction with any anchor points.

Space Syntax Optimisation fig. 84

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Space Syntax Envelope Optimisation Animation 15

This simulation results in an external envelope containing all internal programme. This presents an initial early stage design which can be developed further with consideration into form, materials, light, construction details etc. The ease and speed of this process provides the ability to explore many configurations and leaves more time for the pragmatic resolution of the design.

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9.6

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9.6

Review

The combination of algorithmic processes has granted new applications to the way Voronoi has generally been used in architecture. It exploits Voronoiâ€™s ability to divide space while blending an underlying architectural logic to these divisions. This process ultimately informs both the internal and external composition of a building in a simultaneous process, unprecedented in early stage architectural design. These experiments demonstrate the potential computation capability for early stage architectural design.

Input of the Algorithm - Restating of Design Intention It is vital to understand what the algorithm is doing and what the designer has control over. No output is an accident. The algorithm is a documented reflection of the design decisions made. If it appears the algorithm is determining what happens, then I consider the algorithm to be well coded. An output is an iteration interpreting any given parameters based on recorded, procedural design decisions. In this proposal, the output is entirely a representation of my preferences towards forming space. Idiosyncratically, the first and third designs are entirely different processes, use different tools and have different agendas, yet they share an overall typology. This is not a Voronoi typology, nor is it strictly a computational or Rhino typology. It is a personally favoured style of forming space. I have both consciously and subconsciously related to the streamline and organic nature of transport. The typology is in no way a strict representation of algorithmic design, or even Voronoi for that matter. If anything, it is an appreciation of the Voronoiâ€™s ability to comprehend non-linear spaces. Within the logic, there are options for more orthogonal or faceted building envelopes which may be better suited for different sites or programme.

NORT HERN TERMINAL

spatial arrangement programmatic arrangement formal composition constructibility

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10 10.0

Algorithm Refinement Supplementary Design Studies

This section refines the algorithm before exploring the workflow with several supplementary designs. The section demonstrates the capabilities of the algorithm as a useful tool for early stage architectural design.

10.1

While the algorithms developed in this research were an attempt to understand specific aspects of the computational design process within the context of a specific architectural brief, the advantage of algorithmic procedures is the ability to apply them to other situations. Inadvertently, a procedural tool has been developed that essentially anyone could use, for any type of brief. As Terzidis states, while most algorithms are designed with a specific solution in mind to a problem, there are some problems whose solution is unknown, vague, or ill-defined. In the later case, algorithms become the means for exploring possible paths that may lead to potential solutions (Terzidis, 2006). In order for these algorithms to be a useful tool for early stage design, the process and user interface had to be significantly refined. While the Grasshopper interface, in particular the sliders, are a great way of manipulating input parameters, they have their limits. The main concern is the complexity of the required parameters, often requiring multiple inputs to include data such as programme, size, names, relationships and levels. Each input type requires a unique input and this quickly becomes excessive and unbearable to control. One way to refine the method of input lies in a simple Microsoft Excel spread sheet. Within the spreadsheet, data is established and the seamless flow between Excel and Grasshopper result in a significantly more powerful and user-friendly tool. All programme, names, levels, sizes and relationships are established in Excel while the algorithms in Grasshopper interpret the data and optimise based on the previous form-finding procedures.

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Space Syntax Programming Via Excel Animation 16

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Form Optimisation + Programming Via Excel Animation 17

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Form Optimisation + Floor Plates Via Excel Animation 18

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While the spreadsheet streamlined how data is inputted, I wanted to find the balance between an intuitive self-organising structure and the added input of the user to customise and form the final output. Following Pikerâ€™s analysis of physics simulations in architectural design, he notes that one great advantage of physically based methods is the natural feel we associate with real-world behaviours (Piker, 2013). This ability to intuitively interact with digital mass lends itself well to the design process and was important to include in this tool for early stage design. Instead of using points to attract the programme, as was used in the previous algorithm, boxes represent the programme and any boxes that are manually moved pre-simulation, remain static and provide anchor points for the simulation to work around. This provides the ability to input any empirical data or strict programmatic relationships while the remaining programme is optimised based on the given parameters. Additionally, boxes can be manually moved during simulation to influence and manipulate the structural composition. This constant feedback loop between algorithm and user provides the required intuitive and natural process required for early stage design.

Methods of Adapting the formal outcome using Physics Simulations Animations19 - 23

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Algorithmic Output

Floorplates + Voronoi Frame fig.85

F INAL AL GOR IT H M

spatial arrangement programmatic arrangement formal composition constructibility

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Catalouge of Formal Outputs from Algorithm fig.86

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Design Iterations: Algorithm Includes Structure, Glazing + Cladding

Design Iteration A fig.87

Design Iteration B fig.89

Design Iteration C fig.91

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Design Iteration A1 fig.88

Design Iteration B1 fig. 90

Design Iteration C1 fig.92

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Design Iteration D fig.93

Design Iteration E fig.95

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Design Iteration D1 fig.94 Quick Algorithmic Design Iteration Animations 24

Design Iteration E1 fig.96

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Raw output from Algorithm (Envelope + Floor Plates) fig.96

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plan: Ground Floor

plan: First Floor

plan: Roof

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external roof panel cladding

roof steel beam structure

internal roof panels

glazing + mullions

floor plates

steel framing car ramp external cladding

bus ramp

exisitng aiport carparking

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11 11.0

Final Discussion

11.1

11.1

Conclusion

This research was fundamentally concerned with the relationship of contemporary digital design tools and how they can be used to augment design outcomes for early stage design. The focus was on the use of the Voronoi algorithm, which resulted in the question that shaped the research - how can Voronoi algorithms be used to enhance the design workflow within early stages of architectural design? Through a myriad of technical algorithmic studies, four exploration phases and an array of design outcomes, the usefulness of Voronoi algorithms in early stage design has been extensively explored. While many supplementary algorithms played an important role in developing the final algorithm, Voronoi provided the mainstay through its ability to dynamically divide space and adapt, providing a sturdy yet developable framework for the supplementary processes to revolve around. In response to the research question, the final algorithm has the ability to enhance the design workflow within early stage design by harnessing several aspects existing methods lack: The algorithm has a capacity to interpret raw data from multiple strings and process simultaneously. These parameters reach a complexity generally requiring the designer to conduct the development in chronological phases as each parameter is considered individually. What the amalgamation

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of algorithms has achieved, differentiating it from typical approaches, is to simultaneously process data while an immediate visual response is generated. This combination permits a concurrent process of creation, analysis and optimisation of early stage design problems. Refinement of the algorithm and the use of spreadsheets simplify the process and permit ease of use, allowing extremely dynamic outputs to be generated extensively and rapidly. The refined algorithm grants an ability to achieve an extensive array of design options in a reduced timeframe. Differentiating between existing algorithmic self-organisation techniques, the method developed permits an empirical level of input from the designer, allowing outputs to be tweaked and enhanced based on the perspectives and opinions of the creator. This mediates an interesting, yet balanced juxtaposition between human and computer. Most intriguingly, computation has the potential to provide inspiration and go beyond the intellect of the designer through the generation of unexpected results (Peters B. , 2007). The idea of sketching by algorithm is encapsulated in this research by the rubric nature of transforming data into formal and spatial outputs. This unexpected, however reasoned, characteristic is what captures the potential for computational design tools in the early stage architectural design process. 187

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12 12.0

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Artinfo: http://de.blouinartinfo.com/features/article/38070as-zaha-hadids-guangzhou-opera-house-leaks-andcrumbles-critics-in-china-crack-a-smile OECD. (2001). Ageing and Transport - MOBILITY NEEDS AND SAFETY ISSUES. Retrieved 10 10, 2013, from OECD: http://www.oecd.org/sti/transport/ roadtransportresearch/2675189.pdf ONE News. (2013, May 21). ONE NEWS - NZ smartphone ownership doubles in one year - study. (TVNZ, Ed.) Retrieved August 5, 2013, from TVNZ: http://tvnz.co.nz/ technology-news/nz-smartphone-ownership-doubles-inone-year-study-5443887 Perony, N. (2013, October). Puppies! Now that I’ve got your attention, complexity theory. Retrieved March 2014, from TED: http://www.ted.com/talks/nicolas_perony_puppies_ now_that_i_ve_got_your_attention_complexity_theory Peters, B. (2007). ‘The Smithsonian Courtyard Enclosure: Computer Programming as a design tool’. (B. L. Beesley, Ed.) Expanding Bodies: Art, Cities, Environment. Proceedings of the ACADIA 2007 Conference. Peters, B. (2013, March 12). Computation Works: The Building of Algorithmic Thought. Architectural Design, 83. Picon, A. (2010). Digital Culture in Architecture . Basel, Switzerland: Birkhauser GmbH. Piker, D. (2013, March 12). Computation Works: The Building of Algorithmic Thought. Architectural Design, 83(2). Princeton University. (2012). A* search algorithm. Retrieved October 6, 2013, from Princeton University: http://www. princeton.edu/~achaney/tmve/wiki100k/docs/A*_search_ algorithm.html RIBA. (2012, December 12). RIBA Plan of Work 2013. UK. Rutten, D. (2012). Grasshopper - Voronoi Component. Grasshopper 3D. Robert McNeel & Associates. Rutten, D. (2013). Grasshopper 3D. Robert McNeel & Associates. Santos, G., Behrendt, H., & Teytelboym, A. (2010). Part II: Policy Instruments for Sustainable Road Transport. Research In 194

Transportation Economics, 28(1), 46-91. Schumacher, P. (2009, July). Parametricism - A New Global Style for Architecture and Urban Design. (H. C. Neil Leach, Ed.) AD Architectural Design - Digital Cities, 79(4). Stefanescu, D. (2010, October 28). f* Voronoi. Retrieved January 13, 2014, from d/a/s: http://improved.ro/blog/?p=896 Sullivan, L. H. (1896, March). The Tall Office Building Artistically Considered. Lippincott’s Magazine, pp. 403-409. Taylor, B. (2010, February 4). Voronoi Diagrams in Nature. Retrieved 10 6, 2013, from Wooden Boat Forum: http:// forum.woodenboat.com/showthread.php?112363Voronoi-Diagrams-in-Nature Terzidis, K. (2006). Algorithmic Architecture. Burlington, USA: Architecutral Press. The Bartlett. (2007). Space Syntax Laboratory. Retrieved 11 30, 2013, from The Bartlett School of Graduate Studies: https://www.bartlett.ucl.ac.uk/graduate/research/space/ space-syntax The Scoop. (2013, August 5). $39.5m: the value to Wellington of one season’s cruise ship visits. Retrieved 12 13, 2013, from Wellington Scoop: http://wellington.scoop. co.nz/?p=57959 Theo van Doesburg. (1924). Towards a plastic architecture (Ulrich Conrads, rograms and Manifestos on 20th Centruy Architecture (1970) ed.). Cambridge, MA, USA: MIT Press. Weaire, D. (2008). Kelvin’s foam structure: a commentary. Philosophical Magazine Letters, 88(2), 91-102. Weisstein, E. W. (2010). Voronoi Diagram. Retrieved August 5, 2013, from Wolfram Mathworld: http://mathworld.wolfram. com/VoronoiDiagram.html Weisstein, E. W. (n.d.). Catenary. Retrieved October 20, 2013, from Math World: http://mathworld.wolfram.com/Catenary. html Wilde, F. (2011, November 1). Chairperson’s foreword. Wellington Regional Public Transport Plan 2011-2021. Wellington, New Zealand. Zumthor, P. (2006). Atmospheres . Basel: Birkhäuser. 195

List of Figures Cover Image Algorithmic Output fig.1 Voronoi Grid Variation fig.2 Grasshopper Voronoi Notification fig.3 Beijing Olympic Aquatics Center fig.4 Voronoi Corrals Photo fig.5 Voronois Corrals Plan ArchDaily. (2012, November 16). Voronoiâ€™s Corrals / decaARCHITECTURE. Retrieved January 13, 2014, from ArchDaily: http://www.archdaily.com/294680/voronois-corrals-decaarchitecture/

fig.6 Glorieta Juan Carlos I - Render fig.7 Glorieta Juan Carlos I - Plan ArchDaily. (2010, Novemeber 14). Glorieta Juan Carlos I / ESC Studio. Retrieved January 13, 2014, from ArchDaily: http://www.archdaily.com/88866/glorieta-juan-carlos-i-esc-studio/

fig.8 Serpintine Sackler fig.9 Serpintine Sackler Plan ArchDaily. (2013, October 2). The Serpentine Sackler Gallery / Zaha Hadid Architects. Retrieved October 3, 2013, from ArchDaily: http://www.archdaily.com/433507/the-serpentine-sackler-gallery-zaha-hadid-architects/

fig.10 Bubble Skyscraper Section fig.11 Bubble Skyscraper Render ArchDaily. (2010, December 6). Bubble Skyscraper / M&A Architects. Retrieved from Archdaily: http://www.archdaily.com/93826/bubble-skyscraper-ma-architects/

fig.12 UN Memorial External Render fig.13 UN Memorial 14th Floor Plan ArchDaily. (2009, October 12). UN Memorial / ACME. Retrieved January 13, 2014, from ArchDaily: http://www.archdaily.com/37318/un-memorial-acme/

fig.14 UN Memorial section fig.15 Vertical Village External Visualisation Render fig.16 Vertical Village: Controlling Voronoi Cells Render ArchDaily. (2011, November 9). Vertical Village: A Sustainable Way of Village-Style Living / Yushang Zhang, Rajiv Sewtahal, Riemer Postma & Qianqian Cai. Retrieved October 2, 2013, from ArchDaily: http://www.archdaily.com/109772/vertical-village-a-sustainable-way-of-village-style-living-yushang-zhangrajiv-sewtahal-riemer-postma-qianqian-cai/

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Minimal Spanning Tree fig.17 Route Adaption - Working Algorithm fig.18 Route Adaption - Working Algorithm fig.19 Smart Phone App - Trip Planner Arrive by. fig.20 Smart Phone App - Trip Planner, Depart by. fig.21 Smart Phone App - Purchase Ticket fig.22 Smart Phone App - Map fig.23 Orthogonal Grid over Wellington fig.24 Voronoi Grid over Wellington fig.25 Un-regulated Voronoi Grid over Wellington fig.26 Regulated Voronoi Grid over Wellington fig.27 Final Routing Algorithm fig.28 Schematic Route Framework fig.29 Site Massinging and Road Layout fig.30 Conceptual Mass Iterations fig.31 Bubble Diagram fig.32 Section - Bubble Diagram to Voronoi Space Divisions fig.33 Plan - Bubble Diagram to Voronoi Divisions fig.34 Plan + Axo- Lofted Walls fig.35 3D Voronoi fig.36 3D Voronoi fig.37 Algorithmic Voronoi Sectioning - Single Floor per Cell fig.38 Algorithmic Voronoi Sectioning - Multiple Floors per Cell fig.39 Voronoi Floors pre-cull fig.40 Algorithmic Floor Culling fig.41 Interpolated Path fig.42

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fig.43 Extrusion fig.44 Boolean Difference fig.45 Triangluar Subdivisions fig.46 Rectilinnear Subdivisions fig.47 Offset Rectilinnear Subdivisions fig.48 Parametric Truss System fig.49 Parametric Truss System fig.50 Internal Voronoi Structure fig.51 Internal Voronoi Structure fig.52 Internal Voronoi Structure fig.53 Voronoi Structure within Volume fig.54 Internal Voronoi Structure fig.55 Grasshopper Input Parameters fig.56 Algorithmic Rubrics fig.57 Schematic Shelter Examples fig.58 Sections - Bubble Diagram to Voronoi Divisions fig.59 Circle Packing fig.60 G.H. Circle Packing fig.61 Boundary Recognition - Forces Applied fig.62 Topography Interpretation fig.63 Antoni Gaudi - Hanging Chain Model ColĂ˛nia GĂźell. 1915 fig.64 Structural Analysis fig.65 Structural Analysis fig.66 Traditional Catenary Form fig.67 Catenary Form with Added Columns fig.68 Catenary Columns with Trimmed Roof fig.69 Algorithmic Seating

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Algorithmic Seating fig.70 Algorithmic Shelter - Iteration 1 fig.71 Algorithmic Shelter - Iteration 1 fig.72 Algorithmic Shelter - Iteration 2 fig.73 Algorithmic Shelter - Iteration 2 fig.74 Algorithmic Shelter - Iteration 2 fig.75 Algorithmic Shelter - Iteration 2 fig.76 Algorithmic Shelter - Iteration 2 fig.77 Algorithmic Shelter - Iteration 2 fig.78 Schematic Route Layout fig.79 Bubble Organisation fig.80 2D Space-Syntax Relationships fig.81 Voronoi Floor Plates During Metaball Simulation fig.82 Form Resolution fig.83 Space Syntax Optimisation fig. 84 Algorithmic Output Floor plates + Voronoi Frame fig.85 Catalouge of Formal Outputs from Algorithm fig.86 Design Iteration A fig.87 Design Iteration A1 fig.88 Design Iteration B fig.89 Design Iteration B1 fig. 90 Design Iteration C fig.91 Design Iteration C1 fig.92 Design Iteration D fig.93 Design Iteration D1 fig.94 Design Iteration E fig.95 Design Iteration E1 fig.96

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List of Animations Animation 1 Culling Cells https://www.youtube.com/v/Vg420XWNPwE%26autoplay%3D1%26rel%3D0%26fs%3D1%26iv_load_policy%3D3%26HD%3D1%26autohide%3D1%26showinfo%3D0

Animation 2 Culling Cells https://www.youtube.com/v/S1yA7hEAzSY%26autoplay%3D1%26rel%3D0%26fs%3D1%26iv_load_policy%3D3%26HD%3D1%26autohide%3D1%26showinfo%3D0%0D

Animation 3 Stills from Iterative Optimisation https://www.youtube.com/v/QGHA4tNbvi4&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 4 G.H. Voronoi Circle Packing https://www.youtube.com/v/pK7TVy2DO3Y&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 5 Physics Simulation https://www.youtube.com/v/cl8ZCETv7cI%26autoplay%3D1%26rel%3D0%26fs%3D1%26iv_load_policy%3D3%26HD%3D1%26autohide%3D1%26showinfo%3D0%20

Animation 6 Circle Packed Voronoi Diagram https://www.youtube.com/v/LWJkchlKPvQ&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 7 Hybrid Metaball Voronoi Diagram https://www.youtube.com/v/cltdm5oz7_s&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 8 Space Syntax Optimisation https://www.youtube.com/v/1TKQv5kqCgU&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 9 Final Framework for Shelters https://www.youtube.com/v/KkU4QLHNlco&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 10 2D - 3D Space Syntax Transformation During Simulation https://www.youtube.com/v/3wXX6Dh5bGM&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 11 2D - 3D Space Syntax Transformation During Metaball Simulation https://www.youtube.com/v/ZLQAQVHf6qA&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

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Animation 12 Voronoi Floor Plates During Metaball Simulation https://www.youtube.com/v/ZLQAQVHf6qA&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 13 Form Simulation https://www.youtube.com/v/vkxD2R5QvdQ&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 14 Space Syntax Adaptation Using Physics https://www.youtube.com/v/eVjl-pASWIk&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 15 Space Syntax Envelope Optimisation https://www.youtube.com/v/FzUQMNs3IqA&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 16 Space Syntax Programming Via Excel https://www.youtube.com/v/bfMiY8JBhW0&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 17 Form Optimisation + Programming Via Excel https://www.youtube.com/v/8yomdrwaa8o&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animation 18 Form Optimisation + Floor Plates Via Excel https://www.youtube.com/v/rfSxLzzXO9U&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animations 19 Methods of Adapting the formal outcome using Physics Simulations https://www.youtube.com/v/z5Xox9BYxos&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animations 20 Methods of Adapting the formal outcome using Physics Simulations https://www.youtube.com/v/Hjizt0kfKfA&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animations 21 Methods of Adapting the formal outcome using Physics Simulations https://www.youtube.com/v/Bg88AyOJDHk&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animations 22 Methods of Adapting the formal outcome using Physics Simulations https://www.youtube.com/v/x7C1tbPqp5A&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

Animations 23 Quick Algorithmic Design Iteration https://www.youtube.com/v/1v55snu3AlM&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

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7. 1

. 13 13.0

Appendix This section contains construction drawings and experiments conducted throughout this research that contributed to the final outcome.

Appendix A - Construction Drawings

A

Parametric Transport Canopy

Parametric Transport Canopy

SARC 421: Project 02

Integrated Technologies + Construction

Frano Bazalo 300157293

This design is a parametrically generated series of public transport related shelters and hubs. The strucutures are designed to facilitate the public transport netword across Wellington. The generative logic is designed to optimise these architectural facilities within the Wellington Public Transport Network. The structure is designed to grow and adapt according to the use and demand of commuters. Consequently, the construction methods for the structure had to allow for this shifting architecture. Equally, the logic adapts the structure to suit specific sites. Not one structure is identical. However, it was important to achieve this through a set of modular components that have the ability to mould to the unique site conditions. For this project I have chosen to focus on the construction of the canopy as this is the fundamental part of the design. The central stems of the canopy remain constant on any site while the undulating grid shell is unique and is therefore CNC machined to fit. 4000

It was then important to create a series of components and systems for this central stem as it could be applied to any structure. I have broken this central stem into three sections to detail.

roof height

Top third: Canopy connections relating to the glazing and membrane

Centre: Canopy connection relating to tension ring and membrane

Bottom Third: Canopy footing

S2 A2.02

0 ground level

S1 A2.02

Longitudinal Section 1:100

204 S3

S4

S1

A2.02

Reference Notes:

P1 A2.01

Floor Plan Including Reflected Ceiling 1:100

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B

Appendix B - Algorithmic Exploration Contours This experiment explores an exoskeleton structure. By using the natural mesh, the subdivisions are completely irregular. This causes trouble where the form a “pinches’ in the middle. To create even subdivisions, the form was contoured on two angles resulting in evenly sizes sections.

Natural Structural Edges The other option that was explored was extracting the natural seams of the form. This method accentuated the fluidity of the form but is not a structural resolution in its own right.

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Louvers As part of an exercise experimenting with apertures, a definition was developed to break the external envelope into a functioning, parametrically driven â€˜louvreâ€™ system. This option was favoured for several reasons. As panelling the external envelope presented numerous issues including structural, fabrication, water tightening and constructability to name a few, new options needed to be explored. As the form was based on strong but free-flowing lines this was something that needed to be accentuated. By using these lines as reference points, a dual-skin louvre system was created. The louvres are broken up into manageable sections for both fabrication and construction requirements. The louvre system allows for a more simplistic body construction while the flowing strips re-install fluidity to the form. As they are parametrically operated they can be utilised for the internal environmental conditions.

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Algorithmic Facilities A quick experiment working with algorithms to distribute programme according to the parameters. The definition also includes boolean rules which could be used to insert facilities such as toilets, ATM’s and stores. The experiment is logic not form based. h t t p s : / / w w w. y o u t u b e . c o m / v / B f 6 F Q 5 n Y 2 P Q & a u t o p l a y = 1 & re l = 0 & f s = 1 & i v _ load_policy=3&HD=1&autohide=1&showinfo=0

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Adaptable Parametric Bus Shelter Experiment An early experiment with parametric tools. A simple definition which adapts a bus shelter according to attractor points. As these points are moved the shelter adapts according. The idea is that the points will be taken from the site to produce unique, site specific responses. https://www.youtube.com/v/VYbK444zZY4&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

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Adaptable Parametric Bus Shelter Experiment An early experiment with parametric tools. Experimenting with adapting a parametric bus shelter based on attractor points. As these points are moved the shelter adapts according. The idea is that the points will be taken from the site to produce unique, site specific responses. https://www.youtube.com/v/YDCQ5q13gaU&autoplay=1&rel=0&fs=1&iv_load_ policy=3&HD=1&autohide=1&showinfo=0

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Evolutionary Optimisation Galapagos Solver - Optimising Routes + Passengers Using an evolutionary solver (Galapagos - grasshopper), the variables are optimised. The script aims to return the minimum average waiting time for each patron while using the minimum amount of transport vehicles to meet the defined quota. https://www.youtube.com/v/0zwuuhL8IY0#t=39&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0 https://www.youtube.com/v/s9fBE1bvJx8#t=29&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

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https://www.youtube.com/v/QuXcQbDhvmY&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0 https://www.youtube.com/v/QS_vW7hSgD4&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

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Woolly Paths This definition deforms a grid to creates paths between a city grid. https://www.youtube.com/v/cq1shZdX1fk&autoplay=1&rel=0&fs=1&iv_load_policy=3&HD=1&autohide=1&showinfo=0

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View Shaft Study This definition calculates view shafts from certain targets. The colour indicates the distance (green being close, yellow medium and red distant) The first diagram has several ‘key’ view nodes around the site to show what the existing shafts are. The second diagram follows a path from Thorndon Quay to Lambton Quay taking the bus route. The third 3-dimensional diagram shows an alternative route along the railway station and up Molesworth Street.

http://www.franobazalo.com/wellington-station.html 226

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Responsive Algorithms

An investigation of computational processes in early stage design. Thesis Submission for Masters of Architecture (Prof) @ Victoria Universit...

Responsive Algorithms

Published on Apr 17, 2014

An investigation of computational processes in early stage design. Thesis Submission for Masters of Architecture (Prof) @ Victoria Universit...

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