BACKGROUND/INTRO: technologies in complex projects (Meredith el al.) However,


Parametric can be defined as a tool that provides for
a powerful conception of architectural form . By using parametric, one can
create an infinite number of similar objects, geometric

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Manifestations of a previously articulated form (
forms of variable dimensional, relational or operational dependencies) When we
assign specific values to those variables, and if values change accordingly,
potentially infinite range of possibilities are created. So, in a parametric
design, it is the parameter s of particular design that are declared and not
its shape. By assigning different values to the parameters, different
object/configurations are created.

Parametric design often involves a procedural,
algorithmic description of a geometry. Parametric
are particularly useful for modelling the geometry of complex building forms.
Their successful application requires careful articulation of clear strategy of
tectonic resolution, such that a clear description of interdependencies can be
achieved. Parametric approach to design, if consistently
applied from its conceptual stage to materialization, profoundly the entire
nature and hierarchies of the building industry, as well as the role of the
architect in the processes of a building. 21ST century Architects
started to design the structures not the specific shape but the set of principles
encoded as parametric equations. Parametric design calls for the rejection of
fixed solutions and for an exploration of infinitely variable potentialities.

Recently, the use of the term “parametric design” has
been widely expanded in the architectural work, mainly associated to the use of
advanced digital technologies in complex projects (Meredith el al.) However,
this concept and its applications in architecture have not been properly
clarified. The documents and programs devoted to parametric systems scarcely
indicate definitions, basic characteristics and/or general uses in building
design. They usually mention specific geometrical operations and/or constructive
developments, this article reviews the meanings of the term and its use in
documents referring to architectural design, as well as early works applying
parametric techniques in the generation of the building form; looking for the
identification of its conditions and its participation in the design.   T The first
building brought to life in which the use of parametric systems is said to have
been used are the Philips Pavilion designed by Le Corbusier  in 1958 (though without computational
methods).parametric techniques have been detected, tri-dimensional digital
modeling was used. The explicit use of variable curves for the constructive
solution and cultural expression of buildings that suggest specific properties

Parametric design in architecture


Scope of parametric design in
contemporary architecture i.e structure,forms,materials etc

 Analogue parametric design

One of the earliest examples of parametric design was the upside down
model of churches by Antonio Gaudi. In his design for
the Church of Colònia Güell he created a model of strings
weighted down with birdshot to create complex vaulted ceilings and arches. By
adjusting the position of the weights or the length of the strings he could
alter the shape of each arch and also see how this change influenced the arches
connected to it. He placed a mirror on the bottom of the model to see how it
should look upside-down.
Gaudi’s analogue method includes the main features of a computational of a
parametric model (input parameters, equation, output):

string length, birdshot weight and anchor point location all form independent
input parameters

vertex locations of the points on the strings being the outcomes of the model

outcomes are derived by explicit functions, in this case gravity or Newtons law
of motion.

modifying individual parameters of these models Gaudi could generate different
versions of his model while being certain the resulting structure would stand
in pure compression. Instead of having to manually calculate the results of
parametric equations he could automatically derive the shape of the catenary
curves through the force of gravity acting on the strings.


Gaudi used physical laws to speed up his calculation of parametric
equations, Ivan Sutherland looked to the
processing power of digital computers.

created an interactive computer-aided design program called Sketchpad. Using a light pen, users could draw lines and arcs that could
be related to each other using constraints. These constraints contained all the
essential properties of parametric equations. Users could experiment and
explore different designs by altering the parameters of an entity and let
Sketchpad do the calculations and redraw the geometry according to the
constraints imposed upon it.




the waterloo
international station, London, 1993





Waterloo Station,
located in the heart of London, is a major international

train terminal, moving more than 15
million passengers a year in 60,000m2. In 1993 it had to be extended to become
the main terminal for the Eurostar train which enabled a fast connection with
Paris and Brussels. The extension and complete renewal of the terminal was led
by of Nichols Grimshaw´s architectural office and several engineering teams.
The purpose of the project was to complete the station incorporating an
expression of smooth flow, to evoke the industrial era, but also the new way of
transportation (Grimshaw, 2010; McGuckin et al, 1994). The area available for
the extension had the necessary width to accommodate only five additional
railways, limited by the electrical network on one side and the roads on the
other, in a winding area and that narrowed toward the interior. The extension
had to be added to the existing station. In doing so, it provided uniqueness by
showing new traveling possibilities, especially though its 400 m-long roof. The
cover was a particular technical challenge

due to its asymmetric shape in the acute
profile of the area and due to the fact that it had to rise up progressively to
fit the height of the trains. The eastern side is clad entirely in glass.
Towards the entrance it offers and impressive view of the River Thames and
Westminster and on the other side, it becomes a panoramic showcase for the long
Eurostar trains. Structurally the roof structure consists of pairs of
three-pinned bow strings arches; the central point displaced towards one of the
sides enables the bow shape in the higher area from West to East. This complex
structure covers an area that goes from 50 m wide in the entrance to 35 m
towards the end of the platform. The roof is flexible, with a limited range of
glass tiles of different sizes overlapped that can shrink and expand according
to the different spins of the roof. The structure is formed by two dissimilar
curved trusses, a larger one stretched in the inner side and a smaller one and
curved, stretched in the top end. Also, the beams make up 35 modules that vary
in dimensions.

The design was modeled by Lars
Hesselgren in the software I_EMS, and afterwards it was re-modeled by Robert
Aish with Microstation Generative Components. The trusses were defined by a
program that modifies the inner measurements of each module according to the
proportional scale factor to the length by means of Pythagorean relation
keeping the centres. for the radial layout of the smaller pieces. By propagation
of the formula, changing the wide of the structure (the chords of curves) and
maintaining the central axis like a curved profile. Such produces a continuos
surface with a variable section, with proportional heights of the beams
according the lights of support. The mathematical description enabled the
generation of each design by means of altering the numerical parameters

The covering is the main architectural
challenge of the Terminal and its magnitude provides the perception that almost
the whole building is enclosed. Shifting the attention from the vault work
composing the old terminal (refurbished as warehouses and food courts) to a new
fluid space that covers a parking lot next to the underground and two levels of
viaducts above which stand two floors for passengers (arrivals and departures).
The design shows the variation of structure that resembles mobility and
technology of new transportation media.


The fish, barcelona,

The group of buildings executed by Frank
Gehry in the city of Barcelona from 1989 to 1992, were part of the plan elaborated
for the Olympic Games, with the purpose of recovering the coast line (Dal Co et
al,)  It was an industrial area,
segregated of the city by the railroad lines that had turned the nearby beaches
into waste deposits. Therefore, it was considered to integrate the urban layout
to the coastline through a system of public spaces and equipment. Including the
Hotel Arts and adjacent commercial areas designed by Frank Gehry and associates.
The project considered a surface of 14,000 m2 organized around a central patio
between the hotel and the beach, forming multiple routes with restaurants and

The roofing of the patio considered a 49
m long and 30,5 m tall metallic structure that acts as a protection from the
sun. Two basic parts are noticed: a supporting white steel reticular structure and
a metal cover that evokes a fish surface.

In Frank Gehry´s work, the fish is a
recurrent figure since its beginnings, used in the form of lamps for the
unbuilt project of Smith House and the Collaboration Exposition in 1981. He
worked with a model and scales that revealed him the symbolic potential of this
figure (Gehry, 1988). Also that year, the project for the reinsertion of houses
in Michigan included a fish-shaped hotel. However, he was only able to realize
it in light sources for the Venice restaurant and in other lamp proposals for
the Formica´s in 1982. Two years after he exhibited in Nueva York the design fish-shaped
cells. Also, in the proposal for the Fish Dance Restaurant in Kobe, Japan in
1986, he incorporated it as sculptures in the facade of the

building. For the design of this roof in
Barcelona, the first fish-shaped set up that he uses at architectural scale,
Gehry´s study used the software Catia, by Dassault Systemes, previously applied
to the design of cars and aircrafts. This computer program enabled to work on a
digital model in three dimensions and to be connected with the production or
the digitalization of material models. It is worth mentioning that the

physical models occupy an important place
in Gehry´s design process to encourage designers to experiment and get away
from the outlines of the orthogonal geometry. Therefore, computer programs
combine in a coherent digital representation the demands of the constructive
system and the experimentation with non-conventional shapes. Gehry states that
the relationship between the design solution and the cost that its elaboration demands
constitutes one of the most important variables in the decisions of the shape.
Maintaining the equilibrium between the architectonic characteristics of
volume, plastic expression, constructive system and materiality, is a task
conditioned by the budget. James Glymph, responsible for the digital design,
first made contact witJ. Mitchell, professor in Harvard who, together with the
student Evan Smythe, developed the basic design model in the software Alias

(Shelden, 2002). However, when using it,
it represented a curve-shape. materials and textures, but in smaller elements,
by using the set up of small intertwined pieces forming the support and cover
at the same time. In this case he used flexible strips fitted in the pipe ribs
of the structure, and he required adjust these two arrangements by the digital
model in CATIA. He understood then that he had to separate the supporting structure
from the representative surface, as it has happened often in the history of
architecture, for example, with the renaissance domes and more recently in the
Sydney Opera House; laying out a support inferior scheme and a sustained
variable cover. But this strategy requires a precise trace Of different curves
to combine them with regular distances of the support and accurate fabrication
of pieces. This geometric interrelation between the structure’s modulation and
the complex curvature surface led to the challenge of using digital parametric geometries
that generated a new step in the professional work, allowing construction of
curved profiles for symbolic potential of buildings.



Current Situation – Conventional Design.

current market economy requires project teams to design quickly, efficiently and
cheaply; however, research shows that successful design is largely a function
of clear definition of end-user requirements (Rolland, 2005) and the generation
and multidisciplinary analyses of a large quantity of options (Kelley,
2006).There is always a continuous tension in every project between design
exploration and process efficiency. The design phase is virtually endless. The
designer can stop designing when he feels that the time invested in the process
is not equal to the value added to the artifact. In the meantime, with tight
working schedules and tense project delivery dates, not all designs are
thoroughly studied, assessed and evaluated, and thus better performing designs
are likely left undiscovered. A recently conducted study by Gene & Haymaker
(2008), made a benchmarking survey of existing conceptual high-rise design
practice to determine the performance of leading design teams. It was found
that a multidisciplinary team averaging 12 people can normally produce only 3
design options during a design process that lasts 5 weeks. It was also found
that most of this time is spent by architects on generating and presenting a
small number of design options. Little time is dedicated to establishing and
understanding project goals and running multidisciplinary analysis. These
analyses are inconsistent and primarily governed by architectural rather than
multidisciplinary criteria. From the previous discussion, we can point out a
real need for an approach to design that can explore the undiscovered
solutions. In order to understand the potential change in the organization and
composition of the design process, we need to develop an in-depth understanding
of the meaning of parametric design, parametric thinking and the terms
associated with their use in contemporary architecture.

Design – Basic understanding

can provide for a powerful conception of architectural form by describing a
range of possibilities, replacing in the process stable with variable,
singularity with multiplicity. Using parametric, designers could create an
infinite number of similar objects, geometric manifestations of a previously
articulated schema of variable dimensional, relational or operative
dependencies. When those variables are assigned specific values, particular
instances are created from a potentially infinite range of possibilities. Parametric
design can be defined as a series of questions to establish the variables of
design and a computational definition that can be utilized to facilitate a
variety of solutions (Karle & Kelly, 2011). Instead of modeling an external
form, designers articulate an internal generative logic, which then produces,
in an automatic fashion, a range of possibilities from which the designer could
choose an appropriate formal proposition for further development (Kolarevic,
2003).Parametric thinking is a way of relating tangible and intangible systems
into a design proposal removed from digital tool specificity and establishes
relationships between properties within a system (Karle & Kelly, 2011) From
the previous, we can point out the core idea of parametric design in which
variation and flexibility and information control are the main aspects of this
design approach. It is important to understand that, in parametric design, it
is usually difficult to categorize the implications clearly between the
process, the designer and the tools. It is difficult to imagine parametric
design process without a tool that aids the algorithmic sequencing of design.
In light of these understandings, the next section of the paper discusses the
implications of parametric approach on design thinking.

Conventional to Parametric Thinking

In a deep
sense, parametric modeling is not new: building components have been adapted to
context for centuries. Conventional CAD systems focus design attention on the
representation of the artifact being designed. Currently, industry attention is
on systems in which a designed artifact is represented parametrically, that is,
the representation admits rapid change of design dimensions and structure
(Aisha & Woodbury, 2007). Parametric thinking pushes back on the
conventional architectural design process and negotiates multiple variables
that define a series of rule-sets. It asks architects to operate quicker and
smarter, juggling multiple systems with speed and efficiency. Published
theory concerned with architectural parametric design tasks typically focuses
on conceptual design phase. Significant research by Michela Turin et al. (2011)
was conducted in this area, in which parametric design as well as genetic
algorithms were used to explore performance driven geometries and structures in
the conceptual phase. In the meantime, observations from research and applied
practice show that parametric tools are typically being applied to design
development problems rather than the early conceptual formulation of the design
(Hudson, 2008). In either cases, there is no doubt that some profound effects
on the design process can be observed. We can also find some important
analogies between conventional and parametric design as would be elaborated in
the next section.

Commons of Conventional and Parametric

At one
level, parametric thinking is analogous to conventional design processes
(Figure 1) in that a set of conditions – or parameters – are identified
and analyzed, then preliminarily synthesized, tested and reiterated, and
ultimately implemented. In any design process, if the set of conditions
are misdiagnosed or misunderstood, the resulting design solution has limited
potential to flourish and design integrity suffers (Sanguinetti & Kraus,
2011). It is also worth noting that parametric problem does not need to be
thoroughly well-defined, actually the incomplete description of the problem is
possible in a parametric setting. This can be described as acquiring knowledge
through tinkering or exploration as described by Hudson (2008).


between problem and solution through three activities of design process.The
starting point in parametric problems will also be influenced by knowledge. The
starting state is defined either by choice of an existing solution or similar
solution from a similar problem, or by specifying an initial set of parameters
(Hudson, 2008). The designers tend tolerate and draw analogies between current
problems and previous solutions in the designers memory which is often called
“case based, case retrieval or recall”. The notion of recall has-been
related to problem analysis and selection of initial “prototype”
(analytical descriptions of a problem) based on knowledge of a library of
previous prototypes. This prototype is then adapted to suit the new problem
based on knowledge of the new condition. The prototype includes descriptions of
relational, qualitative, computational knowledge and context knowledge.

Once a
design has been evaluated it may or may not satisfy constraints and
requirements. Through knowledge of the task the designer must either select to
try and improve the designer reformulate the problem. If the design is to be
improved, a method or operator (Mottaand Zdrahal, 1996 in Hudson 2008) must be
selected and applied in order to fix a design so that it satisfies some
constraints. Choice of method or operator is determined by knowledge of the
behavior of the problem. If reformulation is selected (this is common for
architectural problems) the analytical stage of the design must be revisited
and parameters and constraints adjusted


Parametric design has been spread out in
architecture without complete clarification of its particular features. This text
at the beginning reviews the connotations of the term, disclosing its mathematical
and social meaning; as well as the first documents that mention this technique
in computer graphic and architectural design, observing a geometric and
constructive sense. Then three works are described, in which initially these
techniques were applied, manually in the Philips Pavilion by Le Corbusier and

Xenakis in 1958, and with incipient
computer systems in the Fish of the Olympic Village of Barcelona, by Frank Gehry
in 1992 and the extension of the Waterloo Station in London by Nicholas

These projects show a detailed handling
of curve-shape forms in significant elements for construction, using relatively
complex geometrically procedures, in the last cases digitally, which stand out
because the profile in an irregular manner, in the encircling walls of the
Pavilion and the covering of the Fish and the Waterloo Terminal. This variable profile
is the essential property of the parametric equation curves, which suggests a
formal definition of the parametric design; distant from external references,
restrictions or regular alterations, which are the general interpretations of
the concept parameter gathered from documents connected to constructive
modelling. In this sense, a strict parametric design condition is observed in
these architectural works, associated to variable curve-shapes. Using different
procedures and tools, but all related to trace irregular bend shapes, composed by
diverse profiles and modular surfaces related. In order build a coherent three-dimensional
geometry of complex volumes.

parametric techniques that provide the
geometric control of these irregular figures participate in specific actions,
which generate overall attributes of the shape; its constructive resolution and
its symbolic projection within a comprehensive architectural control. In this sense,
the parametric technique plays an instrumental role, but also provides with an
expressive potential. the parametric design capabilities open possibilities to
the architectural work in a formal, as well as in the constructive and cultural

Discussions about how parametric
thinking ought to change the design process is far from conclusive. However,
new programming paradigms, new ways of structuring code, new code libraries,
new environments for generating code and new ways of managing code development
are main stream of Computer Aided Design Research. This paper has shown that
the parametric approach is one way to influence model flexibility, complexity
and information flow.