Surface Reality-web

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SURFACE REALITY:
GEOMETRY, CRAFT and SHAPE OF THE INVISIBLE WORLD.
Peter James John McPherson
ID: 1056759
A thesis submitted in partial fulfilment of the requirements for the degree of
Master of Architecture, Unitec New Zealand, 2014.

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This research project investigates how the
computer and Computer Aided Design software
has influenced architecture in the past twenty
years; from the influence the digital has had on
design thinking to the production of buildings not
before thought possible. A study of the principles
of computer operation helps to establish a position
for a proposal as to how digital tools might best be
utilised by architects from an ideological and
methodological perspective.
A study into geometric principles works in parallel
with a historical survey to gain an appreciation of
the differences between dominant contemporary
architectural theory and the projects being carried
out by practising architects.
Geometry is the constant throughout the study and
the understanding of geometric principles and
digital operations is critical to establishing a
position with which to develop a methodology for
exploring the design proposal for an events centre
on Halsey Wharf in Auckland, New Zealand.
The goal of this research is to inform the practise of
architecture with the benefits of particular
geometric solutions in order to offer an approach to
engage directly with the shaping of architecture in a
digital environment.
ABSTRACT

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I confirm that this thesis represents my own work,
including text and images, unless otherwise stated.
Peter James John McPherson
ID: 1056759
Master of Architecture
Department of Architecture
Unitec New Zealand
DECLARATION OF WORK

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ACKNOWLEDGEMENTS
I owe much thanks to my supervisors, Dr Branko
Mitrovic and Nikolay Popov and, also to Matthew
Bradbury, for their insight and direction throughout
the course of this research.
To my family, friends and colleagues for the
conversations and your encouragement, support
and wisdom I am continually grateful.

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Abstract iii
1 Introduction
1.1 Research Question 11
1.2 Introduction 13
2 Theoretical Background
2.1 Greg Lynn and Folding in Architecture 17
2.2 Calculus 19
2.3 Conservatism 21
2.4 Digital Tools 27
2.4.1 CAD + BIM 29
2.4.2 Computational Design 31
2.4.3 Design or Drafting? 33
2.4.4 Intelligence 35
2.4.5 Simplexity 39
2.5 Foster, Gehry and the Sydney
Opera House 43
3 Geometry 53
3.1 Peter Schröder 55
3.2 Mesh Subdivision 57
3.3 Planar Quadrilateral Meshes 61
3.4 Curves 63
3.5 Surface Types 67
4 Design Proposal
4.1 Project Outline 81
4.2 Brief - Viaduct Events Centre 83
4.3 Project Development 87
4.4 Process 93
4.5 The Proposal 107
5 Reflection 123
6 References
6.1 Bibliography 137

TABLE OF CONTENTS

11
How can an understanding of planar quadrilateral meshes inform an architectural design methodology
with respect to doubly-curved surfaces?
1. INTRODUCTION
1.1 RESEARCH QUESTION

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Where previously geometric possibilities were limited by the ability to
conceive and communicate a design with two-dimensional
representation systems, digital tools offer the potential to move from
design to fabrication to assembly for seemingly any shape one can
imagine.

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1.2 INTRODUCTION
1. Cristiano Ceccato, Advances in Architectural Geometry
2010, (Dordrecht: Springer, 2010), Foreword. “Modern
geometric computing provides a variety of tools for the
efficient design, analysis, and manufacturing of complex
shapes.”
2. Helmut Pottmann et al, Architectural Geometry, (Exton,
Pa: Bentley Institute Press, 2007), 362.
3. John K. Waters, Blobitecture: waveform architecture
and digital design, (Gloucester, Mass.: Rockport
Publishers, 2003), 258.
The computer has come to completely dominate the
architectural office. The computer and the digital
tools it powers have brought a wealth of
calculating potential far beyond what the human
mind can easily comprehend. These tools enable
designers to explore geometric possibilities far in
advance of the traditional methods of the pencil,
triangle and flexi-curve.
This research attempts to understand the link
between architecture and geometry at a time when
these digital tools present to designers a near
limitless number of geometric possibilities.
Building proposals of any shape can be conceived,
engineered and communicated for construction1
.
Some of the leading architects in the world engage
with these fantastical shapes yet proposals for
free-form architectural responses are rare except in
these high profile instances.
History informs us of the fundamental link between
architecture and geometry. The earliest example of
free-form buildings could be considered the wood
and willow dome-like shelters built 400, 000 years
ago2
. Concrete, and later reinforced concrete, gave
designers the ability to construct and the freedom
to design sculptural forms such as Eero Saarinen’s
TWA Terminal (1956-1962) and Le Corbusier’s
Notre Dame du Haut (1950-1955). Later, digital
tools provided the instrument for Frank Gehry to
build the Fish for the 1992 Barcelona Olympics.
Where previously geometric possibilities were
limited by the ability to conceive and communicate
a design with two-dimensional representation
systems, digital tools offer the potential to move
from design to fabrication to assembly for
seemingly any shape one can imagine.
However, this isn’t quite the case. Digital tools
haven’t led to a revolution in the shapes of
buildings we see in our cities every day. There
appears even a conservatism to the shapes of new
buildings given the potential the computer presents.
What are the limitations to free-form shapes being
proposed in architecture? How can we understand
the shapes on our computer screens to take what
exists, in Norman Foster’s words, in “the silent,
invisible electronic world” and bring it into
“physical reality”3
.

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2.1 GREG LYNN and FOLDING IN ARCHITECTURE
4. From the publisher, Wiley: This seminal book from
Architectural Design was originally published in 1993,
at a time of crucial change and on the eve of the digital
revolution. It brought together a series of essays that
many believe created the favourable environment in which
computer-based design could thrive. Considered one of the
most influential architecture publications of the 1990s, this
book ranks as a classic and in itself is a crucial chapter of
history.
5. Greg Lynn, AD: Folding in Architecture, Rev. ed.
(Chichester, West Sussex; Hoboken, NJ: Wiley Academy,
2004), 12.
6. Gilles Delueze, Le pli, (Editions de Minuit; Critique
edition, 1998), trans Gilles Delueze, Fold: Leibniz and the
Baroque, (Univ of Minnesota Press; 1 edition, 1992).
2004), 16.
In 1993 Greg Lynn published what is widely
regarded as a seminal publication on digital
architecture, Folding in Architecture4
. While
digital tools, computers, and their application in
design could first be seen in Ivan Sutherland’s
development of Sketchpad in 1963, with its full
graphical user interface and widely considered the
ancestor of modern CAD software, Lynn’s
publication came at a time which, in Lynn’s own
words, “captured a moment before the discovery of
a new kind of drafting machine, a much more vital
machine than the compasses, adjustable triangles
and rubber spline curves with which most of the
projects were conceived”5
.

Here Lynn is referring to the “moment before” the
advent of affordable computing power that led to
the widespread adoption of graphical software as a
real alternative to traditional ink and trace. This is
important to note as it suggests that the subsequent
digital explorations in shape and form were not due
to critical thinking relating to the computer itself
but rather based upon the theoretical implications
presented by Peter Eisenmann and his formulation
of Gilles Delueze’s at that stage little know text,
Le pli6
. As a consequence, we note that the work
contained within Folding in Architecture is based
upon some other agenda and is not so concerned
with what the “new kind of drafting machine” itself
offered. The machine was merely the vehicle to
explore Deluezian concepts with. In Greg Lynn’s
words;
So we see how an original quest for formal
continuity in architecture, born in part as a
reaction against the Deconstructivist cult of the
fracture, ran into the computer revolution of the
mid-nineties and turned into a theory of
mathematical continuity. By a quirk of history, a
philosophical text by Gilles Deleuze accompanied,
fertilized and at times catalysed each of the
different stages of this process. Without this
pre-existing pursuit of continuity in architectural
forms and processes, of which the causes must be
found in cultural and societal desires, computers in
the nineties would most likely not have inspired any
new geometry of forms. Likewise, without
computers this cultural demand for continuity in
the making of forms would soon have petered out
and disappeared from our visual landscape7
.

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The desire for formal continuity in architecture has
since been explored for two decades. The
explorations in the 1990’s of Deleuze particularly
focussed upon Gottfried Wilhelm Leibniz’s monads
and work on differential calculus and provided the
platform for the smooth forms that dominate the
digital architecture scene today. The fold was
combined with ideas of the infinitesimal and
variable rates of change (from calculus) and the
fractured, sharp and angular aesthetic started on the
drafting table began to smooth in appearance. The
desire to explore shapes that required more
complex mathematical definition, that is curves,
was made possible by the computational power
of the digital tools available. However the theory
underpinning this remained with ideas pre-dating
the existence of the computer.
The theoretical underpinnings of the work from
the early 1990’s is claimed to be due to the cultural
and societal desire to break with Post Modernism
and Deconstructivism. The theories of folding and
pliable architecture occurred at the instant where
affordable computers came to bear and meant that
complex formal explorations could occur,
ultimately leading the fold to evolve into the blob.
The investigation of the blob though relied upon
the text of Deleuze to “fertilize” this exploration
and one wonders if this obscured other potential
benefits that the computer may have afforded
architectural design at the time. As it stands, it
appears the situation that the computer was used
as a means rather than an end. This is interesting
as initially, Antoine Picon notes, the computer was
“expected to reinforce the predominance of
structure and tectonic in architecture because of the
new possibilities it offered to pass almost
seamlessly from the first sketches to detailed
technical solutions”8
. This concept is particularly
relevant today as the idea that what is produced
digitally may be directly translated to fabrication is
one at the forefront of advanced architectural
practise and, even though the idea had been
mooted, these early exploration appear to have little
sympathy for it.
8. Antoine Picon, Digital Culture in Architecture,(Boston,
MA: Birkhaeuser, 2010), 127.

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2.2 CALCULUS
9. Antoine Picon, “Architecture and Mathematics,” in AD:
Mathematics of Space, ed. Legendre, George L, (London:
John Wiley & Sons, 2011), 29.
10. Ibid., 33.
11. Ibid., 33.
2004), 16.
The issue of calculus in architecture is of interest
to this study as we find it being used as the basis
of justification for curved shapes. Antoine Picon
argues that in Renaissance times mathematics could
be said to have empowered the architect9
, enabling
the architect to work within some limits of
geometry and arithmetic to produce architecture
of power or restraint. However, when architects
began searching for foundations in the 19th
Century,
those such as Eugene-Emmanuel Viollet-le-Duc
looked to the biological sciences rather than
mathematics. Mathematics was merely seen as a
useful tool rather than part of fundamental design
techniques. This estrangement of mathematics
from architecture tends to exist today even though
the advent of the computer means that we have
never before used so many mathematical objects
due to the tools that digital software provides us.
Additional to this is the way that calculus has
changed the design process for architects. It can be
said that the laws of approximation of
mathematics in architecture that pre-dated calcu-
lus allowed the architect to work within a system
of sorts. The skill of an architect was in applying
a proportional system to best suit a situation to
derive the most pleasing result, both aesthetically
and functionally. Matters were visual and about
the composition and shape of the building. The
introduction of calculus and biology to architecture
resulted in a different relationship between
mathematics and the architect. Whereas previously
we could say that an architect’s use of mathematics
tended towards some average that could be
manipulated, calculus changed this. Mathematics
is now about “setting some limits to a phenomena,
then modelling them with laws of behaviour”10
.
Picon goes so far as to say that, “Design was no
longer involved”11
when discussing the role of
calculus in architectural design. No longer is it
possible to tinker with proportions but the designer
is beholden entirely to the shape resultant from the
input equation.
The issue of calculus and Leibniz is then one that I
believe is critical in importance when considering
a direction for digital architecture today. In the
search of new shapes through defining changing
form, calculus was taken to not describe an object,
but their laws of change – the infinite, infinitesimal
variations12
and it is the process for describing or
generating the shape that takes priority.

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As discussed previously this description would
appear to infer that the final shape of a building is
of lesser consequence in relation to the process. To
my mind this raises a critical point as to the shape
of the objects and whether indeed the formal
exploration is actually about the shape of the
building or is simply about astonishment and doing
something different.
For example, if one analyses the work of Peter
Eisenman in Folding in Architecture, they will note
the projects are not in fact moving and changing
works as the author desired but schemes that are
frozen in time. Nor do they formally represent
folds but instead fractured forms that break13
. It
is an example of where design cannot be taken to
be a formal exercise with regards to shape but is
instead a process where the formal outcome is but a
single moment in time determined entirely by some
predefined laws of behaviour. We might determine
that the failure to wholly engage with issues of
shape are a legacy of preceding Post Modern and
Deconstructivist theories. We could suggest that
the literary investigation of the term calculus was a
limitation to this work when regarded in the digital
sense and so the digital aspect was naively or
under-represented.
What we see in the early investigations and
experiments with digital tools is what one typically
witnesses when a new technology arrives. Chris
Luebkeman discusses this issue in Branko
Kolarevic’s Architecture in the Digital Age14
.
Luebkeman talks of the initial adoption of a
technology being imitation followed by injudicious
exploration. The third stage of the adoption of a
new technology is the appropriate application of
said technology. While the curved shapes produced
during the explorations of the 1990’s indeed pushed
formal boundaries it might be fair to suggest that
for many architects digital technology has never
moved far from the conservative imitation of the
previous technology, ink and trace.
The early outrageous explorations didn’t take us
far as towards the ‘appropriate application’ of the
technology that Luebkeman calls for but they did
give us a foundation to begin exploring from. In
(re)defining15
the necessity for the combination of
heterogeneous elements, as opposed to the violent
clashes sought by Deconstructivism, we now can
explore what these elements for combination might
best be, in order to meet the challenges that face
architecture today.
13. Ibid., 15.
14. Branko Kolarevic, Architecture in the Digital Age,
(New York, NQ: Spon Press, 2003), 291.
15. I say here ‘redefining’ as it could be argued that Master
Craftsmen and Renaissance architects had a fundamental
understanding of the combination of building science and
architectural concerns. It is sometimes said that these
concerns are again ones that are being explored today.

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2.3 CONSERVATISM
If we consider the architectural propositions of the
nineties described above as being ones of
outrageous exploration, then what we witness today
in many architectural offices can certainly be said to
be an environment of conservatism. The computer
is employed as a drafting machine and rarely is the
tool utilised beyond the description of simple
rectilinear shapes. It is merely imitating previous
technologies. If we compare the majority of
buildings designed and constructed today one sees
very little change in formal appearance to those
buildings built sixty years ago. I believe this point
to be important given the legacy of early digital
explorations and the ability the computer gives us
to explore, visualise and communicate curvilinear
shapes. It seems unusual that the computer isn’t
being used more by architects to explore complex
spatial and formal ideas. Computers are rarely used
in the design process beyond the three-dimensional
representation of buildings for visualisation
purposes. The potential to engage with the
computer as a design tool beyond what is currently
in common practise is obvious so what leads to its
conservative use?
Image far right of the Seagram Building, Mies van der
Rohe, 1958.

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“An architect who is not a master these techniques finds himself in the
painful situation of the man who wishes to compose although he plays
no instrument, is unable to write music, and knows nothing of the art
of counterpoint.”

Pier Luigi Nervi

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Bill Mitchell discusses the issue of conservatism as
being linked to a lack of understanding of the tools
available with digital software. I would equate this
to the act of drawing in such that, if one is unable to
draw a particular shape it is extremely unlikely that
one will design with it. Mitchell states that it is the
issue of mathematics that architects struggle with
when engaging with the computer16
. Without a
fundamental understanding of how computation
works architects will struggle to escape the
conservative application of digital tools. Perhaps
one can reflect on Pier Luigi Nervi’s pertinent
comment in discussing the student that considers
building as form without any knowledge of
structures, and hold it comparable to the architect
utilising digital tools to explore building as form
without knowledge of mathematics or geometry;
An architect who is not a master these techniques
finds himself in the painful situation of the man who
wishes to compose although he plays no
instrument, is unable to write music, and knows
nothing of the art of counterpoint.17

Pier Luigi Nervi
17. Pier Luigi Nervi, Structures, (New York McGraw-Hill,
1956), 24.
Image far right of 7 World Trade Centre, SOM, 2006.

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If a lack of understanding of digital tools can be
considered one reason for conservatism another
issue is the argument that cost is too high for
curved buildings to be a viable option to even begin
with. In a conversation with Greg Lynn, Frank
Gehry talks spiritedly against this idea18
. To
illustrate his point he uses the example of
Beekman Tower (2006-2010) at 8 Spruce Street in
New York City (image opposite). Gehry discusses
the opinions at the time this building was being
designed that “bubbly shit” was not possible due to
the recession and that instead architects should be
looking towards the “budget-conscious sort of box”
to provide their clients with value. The design of
Beekman Tower involved a rigorous process that
included both architect and façade manufacturer in
the design stage. This meant that there was
“no mystery to the design” when it came to costing
the project and yielded an outcome where
construction bids to build the curvaceous twisting
form came in at the same price as a simple flat
curtain wall system. This relationship additionally
resulted in there being only around 250 requests for
information (rfi) throughout construction, whereas
a building of similar size would normally result in
around 1500 rfi’s.
To pick up on Gehry’s comment regarding the
“budget-conscious sort of box”, it is suggestive of a
sense amongst architects there being some virtue in
adopting a conservative approach to shape making
and applying value to the design through
incorporating particular materials. This is in
contrast to Gehry’s approach of maximising the
formal potential of a material. Instead of
engaging with complex spatial or formal
exploration, the qualitative aspect of architecture is
reduced to a narrative19
. The conservative formal
language is justified based on a story, as opposed
to the pursuit of a rich formal language based
upon understanding physical material qualities
and the craft of building with them. The approach
pioneered by Gehry and his associates requires a
design team demanding in their approach in order
to achieve such exceptional formal results within
a standard budget. It also requires the design team
to be able to maximise all tools available to them,
from hand sketches to physical models and digital
models to fabricated scale mock-ups.
18. Greg Lynn & MF. Gage, Composites, Surfaces and
Software: High Performance Architecture, (Yale School of
Architecture, 2011), 122-126.
19. Ibid., 126.

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The idea that architects might be able to explore
greater spatial variety due to the computational
power of the computer is a rich one and something
worth understanding further, particularly given the
claims that the computer opens up new geometric
possibilities in architecture20
. Understanding more
about the possibilities and application of digital
tools for architecture will help the architect move
beyond the conservative use of the computer.
20. Helmut Pottmann et al, Architectural Geometry,
(Exton, Pa: Bentley Institute Press, 2007), I. “Whereas the
variety of shapes that could be treated by traditional
geometric methods has been rather limited, modern
computing technologies have led to a real geometry
revolution”.
Image far right of 8 Spruce Street, Frank Gehry, 2010.

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2.4 DIGITAL TOOLS
Digital tools available to designers today are varied
and plentiful and as such, their purpose also
varies greatly. Let us begin by describing not the
computer but the types of software that architects
commonly use to understand the implementation of
computers in architecture.

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2.4.1 CAD + BIM
For a long while I, maybe naively, considered CAD
to stand for Computer Aided Design. However,
in most instances, the ‘D’ stands for Drafting and
it is most apparent that Computer Aided Drafting
has come to dominate in all architectural offices
across the world. The computer has proved to be a
very efficient pen, triangle and curve, eliminating
drawing boards from architecture offices. Yet this
is where the advantages of the digital tool stops in
most cases. The computer is exploited for its
efficiency at drawing a series of disconnected lines
and nothing more. This seems a strange situation
given that what is considered the ancestor of
modern CAD software, Ivan Sutherland’s
Sketchpad (1963), placed parametric change at the
heart of its system.
We are starting to witness a shift in the mainstream
practise of architects towards what is called
Building Information Modelling, or BIM. In this
case, it is not a series of two-dimensional
disconnected lines that come to represent a
building but a virtual three-dimensional model of
the building. This model comprises actual building
elements; no longer do architects draw series of
disconnected lines but instead walls, floors, roofs,
windows and doors. And each of these elements
can be embedded with all kinds of information.
This information is extremely valuable when it
comes to quantifying what comprises the buildings
(for example areas, volumes, count of materials)
and like Computer Aided Drafting, provides further
efficiencies in the description of a building.
Additionally, architects and engineers can co-
ordinate their models to combine the architectural
model with structural and mechanical systems
providing a comprehensive understanding of the
building before construction has begun. There is
the potential for this model to be used to predict
the energy usage of the building and be used for
post-occupancy activities such as maintenance.
Extending beyond three-dimensional representation
and considering the modelling of behaviours such
as these is an important aspect of BIM.
BIM can be referred to as a parametric model. This
is because parameters and behaviours are
embedded within elements or, because relationships
between elements are established. Some building
elements exist in relationship to other elements,
such as a door in a wall, and if you adjust one then
the other adjusts in kind. If you change something
in the model, such as the composition of parts of a
wall, then the parameters update.

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Whilst we might associate parametric design as
being part of the cutting edge of digital design it is
extremely rare to find BIM be described as a design
tool.
While being very good tools for architects to use in
everyday practise, neither of the two practises
described above have a strong impact upon the
design of a building or how an architect might
conceive of the design of a building. It is true that
even after 20 years of use of digital tools in archi-
tects’ offices much design work is undertaken with
pencils, paper and physical models.
However, all this is not to say that we don’t see
further explorations utilising digital tools that
extend upon the curved forms that we were
beginning to see in the mid-1990’s. At what might
be deemed the fringes of advanced design
practise one can see all manner of wildly curving
and twisting shapes in the architectural context.
The twenty-first century has seen digital design
tools enter the era of the algorithm through
generative and parametric design.

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2.4.2 COMPUTATIONAL DESIGN
21. Merriam Webster Dictionary, accessed July 28 2014.
www.merriam-webster.com/dictionary/algorithm.
There are a number of areas of digital design that
might be tending to be classed in the area of
Computational Design yet all maintain separate
headings. Three common areas in this field are
Algorithmic Design, Generative Design and
Parametric Design. Definitions for each of these
are difficult to find a consensus on yet generally we
might consider them thus:
Algorithmic Design.
An algorithm is, “a procedure for solving a
mathematical problem (as in finding the greatest
common divisor) in a finite number of steps that
frequently involves repetition of an operation”21
.
If we think about this in the sense of design then we
might consider a design being arrived at by a step
by step approach that achieves some outcome. It’s
important to note that algorithmic thinking isn’t
necessarily restricted to computational processes
yet the computer may aid in processing outcomes
more quickly.
Generative Design.
Generative design typically involves the use of
algorithms to achieve some outcome through a
repetitive process or, iterations. This involves the
definition of a rule (often based on some
phenomena) that can be tested and modified with
further outcomes possible. The feedback loop is
important here for outcomes to be considered
generative. Typically generative outcomes may be
considered either self-organisational or
evolutionary. Once again these processes aren’t
restricted to digital design. Pier Luigi Nervi’s
hanging cloth models or Antonio Gaudi’s hanging
chain or plaster models represent analogue methods
for generating a form in an interactive manner.

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Parametric Design.
Parametric design is perhaps one of the more
difficult terms to define. Generative design is
considered to utilise parameters and we might
define BIM as a form of parametric modelling,
that is, the building elements contain some type of
parameter. Essentially we may consider
parametric design as elements that have an
association of some sort to a property or some other
element or elements.
The tools or software available for computational
design is usually from fields outside of the
architectural discipline. One of the most famous
examples is CATIA22
, which Frank Gehry
employed to construct the Fish sculpture in
Barcelona, Catalonia, Spain for the 1992 Olympics.
CATIA was initially developed for the design and
manufacture of aircraft by French manufacture
Avions Marcel Dassault in 1977. Since 1992
Gehry has adapted the technology to be more
specific to architecture and released the software,
Digital Project. There is other software available
and used by architects such as those from the
industrial design field like Autodesk Alias or
McNeel & Associates Rhinoceros, or the visual
effects industry where Autodesk Maya and 3dsMax
are used. More recently visual programming
languages are being adopted where Grasshopper,
Bentley Systems Generative Components and
Autodesk’s Dynamo are providing architects the
tools to create ever more complex formal designs.
22. CATIA – Computer Aided Three-Dimensional
Interactive Application.

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2.4.3 DESIGN or DRAFTING?
23. Real-time; the display is updated instantaneously so
that the view of the object is communicated back to the
user with little to no delay.
Generally, even if only in a conservative way,
architects can be considered to incorporate
computers into the practise of design and, it is
maybe unsurprising that it is the area of
visualisation where computers are readily
employed in this manner. Being able to view a
design from any and every angle is an extremely
powerful tool for an architect as they work through
a design. Ideas can be tested and critiqued based
upon what they look like and adjustments made to
the digital model, usually in real-time23
. The
computational power of the computer is harnessed
to draw and re-draw the multitude of lines that
would traditionally be laboriously constructed by
hand. Additionally, a series of perspectival images
can be prepared in addition to the tradition plans,
elevations and sections, making evaluation of the
design for an eye untrained in architectural
conventions more accessible. In fact, an entire
industry dedicated to the virtual realisation of
unbuilt projects is testament to the value placed
upon being able to see a building before it is
built. This process is becoming more prevalent
as three-dimensional models become standard for
documenting a building via BIM practises.
We see here how the value of the computer is
prioritised by architects around its ability to
visualise works. An architect uses the computer
to see a work and communicate it to others. Aside
from issues of conservatism discussed previously,
perhaps another reason that the early digital works
within Folding in Architecture haven’t made an
impact upon mainstream architecture is that visual
matters were not a priority. Impressive and new
shapes were introduced to the architectural
discourse but with no way to evaluate them in a
visual sense. The priority was upon the process,
not the outcome. In most architectural work the
process is varied, complex and often highly
personal and, the digital tool needs to support this,
not supersede it in generating outcomes that
cannot be questioned. Understanding this will
enable architects to move beyond using the
computer to simply draft and instead open up
opportunities to explore design.

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“The computer is a finite machine” and, “all that computers can do
is to follow simple rules quickly and reliably. A piece of software may
contain thousands of rules and this gives an illusion of intelligence”

Chris Williams

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2.4.4 INTELLIGENCE
In the previous chapter I introduced the idea that
many things influence an architect as they design.
The issue of what the building looks like however
is always a principal consideration and
Buckminster Fuller’s statement, “When I am
working on a problem, I never think about beauty.
I think only how to solve the problem. But when
I have finished, if the solution is not beautiful, I
know it is wrong”, is a position I think many
architects can relate to. To my mind this is
especially important to remember given how digital
tools are currently utilised. In embracing new
technologies one should perhaps heed Sulan
Kolatan’s words of the danger of, “an extreme
reliance upon technology. We ought to be careful
about trusting a new technology to create perfect
solutions on its own”24
. Having looked at various
ways that the computer is used in the architectural
field I feel that in order to focus design practises
specifically about shape and form one should better
understand the computer that powers the software,
how the computer works and some limitations
of the tool. This in order to understand what the
computer might best offer a designer to be able to
pursue engaged formal exploration.
We looked earlier at ideas pervading architecture
in the 1990’s. These ideas placed calculus and the
idea of ‘rates of change’ at the centre of
architectural thought. From here architecture
explored the infinitesimally smooth and
architecture of heterogeneity. These computational
explorations appeared to place emphasis back upon
mathematics and spatial ideas after a period of
Post-Modern representation and Derridean
Deconstructivist linguistic pursuits but they didn’t
explore specific potentials of the computer.
Calculus was the vehicle to introduce curved
shapes to the architectural discourse and yes, the
tools we engage with on a computer utilise
calculus, but the way we interact with a computer is
based upon the algorithm.
What we may understand better today is what the
computer in its own right can offer to the
designer. Whereas previously the curved forms
being portrayed had their origins in a linguistic
theory, increased computational power and access
to software means that anybody is now able to
define a wilfully arbitrary curved object. Merely
having a pseudo-theoretical basis for exploring
curved forms no longer seems enough given as we
see very few built examples.

36
So perhaps we need to better comprehend the
computer as a tool in its own right to make better
use of it within our architectural design process.
What then is it that underlies the computer and how
we interact with it?
“The computer is a finite machine”25
and, “all that
computers can do is to follow simple rules quickly
and reliably. A piece of software may contain
thousands of rules and this gives an illusion of
intelligence”26
. The basis for any computational
activity is the algorithm. An algorithm can be
described as a step-by-step procedure for
calculations. Whenever we interact with the
computer we are asking it to follow a set of
processes in order to reach an outcome. These
computational outcomes are the result of an
algorithmic logic. Therefore, to design
something within the digital environment, one
needs to be aware of this logic. Extending from
this, one can also postulate that the computer is not
in fact intelligent but merely a machine that is very
good at performing calculations. A human on the
other hand is intelligent but with relatively little
computational power27
. We might begin to argue
then that computer aided design needs to align the
advantages of the calculating power of the
computer to the intelligence of the human operator
rather than expecting the computer to produce
Kolatan’s perfect solutions on its own. As Steve
Jobs famously remarked, “what a computer is to
me is it’s the most remarkable tool that we’ve ever
come up with, and it’s the equivalent of a bicycle
for our minds”28
. The computer is a tool, one that
allows us to process large amounts of data and
architects should be using this power to extend
their own intellect.
It is undoubtedly controversial to suggest that the
computer has no intelligence. After all, there are
many investigations happening in the area of
artificial intelligence that certainly hope towards
this not being the case and, a simple argument for
computers being intelligent might be that all we
need to do is understand the human brain in its
entirety and then reproduce it perfectly with the
outcome being an obviously intelligent replica. Or,
if that sounds unfair, then by Alan Turing’s Turing
Test to establish artificial intelligence (AI),
whereby Turing stated that if an interviewer is
unable to ascertain through questioning which of a
pair of responses are human or machine then it does
not matter how the responses are elicited and thus
the machine can be considered intelligent.
25. Peter Schröder, “Digital Geometry,” in Greg Lynn
Form,ed. Mark Rappolt, (New York: Rizzoli), 146.
26. Chris Williams, “Design by Algorithm,” in Digital
Tectonics, ed. Neil Leach, David Turnbull, Chris Williams
(Chichester, West Sussex, UK; Hoboken, NJ, 2004), 79.
27. Ibid., 79.
28. From a documentary Memory & Imagination: New
Pathways to the Library of Congress, link last accessed 25
July 2014. http://www.mlfilms.com/productions/m_and_i
Video: http://www.youtube.com/watch?v=6kalMB8jDnY
. Steve Jobs makes this statement after first discussing
humans as ‘tool builders’, “I think one of the things that
really separates us from the high primates is that we’re
tool builders. I read a study that measured the efficiency of
locomotion for various species on the planet. The condor
used the least energy to move a kilometer. And, humans
came in with a rather unimpressive showing, about a third
of the way down the list. It was not too proud a showing
for the crown of creation. So, that didn’t look so good.
But, then somebody at Scientific American had the insight
to test the efficiency of locomotion for a man on a bicycle.
And, a man on a bicycle, a human on a bicycle, blew the
condor away, completely off the top of the charts”.

37
However, as stated above, the intelligence
demonstrated by a computer is an illusion based
upon the ability to recall information. We have a
number of examples to point to that suggest that no
matter how hard we try, the computer will offer no
more than the ability to give feedback based upon a
set of given instructions.
A simple example of this might be the mobile
‘smart’ phone. You can talk to the phone and have
it set appointments or find you somewhere close to
eat yet none of these activities suggest that the
object in your hand is intelligent, it is responding
to a set of inputs and you aren’t able to have a
meaningful conversation with it. Moreover, we
can compare the computational capacity that we
currently have had for some time and compare it to
that of a bumblebee. While of similar processing
capacities, we do not see computers forming social
structures, fending off threats or reproducing. We
can also consider the intelligence required for a
human to walk, to co-ordinate the enormous
number of impulses to balance as a step is taken
while processing the surrounding environment and
compare to the exploits of robots, even those as
advanced as in the DARPA Robotics Challenge,
where this form of analysis demonstrated by a
human is beyond even these most sophisticated and
powerful of machines. In each of these
situations we note that the computer processes a set
of instructions and provides a result based upon the
inputs. Animals and humans however are able to
make analysis and adjustment based on unknown
variables.
A considered philosophical response to the issue of
artificial intelligence can be seen in the philosopher
John Searle’s Chinese Room situation. This
example explains why a computer cannot be
considered to think. In the scenario, one is to
imagine themselves as an English only
speaker locked in a room. In that room are baskets
of Chinese symbols and some rules so that you
can manipulate the Chinese symbols. These rules
determine the purely formal manipulation of the
symbols, their syntax as opposed to semantics. You
then imagine that Chinese symbols are passed into
the room, ‘questions’, and you are able to pass back
‘answers’, having been provided further rules to
pass Chinese symbols back out of the room. The
responses sent back are unidentifiable to the native
Chinese speaker as being by somebody that doesn’t
understand Chinese and hence imagines that the
person in the room knows and understands Chinese.

38
However Searle asserts that the responses are
merely the result of following a series of
instructions, or programme, and that the
respondent cannot possibly learn Chinese from
simply manipulating the formal symbols. Searle
goes on to restate that, “a computer has a syntax,
but no semantics”29
and that to have a form of
mental state involves more than having a bunch of
formal symbols. Searle goes on to make four
conclusions as to why computers cannot have
minds and therefore no intelligence30
.
If then we are to conclude that the computer is
incapable of intelligence, I would like to set aside
in this study the area of so-called bottom up
digital design processes. These generative
techniques suppose a set of abstract phenomena as
defined by the author and compute a result based
upon the algorithmic description of said phenomena
within the computer. Not being trained in computer
science or able to accurately reproduce biological
algorithms I would prefer to focus the study on the
properties of what a building might look like and
investigate ways to engage the computer to deal
with visual matters. After all, visual matters are
to-date where the majority of my architectural work
and education has focussed and to repeat Antoine
Picon once more, the situation of setting limits to
design can be considered such that “design is no
longer involved”31
, in the sense that the designer is
not directly engaging with and adjusting the shape
of a building.
29. John Searle, Minds Brains and Science, (Cambridge,
Mass Harvard University Press, 1984), 33.
30. Ibid., 28-41.
31.Antoine Picon, “Architecture and Mathematics,” in
AD: Mathematics of Space, ed. Legendre, George L,
(London: John Wiley & Sons, 2011), 33.

39
2.4.5 SIMPLEXITY
32. Cristiano Ceccato, Advances in Architectural
Geometry 2010, (Dordrecht: Springer, 2010), Foreword.
The digital tools available to architects today are
becoming ever more powerful and intuitive to the
operator. This follows a general trend of ease of
use of digital devices witnessed in the way a small
child, monkey or even cat can use a tablet device.
There doesn’t need to be a reasoned or intellectual
engagement with the digital device for the user to
access simple, top level functionality to achieve
some output. We might say that this is also true of
much of the software available to designers. The
tools available, even at the top level, allow an
individual with relatively little architectural
training or digital understanding to create all
manner of curved digital shapes. Modern
engineering analysis tools and construction
techniques would also mean that many of these
shapes would be able to come to full realisation
(even if at huge financial expense).
So then, what value is there in these digital tools
with relation to design? What are the “tools for
the efficient design, analysis, and manufacturing of
complex shapes” 32
that Ceccato talks of and how
might architects start to incorporate these tools into
design thinking?
Mark Burry is an advocate of digital tools and their
positive impact upon the understanding of design.
He is the lead architect on Antonio Gaudi’s Sagrada
Familia and began work on this project at a time
before digital tools were commonplace. Burry talks
positively of the way digital tools have aided in the
understanding of Gaudi’s models and drawings and
the speed enhancements that they have brought to
the project. For Burry, scripting is one of the most
powerful tools an architect can understand to make
benefit of the digital tool. By understanding the
language that drives the computer one can
better appropriate the tool for one’s own needs.
This means however that the architect needs to be
trained to be more than a mere user of the software.
Yet does this mean that an architect need solely
focus upon being a computer scientist? I would
argue no, yet architects do need a greater awareness
as to how the tools that they use function at a
deeper level in order to utilise the computer to
extend their design ability. Mark Burry tells a story
of his introduction to scripting in 1992 to help in
the production of drawings for the Sagrada
Familia.

40
“now that there is massive computer power and software cheaply
available, most scripting has become nothing more than an onanistic
self indulgence in a cozy graphics environment. Endless repetition
and variation on elaborate geometrical schema with no apparent
social, environmental and technical purpose whatsoever.”

John Frazer

41
Burry had been drafting in AutoCAD™ a series of
curves and points, calculating and labelling each
as he went, an entirely laborious exercise and one
taking no advantage of the available computational
power within the ‘black box’. Once he had learnt
to script this process however, the computer was
able to compute each curve in seconds as opposed
to the best part of an hour it was taking him to do
so manually33
. This is a perfect example of
utilising the computer to augment a human’s
intelligence, Steve Job’s bicycle for the mind.
There is a danger when it comes to scripting
however, something that Burry discusses in his
book, Scripting Cultures. Burry talks of how it
is easy to achieve complex formal effects with a
series of simple scripts that simply repeat a number
of times. Burry puts forward the statement of John
Frazer as further evidence of this position, “now
that there is massive computer power and software
cheaply available, most scripting has become
nothing more than an onanistic self indulgence in
a cozy graphics environment”34
. This is something
that we see commonplace in examples of digital
architecture, where this complexity is deemed a
worthy outcome by virtue of the belief that an
outcome is complex simply by producing a
complicated spatial or formal proposition. But
there is little to no consideration as to the basis
for this form making and so it becomes difficult to
assess in any meaningful way. Contrary to this
approach we may argue that it is much more
difficult to understand a complex concept or set
or rules and execute a simple routine to achieve
some desired effect, as in Burry’s example from the
Sagrada Familia. It is at this point one might be
considered in control of the digital tool rather than
being led by it. This being something we might
call ‘Simplexity’.
“Simplexity is a term in system science which de-
scribes the emergence of simplicity out of intricate
and complex sets of rules.”35

Sawako Kaijima and
Michalatos Panagiotis
Burry talks further on his experience in scripting.
Whereas he had previously seen scripting as
something that had to be done for a designer
heading towards the 21st century, the experience of
turning a repetitive, time-consuming and
mundane task into one of rapid production changed
his relationship with the computer.
33. Mark Burry, Scripting Cultures: Architectural Design
and Programming, (Chichester: Wiley, 2013), 28.
34. Ibid., 52.
35. Ibid., 92.

42
36. Ibid., 30.
38. Ibid., 294.
39. Ibid., 294.
40. Ibid., 65.
Now with an understanding of how the computer
might work for him, Burry felt able to transcend the
limitations of the software and use it with the same
authority as a pen and compass 36
. We see above
that Burry was originally employing the
computer as he would a pencil and paper. Only
when he appropriated the tool specifically to his
intended purpose was he able to see the
computational advantages that the computer offers.
The idea of understanding the toolkit available in
modern architectural software is one that Robert
Aish discusses with passion. Aish is a long time
user and designer of digital software and a
founding member of the Smart Geometry Group.
He has served as lead software designer for
architectural software produced by both Bentely
Systems and Autodesk. Aish discusses the
existence of a powerful and general geometry
toolkit that exists below the top level tools that
most architects engage with.
Through understanding how to access these tools
an architect can begin to build their own semantics
for design, as opposed to being limited to the
grammar offered by the basic set of top level
commands. A grammar thatAish argues is pushing
a conservative semantics for much of architectural
design37
. The idea of “a tremendously conservative
situation”38
is a product of architects not having
a fundamental understanding of mathematics and
computation. Without this architects are not seeing
the full benefits of digital tools and are “trapped
irrevocably in this cycle of conservatism that I
think one can observe in a lot of work”39
.
The computational power of the computer then
is not being fully harnessed by architects and the
computer exists in the main either as simply a very
efficient drawing board or, where architects do
utilise advanced software tools, we note that it
often accompanies a preoccupation with the
unchecked proliferation of unbuildable shapes.
These shapes we need to start understanding more
fully and consider further their foundations. If
we take Jim Glymph’s position that, “architecture
needs to return to a more direct association between
material, craft, the physical reality of the building
and its own design process”40
we may discover a
starting point for Chris Luebkeman’s “appropriate
application” of the new technology.

43
2.5 FOSTER, GEHRY + THE SYDNEY OPERA HOUSE
41. Norman Foster’s early sketches for the Willis (Faber
Dumar) building in Ipswich 1970-75 show a free-form
curved, dome-like structure over the office space, a lan-
guage that we see used in much later buildings such as the
Berlin Free Library where digital tools were available (see
David Jenkins, Foster 40 Themes, (London, UK: Prestel
Publishing Ltd, 2007), 40.). Similarly, Frank Gehry was
unable to design and communicate the Barcelona Fish for
construction without digital aids.
43. Bustler, accessed 3 August 2014. www.bustler.net/
index.php/article/frank_gehry_at_work_on_view_in_new_
york_city/
Two very influential current practising architects are
Norman Foster and Frank Gehry. These are two
significant architects working at the forefront of
digital design. Their work has developed over a
number of years with various theoretical concerns
and digital technologies have allowed each to build
previously unworkable projects41
. Foster has an
in-house Specialist Modelling Group (SMG) that is
a multi-disciplinary group researching and
investigating the use of digital tools and their
application to digital design. This group provides
custom tools beyond those accessible at the top
level of the software package for architects within
the office to use on design projects. Gehry goes
even further and has developed his own software
package, Digital Project, which other architects are
now adopting. This software allows for the link
between design and fabrication processes of
architecture. These approaches are representative
of those that we note Robert Aish discussing earlier,
in that these architects are removing the constraints
exhibited by the top level CAD tools and utilising
the “very powerful and general geometry toolkit”42
underneath to invent their own semantics.
Frank Gehry models on display at Leslie Feely Fine Art, Manhattan,
2012. Image Credit: Leslie Feely Fine Art, LLC43
.

45
Looking at the work of these two architects one
notes a very different aesthetic – you could not
mistake eithers work for the others. While Foster’s
work appears very rational and organised Gehry’s
comes across as playful and whimsical. Could
there be something that links the work of these two
architects together? Through analysing buildings
of the two architects we can begin to draw some
parallels in the approach to design. And that
approach begins with a tacit knowledge of how
their buildings might be constructed.
Frank Gehry developes his buildings
physically. From sketches he builds large models
that are digitised for further analysis, development
and ultimately to describe the building to those that
will be building it. Gehry often uses strips of paper
in his physical models to describe the surfaces of
his buildings. We can describe these building
surfaces as a developable or ruled surface44
. These
types of surface can be built, like their modelled
equivalents, out of a flat and or flexible material as
they only curve in a single direction. For reasons
of economy Gehry is conscious of how many
surfaces in his designs are flat, of single curvature
and doubly curved keeping the highly shaped
pieces to five percent45
.
“Flat pieces cost one dollar, single curvature
pieces cost two dollars; double curvature pieces
cost ten dollars. The good thing about the
computer is that it allows you to keep a close
control over the geometry and the budget. It was
not just speculation; it was real.”46

Frank O Gehry
44. See section 3.5 ‘Surface Types’.
45. Bruce Lyndsey, Digital Gehry, (Basel; Boston; Berlin:
Birkhäuser, 2001), 71.
46. Ibid., 71.
Image far left of 8 Spruce Street, Frank Gehry, 2010.
Image left of 30 St Mary Axe, Foter+Partners, 2004.

47
The process used by Gehry to model his buildings
is interesting and it is here that we can see a
parallel with Foster. The understanding and
awareness of the physical construction of a building
is similar to Foster’s buildings, in particular a series
of buildings designed and built from 1987 to 200448
that explored the ‘torus patch’49
. In these
buildings, the torus was sliced to give canopies for
the Canary Wharf underground station and the roof
of Copenhagen Zoo’s Elephant House as well as
being combined, revolved and translated to give
shape to buildings such as 30 St Mary Axe, Albion
Apartments, Chesa Futura and the Sage Theatre.
In each case the underlying geometry allowed for
economic construction of the buildings from flat
building materials and, like Gehry, providing
apparently curved buildings within reasonable
economic constraints.
There is a clear difference when we look at the
work of these two architects however. Foster
continues to celebrate technology and structure in
his buildings as in what was deemed the High Tech
style of his earlier work. One is able to clearly
articulate the outline of the exterior of a Foster
building and see a relationship to the interior
volumes, which continues an early design
direction of Foster to integrate the skin, structure
and services of a building, notably seen in the
Sainsbury Centre for Visual Arts, Norwich, UK
(1974 – 1978). Gehry on the other hand seemingly
works skin and structure separately and perhaps is
a reflection of the Deconstructivist style. In much
of Gehry’s work the interior and exterior often bear
little resemblance to one-another and between these
two worlds the structure is hidden away. Bruce
Lindsey describes this process as, “skin in”; the
system is “skin, a space for connection, and a space
for the structure”50
. Lately we might perceive a
shift in Gehry’s work, back to what one might have
read in his early work where the structure is pulled
out and put on display. For example, in the Walt
Disney Concert Hall (1999-2003) in Los Angeles
we can see the outer panels being aligned with the
underlying structure, strengthening the material,
structure and fabrication relationship. Perhaps we
can start to read this as an acknowledgement of the
importance that geometry and structure play in
Gehry’s work and the expression of a wider reading
of it.
48. These buildings include The American Air Museum,
Cambridge, UK 1987-1997, Canary Wharf Underground
Station, London, UK 1991-1999, Albion Riverside, Lon-
don, UK 1998-2003, The Sage Gateshead, Newcastle, UK
1997-2004, 30 St Mary Axe, London, UK 1997-2004 and
Chesa Futura, St Moritz, Switzerland 2000-2004, Elephant
House Copenhagen Zoo, Copenhagen, Denmark 2002-
2008.
49. See section 3, ‘Geometry’ for further explanations.
50. Bruce Lyndsey, Digital Gehry, (Basel; Boston; Berlin:
Birkhäuser, 2001), 35.
Image far left of Sydney Opera House, Jorn Utzon, 1957-
1973.

48
Drawings of the Sydney Opera House. The drawing on the left depicts the reinforced concrete shell competition scheme (1957) with the
drawing on the right from the Yellow Book (1962) portraying the ribbed precast shells. Image credit: NSW Government State Records47
.
47. NSW Government State Records, Accessed 03 August
2014. www.gallery.records.nsw.gov.au/index.php/galleries/
sydney-opera-house/sydney-opera-house-drawings/ and
www.gallery.records.nsw.gov.au/index.php/galleries/syd-
ney-opera-house/sydney-opera-house-the-yellow-book/,

49
51. NSW Government State Records, Accessed 03 August
2014. www.gallery.records.nsw.gov.au/index.php/galleries/
sydney-opera-house/sydney-opera-house-the-yellow-book/
52. Concrete structures suffered from the need for expen-
sive and often single use form work for freeform surfaces.
53. Good explanations of the solution can be found in: Mi-
chael Moy, Sydney Opera House: Idea to Icon, (Ashgrove,
Qld: Alpha Orion Press, 2008); Peter Murray, The Saga
of Sydney Opera House, (New York: Spon Press, 2003);
Philip Drew, The Masterpiece: Jorn Utzon: a secret life,
(South Yarra, Vic: Hardie Grant, 1999).
54. The ‘Yellow Book’ drawings, March 1962 contained
this detail. Utzon looked to Raphael Moneo, a young
24 year old at the time, to derive the roof shells from a
generic sphere. This process, as described by Moneo,
sounds very similar to the one Mark Burry describes in his
work on the Sagrada Familia that led to his discovery of
scripting to aid in such laborious tasks: Philip Drew, The
Masterpiece: Jorn Utzon: a secret life, (South Yarra, Vic:
Hardie Grant, 1999), 199.
We can describe the systems for design employed
by Foster and Gehry as relational. In contrast to
modernist systems, based upon a standardisation
and separation of structure from walls, these two
architects work with elements of the building that
depend upon each other. While it is obvious to
see the relationship between skin and structure in
a Foster building it is no less important in a Gehry
building. Here is maybe a link back to those digital
explorations in the 1990’s where parts of a
building are ‘folded’ together in order to realise a
new aesthetic. This describing of a relationship of
parts is not new nor is it unique to Norman Foster,
Frank Gehry. We can see the origins of this
approach to architecture in a much earlier building.
Geometry and structure play a fundamental role
in the realisation of one of the twentieth century’s
great buildings, the Sydney Opera House (1957-
1973). In 1957 Jorn Utzon produced a competition
winning scheme of organic looking shells sitting
atop a podium. The project at this stage was e
nvisaged as a single skin, reinforced concrete shell,
similar to other reinforced concrete buildings like
Le Corbusier’s Notre Dame de Haut (1950-1955)
and Eero Saarinen’s TWA Terminal (1956-1962).
These curvaceous monolithic structures were made
possible in the nineteenth century to the
mid-twentieth century through industrialisation
and the development of iron, steel and reinforced
concrete and peaked in their use in the 1960’s. In
the years that followed the engineers tasked with
realising the structure for the Sydney Opera House,
Ove Arup and Partners, struggled time and again
with achieving a solution that aligned structural and
aesthetic sensibilities. The parabolic shell solution
simply wasn’t achievable due to either the weight
of the structure or the cost52
.
The resolution for the shells presented itself in
mid-1961 after a series of at least a dozen
explorations including schemes with parabolas,
ellipsoids and circular ribs53
. The solution involved
using spherical geometry so that all shells could be
formed from the same arc54
. This rationalised
solution allowed for the re-use of moulds for
tructural ribs resulting in benefits in cost while also
expediting construction with less waste when
compared to a reinforced shell system.

51
There are interesting things to note here. The first
point is the significantly altered shape of the
building. The low smooth shells of the
competition scheme were replaced by taller arches
finished in the now distinctive striped panelling.
The lack of geometric knowledge at the outset
resulted in a building proposition unable to be
realised. This leads to the second point, which is
the significant impact geometry was to bear upon
Utzon’s subsequent work, as seen in the National
Assembly Building in Kuwait (1971-1983). What I
find extremely interesting is that while admitting to
a limited understanding of mathematics, Utzon was
still able to understand and solve structural
architectural solutions geometrically. This suggests
that numerical mathematics might not be an
absolute entry criteria to gaining advantage from
digital tools but, geometric mathematics very
possibly is.
The Sydney Opera House “made it clear that
complex freeform shapes needed sophisticated
techniques of geometric description and integration
of structural and fabrication principles to make
them buildable”55
. The traditionally held
relationship of the architect designing the formal
concept for a building and then working with an
engineer to find a suitable engineering solution in
the nature of ‘form, structure, material’ was
reversed in the relationship developed between
Utzon and engineers Jack Zunz and Ove Arup.
Peter Rice in, An Engineer Imagines (1994),
identifies this collaboration as one where, in order
to find the final solution, the process was flipped to
become ‘material, structure, form’; the final
solution for the geometry for the Sydney Opera
House comes from the covering tiles that
influenced the design of the rib structure and the
overall form of the roof 56
.
In the example of the Sydney Opera House we see
once again, as with Foster and Gehry, an
understanding of the physical properties of a
material leading to exceptional structural and
formal solutions. This linking of the material craft
in architecture with shape making is one of the key
elements of interest for this thesis. It is the link
between geometry, structure and shape that I am
most interested in developing with this project.
55. Helmut Pottmann et al., Architectural Geometry, (Ex-
ton, Pa.: Bentley Institute Press, 2007), 364.
56. In AD: The New Structuralism, (July/August 2010)
p15, Rivka and Robert Oxman describe this moment as
the ‘point of departure’ for their term ‘new structuralism’.
This term deals with the prioritisation of material matters
and the cultural evolution of the expanded collaborative
relationships developed between architects and structural
engineers and their responsibility for the production of a
worldwide series of iconic buildings. Beyond the example
of the Sydney Opera House they go on to describe similar
works and relationships between architects and engineers
such as Peter Rice and Richard Rogers and Renzo Piano,
Centre Pompidou, Paris as well as Frei Otto, Edmund
Happold, Jörg Schlaich and Mamoro Kawaguchi; Cecil
Balmond with Toyo Ito, Matsuro Sasaki with Toyo Ito, and
Buro Happold with Shigeru Ban.
Image opposite page depicting the geometrical
construction showing the shells for the major hall
(elevation). Image credit: NSW Government State
Records51.

53
3. GEOMETRY
Given that the study of geometry is critical to this
project it is necessary to understand how geometry
is represented in the computer. Principally, shapes
in digital space are described with points, lines or
curves and surfaces. Curves and surfaces are the
basic elements by which we can explore
architecture. We may consider curves as the
profiles that are used to define a surface. In their
724 page book, Architectural Geometry, Helmut
Pottmann, Andreas Asperl, Michael Hofer and Axel
Kilian explain the mathematics of curves and
surfaces in far more depth and detail than I could
ever hope to in this study. From their work
however, it is useful to identify some specific
properties for defining surfaces and, types of
surfaces useful for this architectural project.
Before doing so, I would like to discuss further the
way that shapes are represented on a digital display
to further explain the approach for considering the
project to be comprised a series of flat panels.

54
“we must elevate to first-class citizens the discrete facets of the
structure – the mesh, in the case of the computer – as the building
blocks of our designs”

Peter Schröder

55
3.1 PETER SCHRÖDER
57. Peter Schröder, “Digital Geometry,” in Greg Lynn
Form, ed. Mark Rappolt, (New York: Rizzoli), 146.
It is useful to discuss the representation of the
shapes we define on the computer screen as it is
important to understand the technology and there is
also the potential that it could also form a basis for
an approach to a formal design language. We have
already discussed computer software being used to
explore ideas of the infinitesimally smooth
(Greg Lynn et al.), however the shapes that we see
on the computer screen are not actually smooth at
all. They are comprised of many faceted pieces to
give the illusion of smoothness. This is interesting
if we consider a building that will be made from
physical materials. In most instances the building
will comprise straight members of steel and glass
due in large part to established construction
practises and issues of economy; curved materials
are expensive and specialised. Like a pixelated
digital image, our buildings are formed of finite
pieces that achieve seamlessness and the smooth
aesthetic as we move away from them. In
understanding the digital medium in this way,
Peter Schröder suggests that the “mathematics of
the smooth curve should still guide us, but we must
elevate to first-class citizens the discrete facets of
the structure – the mesh, in the case of the
computer – as the building blocks of our designs”57
.

56
The mesh is a way in which one may consider a
surface, as represented by its component parts.
A mesh can be defined as “a collection of points
(vertices) arranged into basic elements called
faces. The faces are bounded by polygons and the
polygons fit together along common edges and
roughly describe the shape of a smooth surface”58
.
The development of a mesh as an architectural and
structural solution can be seen as an early example
in the double-curved shaped roofs of the Sydney
Opera House discussed earlier.
Schröder’s argument reinforces earlier research in
this study and contributes to an ideological
position for meshes to be considered as a
fundamental aspect of digital architectural design.
If we look at the physical properties of the
materials that we use then we see that it is most
likely that rigid flat elements will be necessary.
Issues related to cost are significant where curved
components increase costs to unrealistic levels.
Concerns of the environment and quantity of
material used should also be a consideration and
the efficient application of particular types of mesh
is important to understand. We have the argument
above by Schröder, highlighting the significance of
the mesh for digital design thinking.
If we combine the factors studied so far there is
a compelling argument to investigate appropriate
surface conditions for a mesh that works with these
ideas.
(Exton, Pa: Bentley Institute Press, 2007), 381.
vertex face polygon edge
Image depicting elements of a mesh.

57
3.2 MESH SUBDIVISION
With the use of a mesh to form the basis for the
exploration of building shapes established, we
should understand how a surface might be
broken down into mesh elements for construction,
given curves and surfaces are a principle means
of describing shapes with computer software. A
mesh is derived from a surface where typically the
surface is divided into triangles, quadrilaterals or
sometimes hexagonals and occasionally some other
pattern such as a voronoi. I will focus on the first
two as they are the more common mesh solutions.
The most basic and common technique to derive
a mesh from a surface is to divide it into triangles.
This is the most efficient method due to
convenience. It is a basic approach and triangles
easily represent all surfaces. The three points of a
triangle exist in a flat plane so the panels are always
planar and there is an inherent structural stability
when utilising triangular meshes.
Figure showing the same surface represented as a triangular and quadrilateral mesh.

58
Figure showing images of the Smithsonian Institution roof, Foster+Partners, 2007. Image credit: Nigel Young, Foster+Partners59
.
59. Foster+Partners, Accessed 03 August 2014. www.
fosterandpartners.com/projects/smithsonian-institution/

59
60. I say ‘thin’ as the building element is a single
thickness, like a two-dimensional surface in digital space.
62. Ibid., 676.
Triangular meshes are commonly seen in
architecture as a ‘thin’60
skin across a building.
Examples of this include the glazed roof by
Norman Foster over the Great Court at the British
Museum (1994-2000) and the glazed roof over the
DZ Bank atrium (1995-2001) by Frank Gehry. It
is uncommon to see triangular meshes being used
to provide thickness to building elements. This is
because triangular meshes are not well suited to
offsets. When offsetting a mesh we look for a
common node axis. The issue with a triangular
mesh is that the offset parallel mesh is a scaled
copy with respect to some centre resulting in ap-
proximate solutions that uniformly distribute the
error throughout the nodes of the mesh. The
consequence of which is complicated, inefficient
and costly construction. Offsets are important to
consider in architecture as the buildings we
construct are not like digital surfaces without
thickness.
Yet if we consider that the surface will comprise
quadrilaterals we initially discover that there are
issues with planarity. Yes, we could divide any
surface into quadrilaterals but this would usually
result in the need for curved elements. If we look
at the example of Foster’s roof at the Smithsonian
Institute, Washington DC, USA (2004-2007) we see
clearly that flat quadrilaterals are unable to define
any surface.
While more intellectually challenging to the
designer, there are a number of advantages with
quadrilateral meshes over simply triangulating the
surface and the benefits offer interesting areas for
architectural exploration.
The benefits of planar quadrilateral over triangular
meshes are notable in architectural terms. Firstly, a
quadrilateral mesh has greater surface area and less
structural members. This results in greater areas of
glass or cladding panels which points to less weight
overall for the quadrilateral system. Cost per-area,
quadrilateral panels are cheaper than triangular61
.
Since fewer members meet at each intersection
(four vs six) the node junction for the quadrilateral
system is less complex. In addition, it is not
possible to generate torsion free nodes for
triangular meshes which are preferable for
construction62
. Offsets with planar quadrilateral
meshes offer greater architectural potential
compared to triangular meshes.

61
3.3 PLANAR QUADRILATERAL MESHES
If we think of curved buildings with regards to
physical material qualities, construction practises
and structure, we can consider geometric principles
that might be employed to conceptualise and design
such structures. Instead of starting a design within
the digital environment without any constraints, we
consider the material, its physical qualities and the
geometric solutions that work with those properties
and explore such geometric potentials to respond to
an architectural brief.
It seems an absurd assumption that we begin
designing a building without any sense of the
material we will use or how it might be constructed
yet one can note a number of examples where this
is in fact the case, the Sydney Opera House being
just one. If we consider a building as a series of
elements, or faces, connected together then the way
in which we consider these faces is important in
an architectural sense. If we consider that the face
is to have some restriction, say, to be planar, what
are the limitations and possibilities for the various
shapes we might define? Why planar? One
assumption is that we see little free-form
architecture due to issues of cost. Curved building
components are more expensive than flat materials
which are in most common use. It has been
noted how Norman Foster and Frank Gehry
employ flat materials in their apparently curved
buildings. Often these materials are not just flat
but also quadrilateral. Not every surface can be
described as a planar quadrilateral mesh and we
need to understand specific qualities of a surface
that will result in planar quads. Benefits of planar
quadrilateral meshes to architecture are discussed
above but what additional constraints might planar
quadrilateral meshes present over triangulation
when considering the type of surface to design.
One can consider surfaces as belonging to
various classes. These classes determine the types
of mesh that can be derived. Examples of such
classes are Conic Sections, Traditional Surface
Classes, Freeform Surfaces, Quadrilateral Meshes,
Sweeping and Skinning and Developable Surfaces.
Let’s examine some types of surfaces that might
be available to design with now that we have this
restriction for planar quadrilaterals.
The following two sections give an overview of
surface types and, or ways of defining a surface that
have been found useful for this thesis in terms of
defining planar quadrilateral meshes.

63
3.4 CURVES
Where numerical mathematics is used in this
section it has been derived from Pottmann et al. and
is used to highlight the difference in numerical and
geometric mathematics. The geometric aspects are
focused upon in order to provide principles for a
designer to use in design exploration which can
later be refined using associative models and
numerical mathematics.
Before discussing surfaces it is useful to first
discuss curves. Curves are used to define a surface
and can be considered as comprising a string of
points. Pottmann et al. describe a curve as a
“connected one-dimensional series of points”63
.
Special types of curves are straight lines, circles,
helixes and the conic sections. Curves can be
classed as ‘planar’ or ‘spatial’. A helix is a true
spatial curve as it does not fit into any plane. We
find the helix used in architecture on columns and
as staircases. It is the planar curves that are of
greater interest to this study.
The conic sections are of particular interest and a
conic can be described as a curve by the quadratic
equation64
:
a•x² + b•x•y² + c•y² + d•x + e•y + f = 0
Equally we may understand them visually as
demonstrated on the following page.
Conics shouldn’t be confused with a catenary
which appear similar and can be best described as a
rope or chain hanging under gravity. The
mathematical description for a catenary is:
Y = a•cosh(x/a)
Catenaries are useful to us for the creation of a
minimal surface, which can be generated by
sweeping a catenary around an axis. A minimal
surface is defined as a surface of zero mean
curvature and can be investigated using a wire
boundary and soap film. These types of surfaces
are common in the work of Antonio Gaudi, Felix
Candela, Pier Luigi Nervi, Frei Otto and Heinz
Isler. Often realised in reinforced concrete these
shapes reached a peak of their use in the 1960’s.
64. Ibid., 231.

64
Ellipse: b²•x² + a²•y² - a²•b² = 0 Hyperbola: b²•x² - a²•y² - a²•b² = 0 Parabola: x² - 2py = 0

65
Further types of curves are those that can be
described as ‘freeform’. These include
Bézier, B-spline and NURBS (non-uniform
rational b-spline) curves. These curves are shaped
by a number of control points that define a
‘control polygon’ and are more recent in their use
than those curves described above. These curves
can be found in tools developed from the 1950’s
but have their origins in the lofting table of boat
building as a weighted spline. The differences in
these curve types is generally to do with the level
of control offered by each. Control is offered by
design handles; Bézier curves are controlled by
‘control points’ only, B-spline by ‘control points’
and ‘degree’ and NURBS by ‘control points’,
‘degree’ and ‘weights’. The ‘control point’ is
used to define the curve. The ‘degree’ controls the
proximity of the curve to the control points. For
instance, Degree n = 1 is considered a
‘linear’ B-spline and consists straight lines between
the control points and is otherwise known as the
control polygon. As n increases the curve moves
away from the control points. The ‘weight’ drags
the curve towards or away from the control point
which occurs locally to the individual control point.
NURBS curves can be used to describe all of the
conic sections.
If we are to consider the usefulness of these curves
we may consider it thus; For a Bézier curve any
change to a control point has an effect on the
overall curve. Adding or subtracting control points
makes a global change to the curve. The greater
the number of control points in a Bézier curve the
less the curve will represent the control polygon.
B-spline curves adhere to the shape of the control
polygon better than Bézier curves and can be
controlled locally at each control point. NURBS
add the effect of being able to adjust locally the
weighting of the individual control points.

66
Figure demonstrating the discretization of a sphere surface to a polyhedral mesh.

67
3.5 SURFACE TYPES
From curves we can begin to define surfaces.
Surfaces can be smooth or they can be defined as a
‘polyhedral’ surface. A polyhedral surface is one
bounded by planar faces, something that this study
is aiming to work towards. The most basic way to
think of a polyhedral surface is a pyramid but also
the Platonic solids; tetrahedron, cube, octahedron,
icosahedron and dodecahedron. Geodesic spheres
are a further example. A geodesic sphere can be
thought about as taking a smooth spherical sphere
and ‘discretizing’ it into a fixed number of
elements, or faces. As the number of vertices
increase the shape becomes smoother.
The concept of discretization is an important one.
It is taking a smooth shape and reducing it to a
lesser number of discrete parts. In terms of a
building this is the process we take when
translating a smooth surface into one that we can
make buildable from flat elements.
In the following I investigate surface classes paying
particular interest to those surfaces that result in
planar quadrilaterals through the process of
discretization.

68
Figure illustrating a curve rotated to achieve a smooth surface and a polyline rotated and a resulting polyhedral surface.

69
Let’s start with Traditional Surface Classes. These
are based on what is termed ‘kinematic’ generation.
An ‘extrusion surface’ is created by moving a curve
along a straight line. A ‘rotational surface’ rotates a
curve around a straight line or ‘axis’. A ‘ruled
surface’ is generated by moving a straight line
along a curve and a ‘translational surface’ moves a
curve along another curve.
I touched on rotational surfaces earlier when
discussing a series of buildings by Norman Foster.
The building 30 St Mary Axe (1997-2004) is an
example of a curve being revolved around a
centre. The interesting thing about rotational
surfaces is that a smooth curve can be
approximated by a polyline. We can additionally
discretize the rotation to create a polyhedral
surface.

70
Figure showing the cylinder, cone and torus.

71
If we look at special cases of rotational surfaces we
have cylinders, cones, spheres and tori. The first
two cases are generated by rotating a straight line
around a centre while the second two utilise a
circle. If we rotate a circle around any of its
diameters we achieve a sphere. If we move the
rotational axis away, in the same plane as the circle,
we generate the torus; spindle, horn or ring torus
depending if the rotational axis is less than, equal
to, or greater than the radius.
The Foster projects mentioned previously explore
the properties of the torus, or toroid, patch, a part
of the torus. This is useful in an architectural sense
in that two circles define the shape and hence it is
possible to extract planar quadrilateral meshes.

72
Figure demonstrating cutting plane through a cone to produce an ellipse and parabola.

73
The ability to generate a cone through a simple ro-
tational translation of a line is useful to help under-
stand the benefits of the conic sections, the ellipse,
parabola and hyperbola.
When rotated the conic sections begin to provide
interesting surfaces that have a history in archi-
tectural design; the ellipsoid, the hyperboloid and
the paraboloid. The surfaces are now starting to be-
come more complex than a simple spherical geom-
etry but follow similar laws of logic and are useful
when considering their construction. We start to
see a greater range and level of control of complex
surfaces with double curvature.

74
Figure showing translational surface with ‘generatrix’ and ‘directrix’.

75
The ruled surface is alluded to above in the
description of the cylinder and cone. Ruled
surfaces are of particular interest in architecture as
they consist of a family of straight lines that can be
unrolled onto a plane and thus can be constructed
more easily. These surfaces are created by
revolving a straight line in space. Ruled
surfaces can also be created by sweeping a straight
line along a profile curve. In most instances a ruled
surface is singularly curved yet there are special
cases such as the hyperbolic paraboloid (saddle)
and one sheet hyperboloid (cooling tower) where
the surface is doubly curved. A ruled surface can
also be generated by moving a straight line along
another curve, the ‘genratrix’. If the direction of
the line stays constant we produce a simple
extrusion surface however if we adjust the direction
of the straight line as we move along the curve we
create a ruled surface with a more complex shape.
Ruled surfaces are implicit in the use of paper strips
in the model making process utilised by Frank
Gehry.
Translational surfaces are similar to the idea of
extruding a curve to achieve some surface. This
time we move, or translate, the curve along another
curve. The first curve is known as the generatrix
and this is translated along the ‘directrix’, as
defined by Jim Glymph65
. This process will result
in a surface consisting of planar quadrilateral mesh.
Glymph determines the basic principle for a planar
quadrangular mesh as maintaining a parallel set of
vectors that connect to a sectional curve. This is
similar in principle to the ruled surface above in
that we can think about it as straight lines being
used to connect a series of generatix curves.
65. Jim Glymph et al., A parametric strategy for free-
form glass structures using quadrilateral planar facets in
Automation in Construction, volume 13, issue 2, (Elsevier,
2004), 187-202.

76
Figure depicting various transformations of a curve into a surface; beginning with a straight polyline, moving to a curve; extruded surfaces
with affine transformations; translated surfaces, ruled surfaces and finally a complex translational surface.

77
It is the visual geometric representations over the
numerical mathematical descriptions that I find
most useful as a designer trained in visual matters.
While it is necessary to define a curve using
formulas within software packages to create a
relational or associative model, I first need to be
able to see what it is that I want to create. The
digital ‘parametric’ or ‘associative’ model then
enabled me to investigate versions or iterations of
this model visually. The limitation of this
technique in a design sense however was that once
relationships were established there was no way to
explore options outside of the implied limits. The
investigation needed to work towards a more
flexible system for modelling.

81
4.1 PROJECT OUTLINE
The project for this study is entirely hypotheti-
cal which has afforded freedoms a real project
otherwise might not. Throughout the process of
this thesis it became apparent to me that the most
important issue was not specific project outcomes
but instead the impact that the study has had upon
my design thinking in general. I am satisfied with
this as I had hoped that the course of study would
provide reflection upon design practises that I have
been using for a number of years and in particular
highlight the greater relevance and application of
digital technologies in my work. However, while I
hopefully demonstrate the application of my de-
veloped methodology in a wider sense, there does
need to be a design project to which it has been
applied.
The proposal then is as follows.

83
4.2 BRIEF - VIADUCT EVENTS CENTRE
The type of structures that this study has been look-
ing at lend themselves to being of an open, long-
span type building. A freeform building might sit
best in an open site where it can act as a focal point
for other activity around it. There is such a location
in Auckland in the newly developing
Wynyard Quarter precinct. More exactly, the
location of the recently completed Viaduct Events
Centre on Halsey Wharf.
This is a fantastic site at the edge of Auckland’s
central business district. It is close to the heart of
the entertainment areas and has connections to the
water on three sides as well as impressive views
back to the city, the marina and out to the
Waitematā Harbour. The area is a working portside
with commercial boats coming in and out which
require access to the west side of the wharf.
The brief for the design itself comes from the
existing building. This project aims to work with
those criteria, set out as follows:

A multi-purpose events centre;
Exhibition hall, meeting rooms,
conference spaces, offices.
Public promenades to the east and west.
12 meter clear internal height.
Area ≈ 6400m²
The project will also engage with the following
considerations:
Consideration of the overall site and
potential engagement.
Legible overall form.
Defined entry.
The considerations above are due in part to possible
criticisms that I have of the existing building.
Further, in the interest of this study the design pro-
posal should also consider:
Double curved surfaces.
Offset surfaces.
Environmental considerations;
Daylight, minimise shading by building to
the south, shading from the northern sun,
wind protection (particularly to entry).
With these criteria established I’ll outline the
development of the design.

85
Figure locating the site: Halsey Wharf, Auckland, New Zealand.

86
Figure illustrating digital analysis of wind across the site.

87
4.3 PROJECT DEVELOPMENT
It is important to understand the site from the
outset of a project to recognise where the greatest
potential might be. Multiple visits to the site were
important to see how it is being used and what the
environmental conditions are like. Digital tools can
aid in gaining an understanding of the environment,
particularly over a longer duration of time.
Combining the digital and first hand analysis
highlighted the potential of the northern most tip
of the site as being one with direct sunlight at all
times. Further, the eastern edge of the site is well
sheltered from winds year round. These two factors
highlight the potential for some public activity in
these zones and are suggestive that the building
should not be placed in either position. The
western edge of the wharf is heavily used for
marine activity by large boats, as is the rest of the
harbour edges to the west. The harbour to the east
is more recreational with smaller craft using the
water. There is a strong pedestrian connection
running east-west at the southern edge of the site.
Views are excellent in all directions with
particular focus south-east to the city, east to the
marina, north to the harbour and west to what will
become a large park. The wharf itself sees nearly
no people using it due to a distinct lack of public
activity.

89
Figure showing view north to Waitematā Harbour.

91
Figure showing view to east across the Viaduct Marina to Auckland CBD.

92
Figures showing various explorations using gravity driven cloth modelling and geometric processes.

93
4.4 PROCESS
I began the exploration of shape with parallel
exercises. The first by looking at geometric shapes
influenced by the hanging cloth models of Pier
Luigi Nervi and Heinz Isler and more generally by
exploring geometric shapes based upon the conics
through translational surfaces (ellipsis,
hyperbolic and parabolic surfaces) along with
instances of the torus patch. This was done within
the existing building footprint as an initial exercise
to understand the scale and potential for shapes
within the constraints.
The hanging cloth, or gravity driven models were
interesting in that they begin to define a curved
shape based upon physical properties set for the
material. The outcomes are in themselves
pleasing to the eye as forces can be traced across
the shape to the ground with shadows falling
enjoyably across the surface. There are obvious
restrictions with regards the initial state (a
rectangle) but numerous outcomes could still be
explored depending upon the anchor points
constraining the surface to the ground. Shapes
other than rectangles were explored later through
more complex modelling methods that defined a
variety of original mesh states.
A major benefit of this approach is the already
proven outcome that the shapes become buildable
due to their inherent structural stability that comes
from the production of a minimal surface.
However, they are not necessarily easily definable
as a series of planar square panels and more
importantly, they work within set limits of a
phenomena, in this case gravity, which is
something that I was seeking to avoid in this study.

94
Figure showing parabola with various levels of subdivision.

95
The second study investigated parametric, or
associative, models based on some strict geometric
principles. I also investigated transformation of
surfaces by moving or scaling curves that defined
the surface. This maintained the planarity of the
quads and so proved a useful experiment that could
be applied later. The most interesting part of this
research in terms of the thesis overall however is
demonstrated in the images opposite exploring a
parabola.
I defined an associative model using Grasshopper
and Rhino to first describe the parabola (see
following page). This was used to create a
translational surface. The definition was driven
through a numerical mathematical formula and
could result in a parabolic arch, a plane or a
hyperbolic paraboloid (saddle). When I introduced
a further definition to subdivide the surface I made
an important discovery for myself. Even with just
four faces defining the overall mesh the
approximation of the parabola was already obvious.
As further vertices were added the coarse mesh
came to more closely represent the original
parabolic surface.
Having found defining associative models early in
the design process to be limiting and tedious, not to
mention already requiring some idea as to what the
outcome needed to be, this felt like a useful
realisation in order to shift the design process
towards looking for a method to utilise the
computers potential to visualise shapes quickly.
This led me to search for a technique to interact
with simple coarse shapes from the outset and then
apply a subdivision routine later once the general
shape was determined.
Working in this manner would enable me to
interact with the digital shapes directly,
manipulating as few points as necessary with
complex surfaces being the outcome.

97
Figure showing the Grasshopper associative model algorithm based on a parabolic translational surface.

98
Figure showing an architectural model with the mesh model and line model extracted from the underlying geometry.

99
The early experiments with the virtual hanging
cloth models had developed a workflow with 3ds-
Max for taking base geometries and manipulating
them in a non-destructive manner. This concept of
non-destructive modelling is important as it allows
the designer to apply a variety of transformations
and move between them as required. In the case
of the modelling process I was seeking to establish
this concept would allow me to move back and
forth from the coarse geometry to the more refined
shape.
Processing a coarse mesh is less processor intensive
and returns results more rapidly. This is why
meshes are used in modelling analysis and
engineering process such as finite element analysis
or for fluid dynamics or daylighting simulations. If
we consider the human brains capacity to
compute information in comparison to the
computer, we can imagine the situation that the
human brain can comprehend the coarse mesh
(while having an idea about the refined shape)
while the computer performs the heavy
computation to actualise and visualise the refined
mesh.
Throughout the design process I developed this
method to ensure further amounts of data are able
to be extracted from the model to move across
software platforms with minimal rework of
information.

100
Figure demonstrating physical modelling procedure from unrolled surface.

101
Explorations with this technique required the
informed judgement of the initial geometry study.
Without this background I would have again been
back at step one, wilfully shaping digital forms.
It became useful to test the process with physical
models as well as the digital ones as, after all, the
driving aspect of the project is the realisation of
digital shapes in the physical world. What was
additionally helpful at this juncture was that it was
evident that the coarse models would be just as
useful as the smooth ones in determining planarity,
after all, “garbage in, garbage out66
. If the coarse
model wasn’t working neither would a more refined
model67
. This made testing faster through building
simpler models rather than their more complicated
counterparts.
66. Greg Lynn & MF. Gage, Composites, Surfaces and
Software: High Performance Architecture, (Yale School of
Architecture, 2011), 125.
(Exton, Pa: Bentley Institute Press, 2007), 643. “Any
optimum is only an optimum within the
conceptualization of the problem space and the boundary
conditions applied.”

102
Figure showing curvature analysis and mesh rebuilding from original underlying geometry.

103
Later stages of the process involved developing a
planarity algorithm within Grasshopper for Rhino.
The meshes exported from 3dsMax were able to
be imported into Rhino for analysis and
modification to planarity if required. This was
explored with Gehry’s comment on having some
flat and some curved surfaces in mind. This could
then be employed as a building became
necessarily more complex. At a later stage I also
became aware of extracting underlying geometry
to alter the method for describing the surfaces,
for instance where ruled surfaces might be a more
appropriate solution, proving the method developed
had additional flexibility.
At this later stage the benefit of the associative
model becomes apparent. Now having an idea as
to the required shape for the building one is able to
create a definition that accurately describes the
building shape numerically. This can be
investigated through an iterative process while at
the same time introduce further layers of
analysis; for structure, solar gain, shadow casting,
fluid dynamics/wind simulations, daylighting and
so on. This is where the additional collaborative
nature of digital processes comes to the fore as
models can be shared with architects and engineers
contributing to the same design model.

105
Figure showing the Grasshopper planarisation algorithm.

107
4.5 THE PROPOSAL
The design for the Viaduct Events Centre
developed with the fundamental ideas being about
how the building is used and the impact that it has
upon the surrounding areas.
Programme + Design Rationale:
The programmatic aspects are relatively basic; a
large open space, separate flexible meeting spaces,
offices and utility spaces. Views out of the building
are important and so the interior was to remain as
open as possible which also aids in way-finding.
This led to utility spaces being centralised with
the other spaces moved to the edges. The building
began to separate into two more distinct parts; the
public exhibition and meeting spaces and, the office
spaces and utility spaces (toilets, kitchen and
preparation areas).

108
Section aa nts
Exhibition SpaceMeeting Space
Conference and meeting pods
Section through building and site.

109
The main exhibition hall has the requirement for
a twelve meter tall unobstructed space. With this
being the main public zone it is logical to push the
space to the north where sun and views are greatest.
This also works with the orientating of the majority
of the building to the north. There is the benefit too
of placing the smaller office spaces to the south of
the site and the potential to reduce the height of
the building in this zone, reducing the mass and
lessening the shadow cast by the building onto the
site. The kitchen areas are located on the south
western edge with access from the western
‘working’ edge. Two levels of kitchen service the
exhibition space and meeting pods.
Numerous placements for the meeting spaces were
investigated and moving them up from the ground
floor created the potential for views in various
directions. The decision to contain the meeting
spaces within pods came about with the thought to
make them an object within the large open space.
This meant that the meeting spaces could be easily
recognised from the exhibition space and could also
view back into the exhibition space. The pods have
a completely contained element as well as utilising
the space on top of the pods. The space beneath the
pods becomes more intimate within the overall
volume of the building and can be used for
seating and breakout spaces. The external skin of
the building is opened to provide views in different
directions enhancing the experience of the building.
The entry space was brought to the centre of the
building to enable direct entry to the exhibition
space.

110
Figure showing image sequence demonstrating non-destructive modelling process.

111
Shape:
The shape of the building went through numerous
iterations and types. Key drivers for the shape of
the building were to minimise the shading effect of
the building to the south, bring a self-shading effect
to the northern elevation in order to maximise
views and daylighting into the building, define an
entry experience and, to provide an overall
cohesive outline for the building. Throughout the
design exploration a roofscape was considered in
terms of making the space usable. This was
abandoned as it became apparent that there was the
potential for large amounts of usable open public
space on the site. Moving the building from its
current location to the northern edge of Halsey
Wharf and altering the orientation to maximise the
north elevation was a key part of this realisation.
The development of the final shape started from
a simple tube solid. This shape was manipulated
to account for the programmatic ideas discussed
above. At the same time solar studies were
dynamically used to adjust both the slope of the
northern elevation and the overall height of the
building from north to south. Maintaining
sufficient height at the southern side of the building
for two levels of office was important and fitted
well with the overall building shape pushing to
over twelve meters tall in the northern exhibition
space. Maintaining views through the building
was important as the design became more detailed.
The changing curved shape additionally works to
improve accoustic performance of the building.

113
Perspective of building from Waitematā Harbour looking back to Auckland City.

114
Plan - Level 01 ntsPlan - Ground nts
a
a
Reception
Exhibition Space Exhibition Space below
Meeting Space with
Conference Pods above
Meeting and Conference Pods
Offices Offices
w/cw/c
Entry Courtyard
Kitchen and
Preparation
Delivery
& Access
Kitchen and
Preparation
Ground floor and first floor plans.

115
Experience:
The tube was selected as the base geometry because
of its open centre. This was to become the entry
courtyard for the building, a smaller more enclosed
space within the vastness of the open wharf,
protected by wind from both predominant wind
directions and shaped with vertical walls to reflect
light into its centre. As you approach the entry
you can see through the building to the Waitematā
Harbour beyond.
You enter the building into a space with the
meeting pods overhead. This provides a more
human scale area for the reception and lounge and
you are immediately orientated with the exhibition
space, meeting spaces and, utilities that separate the
public and private zones. A staircase from the
exhibition space takes you up to a platform to
access the enclosed meeting pods. From here the
top of the meeting pods can also be accessed. The
exhibition space is a large open, column free space
viewing out to the Waitematā Harbour. The
southern elevation of this space is vertical
providing access for tall exhibition items along
with general facility access from the west.
The north wall of this space reaches out over the
edge of the wharf presenting a view directly down
to the water below. This angle also works with the
angles of the summer sun to self-shade the
elevation meaning that greater amounts of
glazing can be used to maximise daylight to the
space and views outwards. This also increases
sunlight in winter months to contribute to the
heating of the space. To the south are two levels
comprising office space of various types.
Mechanical services are located to the west of the
building.

116
Entry Courtyard
City Beach
Working Port Edge Park and Wetland Landscaped Buffer
Landscaped Buffer
Hospitality Facilities

117
Site:
As I developed the project I realised that I really
should consider the potential of the entire wharf in
a greater sense as it would have an impact upon the
design decisions for the Viaduct Events
Centre. With this being a hypothetical project I had
the luxury to do so. Retaining the western edge of
the wharf for wharf activity was part of the original
brief. This makes sense as the entire area to the
west of Halsey Wharf is used for commercial
activity and provides an interesting backdrop to
other activity taking place in this part of the city.
Having identified from the site analysis the
potential for zones of public activity I thought of
ways to incorporate them into an overall
masterplan proposal. The northern finger of the
wharf is bathed in sunlight all year round with the
area to the south protected from winds by the
buildings on Wynyard Quarter and the wharf itself.
This part of the wharf is extremely underused at
present so introducing some activity to make use of
these environmental advantages seemed obvious.
In other areas nearby people readily interact with
the water’s edge where there is the small provision
to do so and a major criticism of the entire
waterfront area might be the lack of opportunities
to get close to the water. There is the added
advantage of only smaller recreational sea craft
using this side of the wharf, moving in and out of
the marina. Considering the original requirement
for a public promenade I thought to extend this to
provide a city beach with a saltwater swimming
pool right at the end of the wharf. Additional
hospitality facilities were included to give further
reason to use this part of the wharf and also to
provide nearby facilities for the Viaduct Event
Centre.

118
Perspective of building from south of Halsey Wharf looking towards Waitematā Harbour.

119
Moving the building to the north of the wharf
provided less of a barrier to the wharf itself. The
current building casts a shadow to the south which
creates a poor space along what has become a
major pedestrian route from the marina in the west,
into Auckland City centre and beyond. This
proposal creates the possibility to utilise this space
for parkland with trees sheltering the space and
swales collecting water.
Landscaping can be introduced to provide grassed
mounds for running and playing over or laying and
resting on while also creating a noise and visual
barrier to some of the commercial activity in the
west. There is the potential to create a variety of
types of spaces here with soft and hard surfaces
that connect to the water, continuing much of the
excellent work already happening in the area. The
current existing building location makes it difficult
to see how this design language might be
incorporated and continued.

120
Detail of segment of building envelope.

121
Final Comments:
The proposed design satisfies the criteria originally
set out and I believe it enhances the area beyond
what the current building provides. I consider the
dominant factor here is to do with the overall siting
of the building, most likely out of the
architects control. By shifting the building
footprint many opportunities for the site are opened
up and this proposal presents just one. In
prioritising and allowing for the effect that the
building has on its immediate surroundings I
consider that this proposal provides benefits that
the existing building does not. Shading of the area
to the south is a critical one and something where
I think the existing building fails on two counts; it
provides a poor urban experience, shading a major
pedestrian link and also, it offers an underwhelming
entry experience to the building itself. Orientating
the main exhibition hall to the north was a critical
step in the design process to give good access to the
entire wharf. Without this, the finger on the north
edge appears cut off from the rest of the wharf with
just a thin connection to it. Now there is a large
area connecting the two parts of the wharf with
landscaping proposed to highlight this connection.
The final shape of the building has tended to be
something of an oddity to me. Without any
conscious desire the shape has come to resemble
that of a Golden spiral of Fibonacci. This has
useful benefits in the determination of numerical
exploration but has the unusual outcome of it
appearing as though I have simple resolved to
place a shell at the end of the wharf. At each step
decisions to move faces, edges or vertices here or
there depended upon functional, environmental or
aesthetic judgement, with the final shape being a
response to these criteria. This final shape, the
nautilus shell, is the outcome of that process and I
am not uncomfortable with the result given the
decisions involved. I wouldn’t contemplate
altering the shape because of external formal
associations and it could be considered they might
even strengthen the idea. A story of
Foster+Partners, City Hall London, (1998-2002)
was that the concept was to design a pebble by the
Thames, even though the project was driven by
formal and environmental considerations. If such
comparisons were to be made with my own work I
would consider them flattering.

123
5. REFLECTION
Upon commencing this project, it seemed a
straight-forward task to explore planar geometric
typologies and produce an architectural response
demonstrating the application of planar
quadrilateral meshes. Quickly however it
became apparent that the project extended in scope
far beyond the initial parameters and that a wider
investigation was required in order to bring greater
understanding as to why it might be necessary to
utilise planar quadrilateral meshes in architectural
design processes. This was driven by a perception I
had in the underutilisation of digital tools in a
design sense, particularly given that the computer
has come to be such a dominant tool in
architectural offices. It was therefore critical to
establish robust links between architecture that we
design in the virtual world and architecture that we
build.
This being a practical, project based course of study
it seemed appropriate to focus the outcome on the
way we construct buildings today and materials
typically in use. The types of materials that we
employ tend to be rigid and flat, or planar, due to
cost. Even introducing curves in a single direction
dramatically increases cost and is generally
avoided. The way then that we use material for
construction is at odds with the types of buildings
that computer software enables architects to design
beyond the conservative box.
For more than twenty years various software has
allowed architects to postulate with buildings full
of complex compound surfaces. While the
software additionally allows for the description in
space the points defining these shapes in order for
them to be built, it is not exactly a fair claim for
architecture to suggest these buildings are possible
to be built today with financial restrictions always
an issue, seemingly no matter the budget for a
project. When we do see examples of curved or
‘blobby’ architecture it is usually reduced to a
triangulated mesh of flat panels, often covering
atriums and rarely exhibits all the characteristics
that we have come to expect from architectural
elements such as roofs and walls, depth of which
being a primary example.

124
The ‘smooth’ surface of the digital environment is
thus rationalised to a ‘thin’ faceted polyhedral in
order to be constructed. There seems to be a
disconnection between theoretical positions that
suggest computer software should enable us any
smooth surface when designing and the buildings
that are eventually built. One wonders if architects
are aware of this. Or if it matters given that much
of what architects produce with a computer is
rather conservative given the formal possibilities.
This realisation became the moment for me in the
project when it seemed important to widen the
investigation more generally into what digital
design in architecture might be influenced by.
At first glance the field of digital architecture is full
of many terms and much jargon. As one
investigates further it becomes apparent that these
terms have definitions which are sometimes various
and often overlap in meaning with other terms. It is
then difficult to ascertain where one might position
oneself within this and often one finds themselves
establishing their own definitions. Dominant topics
within digital design include computational,
parametric, generative, algorithmic and building
information modelling (BIM) as described in the
chapter ‘Digital Tools’.
Rather than attempt to work within this area to any
dominant existing theory, for this study I looked
towards the source of digital design, the computer,
in order to try to understand how one might best
use the computer to complement or inform a design
methodology. I looked into what the computer is,
how it works and attempted to ascertain what it
offered for architects to inform a design practise.
Taking the position that the computer has no
intelligence of its own focussed me to investigate
how information is input to the computer. There
are numerous examples one can cite when taking
this position, John Searle’s Chinese Room scenario
being just one. From this position one essentially
sees the computer as a finite machine with
xtraordinary computational power. Any
intelligence a computer exhibits is merely a
function of how well it is able to return
information from its storage banks, now extended
globally via the World Wide Web. This isn’t an
exhibition of intelligence, merely an example in
the spirit of Searle’s Chinese Room where an input
elicits a pre-programmed response. This position
places the emphasis upon the designer and their
understanding of formal matters over abstract ones.

125
The real value of a computer then might be when
we align its computational power with that of
human intelligence. If we consider that humans are
computation poor relative to a computing machine,
we see that the computer extends the capacity of
humans to deal with large amounts of information.
In the case of CAD software, that information is
predominantly to do with points in space and the
computer’s ability to quickly manipulate and
visualise them. With visual concerns highlighted
we can now consider how we best use the
computational power to carry out intellectual
endeavours.
At this point Antoine Picon becomes an important
figure. Rather than continue to argue for the use of
computers to model abstract phenomena that leads
to the ‘generation’ of architectural form, Picon
argues that this is in fact a process that involves no
design at all. If we consider the areas of an
architect’s training primarily involving the
understanding of shape and space alongside dealing
with programmatic and technical matters, guided
by history, then we could suggest that the architect
brings a knowledge of shape, space and human
behaviour that the computer and its
computational powers are there to compliment and
amplify. What we tend to witness with digital tools
however is an entirely different set of knowledge
applied by architects to the shape-making process.
The shape isn’t being designed but an algorithm
that will generate some shape. This algorithm is
most often sought from the biological sciences but
most certainly are events attributable to physical
affects. These are either not well understood by the
architect (through having limited, if any, training in
biology or physics) or are extremely complex and
the programming of which into a computer cannot
contain all variables and data that we witness in
nature (again, especially as an architectural
education usually contains very little computer
programming training). This then results in
architects attempting to deal with something they
have only a limited understanding of, leading to
results that may appear complicated but are at their
core simplistic or overly simplified. It might also
distort the real issue for architects designing with
computers which is to be more familiar with
geometry, maths and computation.

126
The idea of complexity is an interesting one. In
Airman’s Odyssey (1942) the French writer Antoine
de Saint-Exupery (1900-1944) wrote, “Perfection
is achieved, not when there is nothing more to
add, but when there is nothing left to take away”.
As an aviator this concept would seem obvious to
Saint-Exupery, aircraft rarely have extraneous
detailing. The concept is not foreign in
architecture, particularly in modern times. Mies
van der Rohe’s, “less is more” being an obvious
candidate. In neither case are the authors of these
words calling for simplistic responses to a problem
but one that is considered and complex. Mark
Burry continues this idea in his discussion of
Simplexity.
Burry comments on the tendency for architects to
combine and repeat simplistic algorithms to achieve
highly complicated visual outcomes. This reflects
unfavourably upon the architect’s ability to
understand complex mathematical functions that
are not part of their formal training. Software
provides a way to visually engage with
mathematics, but without a real understanding of
the algorithms behind the shapes displayed
onscreen architects might merely be considered to
be fiddling as sculptors in this realm.
So then, how do architects engage with the
computer as a tool to enhance the exploration of
form? At the heart of all architecture is geometry.
It is a fundamental aspect of our art and has been
for centuries. Renaissance architects worked with
proportions to sculpt architecture and later,
Modernist architects sought to impose new
proportional systems based on units and
standardisation. In these cases there is the ability to
work within a system, it is not an absolute answer
and the variables are multiple. As the architect
defines a space they are aware of the
consequences upon the appearance of the building
and how the inhabitants might use the building.
Whether dealing with symmetry or asymmetry the
architect, through their training and experience,
aims towards designing a building of beauty,
considering rhythm, proportion and harmony.

127
Why then do we appear to ignore this history and
tradition when attempting design with a
computer? Why do architects adopt an approach
where a system defines absolutes that must be
adhered to and cannot be manipulated? Why
produce curved shapes for their buildings that
require modification to their shape in order to
become structurally and economically sound? It
seems to my mind that rather than expecting the
machine to produce the answer, architects should
be more engaged with a geometry understanding
when using a computer, particularly given the
computer has the wonderful ability to visualise
instantly the three-dimensional qualities of the
shapes we design. Yes, computational analysis aids
in further informing our designs but is there not a
place for the guiding hand and eye of the architect
defining the shape in the first instance?
Where to begin in understanding the shapes that we
define within a virtual space? If nearly any shape
is conceivable and able to be constructed, at least in
theory, then how might we initiate a methodology
for using the computer to satisfy Chris
Luebkeman’s “appropriate application” of the
technology? Norman Foster talks of the, “silent,
invisible electronic world” of the computer and that
this must become a physical built reality at some
point. This suggests that fundamental to the
process is the consideration of the physical material
properties that a building will be constructed from.
Jim Glymph, of Gehry Partners, considers
material to be at the heart of the process;
“Architecture needs to return to a more direct
association between the material, craft, the physical
reality of the building”68
.

128
Detail of building demonstrating integrated structure, skin and services, developed from a planar quadrilateral mesh.

129
After these attempts to more completely understand
how and why digital tools are implemented in the
architectural discipline, I found myself coming
back to the instigating proposition; to establishing
some constraints in the use of geometry in a
computer, in this case, planar quadrilateral meshes.
First of all, planar. The materials that are used to
construct buildings today are flat, predominantly
steel and glass but also timber and composites.
To introduce curved surfaces, singular or doubly
curved, increases the cost of projects beyond what
is reasonably expected and we see in this document
how Frank Gehry uses digital tools to control this.
Here we see one of the great proponents of digital
architecture and architect of many ‘bubbly’
buildings telling us that his buildings are
predominantly comprised of flat surfaces. What is
interesting about Gehry is how closely his
design methodology is linked to the fabric of
building. From initial sketches design models are
built utilising strips of material forming ‘ruled
surfaces’. Right from this initial stage there is the
intrinsic knowledge that the building will be able
to be defined by a series of flattened or straightened
elements. In analysing this process and
understanding methods to construct digital
surfaces, it becomes clear that perhaps there is
some way to understand and explore geometric
shapes within the computer in a similar way, a
digital Gehry if you like.
Quadrilaterals. We establish that the quadrilateral
mesh has a number of advantages over triangular
meshes and these advantages give reason to
introduce this constraint. One might argue that it
is the lack of constraints that has hindered curved
shapes becoming a mainstream part of architecture,
leading to digital tools being employed for
computer aided drafting as opposed to computer
aided design. Yes, architects use computers for
efficiency in the production and communication of
construction documentation but when we consider
design, it appears that digital tools have brought
limited benefits or advancement in formal
responses.
And meshes. We see that the mesh has a sound
ideological basis for digital design when
considering Peter Schröder’s arguments and, also
that the mesh is really how we see a constructed
building. The smooth surface is an illusion, the
polyhedron is what the buildings around us really
are.

131
This leads back to the study of geometry. In the
Preface of Architectural Geometry, Helmut
Pottmann describes “modern computing
technologies” leading “to a real geometry
revolution”, particularly when considered against
the “variety of shapes that could be treated by
traditional geometric methods” being “rather
limited”. We may argue that architecture can exist
on paper or in digital realms but architecture is
really best experienced in its full, built wonder.
The ability to define any geometric shape with
digital tools is thus meaningless unless we can
build it, within all the rules and constraints that
exist with the current construction environment.
The course of study consequently explored what
rules exist with which to explore surface types that
would result in planar-quadrilateral meshes.
Alongside this research a method to use digital
tools for direct manipulation of shapes was
pursued, to enable one to ‘sculpt’ within the digital
environment with the knowledge that the shapes
defined will be buildable.
The approach to modelling developed for study
here can better be described as poly-modelling or
sub-division (sub-d) modelling. The approach is
common in the visual effects and games industry
but is not one common to architecture. This I find
peculiar given the early adoption of visual effects
industry software to explore or ‘generate’
architectural form. This software was utilised for
its physical systems, particles and wind for
example, things to amaze spectators. This may
have tied well to the rhetoric for a calculus based,
systems driven architecture of the time but we have
seen that this may have been a limited position.
That calculus, as argued by Antoine Picon,
“provided firm boundaries that could not be
tampered with”69
, tells us that for these architects it
was not the resultant form that was of interest but
rather the processes in generating it. Again, I find
this an interesting point to note given that digitally
produced buildings are often seen as gregarious
form making exercises where in reality the shapes
produced are more a result of a scientific or
numerically mathematical endeavour.
69.Antoine Picon, “Architecture and Mathematics,” in
AD: Mathematics of Space, ed. Legendre, George L,
(London: John Wiley & Sons, 2011), 33.

133
Sub-d modelling is utilised in the visual effects
industry to produce geometry outputs of various
mesh densities depending upon the amount of
‘memory’, or ‘RAM’ (Random-access memory), an
application requires to render or process
geometry. I have argued that the computer is a tool
to aid the limited computational capacity of humans
and we might draw a parallel here between the
limited ‘RAM’ of a human operator in this sense.
Thinking in this we we can understand how a
designer is more readily able to interact with the
digital sculpting of an architectural shape with this
method.
In my eyes then, geometry comes back to being the
basis for a methodology that enables architects to
utilise the computer for the design of doubly-curved
surfaces; to explore the geometry revolution
digital tools are said to bring. The development of
a digital process to explore architectural form in the
classical sense of proportion and adjustment takes
precedence over the formulation of arbitrary
abstract phenomena to describe curved shapes.
This is important so as to connect architects with
the tool in front of them such that the computer
becomes a design partner, supporting the
application of design decisions, not leading them.
No-one can be expected to fully embrace
technology unless the advantages can be expressed
in terms that make sense to them. For architects,
the fundamental act of describing geometry is the
act to make sense of. In harnessing a
digital methodology that enhances the
exploration of geometry, architects can move
beyond any perceived conservatism and utilise the
computer to explore architecture in a formal sense
and stimulate computer aided design.

137
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