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PARAMETRIC DESIGN
What Is PARAMETRIC DESIGN ?How to design with A PARAMETRIC Equation ?
What is SHAPE GRAMMAR ?
Examples
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What is PARAMETRIC DESIGN ?
It is generative mathematical driven design
Often when You draw/model your concept, Youfollow certain operations which are monotoneand repetitive, they are algorithms .
For example, think of an elevation with windows, eachwindow must have an area equal to 1/8 of room's floorarea. It's simple, but when next day You'll decide that1/7 will do better, and there are 1000 windows ? Let thePARAMETRIC design handle this algorithm.
PARAMETRIC DESIGN
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How to design with A PARAMETRICEQUATIONS ?First before to know how to design with A parametric
Equation you have to know WHAT IS THE PARAMETRICEQUATION ?
PARAMETRIC DESIGN
In mathematics, parametric equation is a
method of defining a relation using parameters.
A simple Kinematical example is when one uses a
time parameter to determine
the position, velocity, and other information
about a body in motion.
Abstractly, a Parametric Equation defines a
relation as a set of equations. It is therefore
somewhat more accurately defined as parametric
representation. It is part of regular parametricrepresentation .
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How to design with A PARAMETRIC EQUATIONS ?PARAMETRIC DESIGN
2D Example :
ParabolaFor example, the simplest equation for a
Parabola,
can be parameterized by using a free
parameter t, and setting
Circle
Although the preceding example is asomewhat trivial case, consider the following
parameterization of a circle of radius a:
where t is in the range 0 to 2 pi.
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Solve and graphx=5sin(t), y=5cos(t)
Try to plot this graph without using your
graphing calculator.
What does this look like? It is looks a Circle
What is the radius?? The radius is 5
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Solve and graphx=5sin(t), y=5cos(t)
Lets determine the rectangular equation of
this graph. How do we proceed when the
parametric equations contain trig functions?
Sometimes we can solve for the trig functions
(not for t itself) and make use of trig identities.
What trig identity could we try here?
When we have sine and cosine both present,
we should try the Pythagorean identity.
What is that? sin2 (t)+cos2 (t)=1
Solve the original equations for sin(t)
From the x equation, we get
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Solve and graphx=5sin(t), y=5cos(t)
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PARAMETRIC DESIGN3D Example :
Helix
Parametric equations are convenient for describing
curves in higher-dimensional spaces. For example:
describes a three-dimensional curve, the helix ,which has a radius ofa and rises by 2b units per
turn. (Note that the equations are identical in
the plane to those for a circle; in fact, a helix is
sometimes humorously described as just "a circle
whose ends don't have the same z-value". (This is
not exactly true, as a circle is by definition a two
dimensional curve and a helix is by definition a three
dimensional curve.)
Such expressions as the one above are commonly
written as
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PARAMETRIC DESIGNParametric Surfaces:
A Torus with major radius R and minor radius r may be defined
parametrically as
x= cos(t)(R + rcos(u)),y= sin(t)(R + rcos(u)),
z = rsin(u)
where the two parameters t and u both vary between 0 and 2
As u varies from 0 to 2 the point on the surface moves about a
short circle passing through the hole in the torus. As t varies from
0 to 2 the point on the surface moves about a long circle aroundthe hole in the torus.
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Parametric shape grammars are anadvanced form of shape grammars. The new
shape in the RHS of the shape rule is defined by
parameters so that it can take into accountmore of the context of the already existing
shapes. This typically affects internal
proportions of the new shape so that a greater
variety of forms can be created. In this way,attempts are made to make shape grammars
respond to structural conditions, for example
the width of beams in roof structures which
depends on span.
Despite their popularity and applicability in
academic circles, shape grammars have not
found widespread use in generic Computer
Aided Design applications.
PARAMETRIC DESIGN
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Examples 1:30 St Mary Axe30 St Mary Axe, also known asthe Gherkin, the Cucumber Building andthe Swiss Re Building, is a skyscraper inLondons main financial district, the City ofLondon, ( by Foster and Partners )
PARAMETRIC DESIGN
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The parametric 3D computer
modeling process works like a
conventional numericalspreadsheet. By storing the
relationships between the various
features of the design and treatingthese relationships like
mathematical equations, it allows
any element of the model to be
changed and automaticallyregenerates the model in much the
same way that a spreadsheet
automatically recalculates anynumerical changes.
PARAMETRIC DESIGN
Parametric nodes of the tower's
computer model.
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As such, the parametric model becomes a
"living" model one that is constantly
responsive to change offering a degree of
design flexibility not previously available. Thesame technology also allows curved surfaces to
be "rationalized" into flat panels, demystifying
the structure and building components of highly
complex geometric forms so they can be builteconomically and efficiently.
PARAMETRIC DESIGN
parameters, the design team was abquickly test
numerous forms.
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Aerodynamic form
The Swiss Re Tower has a circular plan that widens as it
rises from the ground and then tapers towards its apex.
This form responds to the specific demands of the small
site
The aerodynamic form of the tower encourages wind to
flow around its face, minimizing wind loads on the
structure and cladding, enabling the use of a moreefficient structure.
PARAMETRIC DESIGN
Changing certain form-giving parameters
created variations in the building profile
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Example 2:Museum of contemporary Art In warsaw- The use of real timesimulation in design process
The museum is an annex of the Center of Contemporary Art, located inthe XVIth century Ujazdowski castle in Warsaw. It is situated in a strategicpoint above the highway cutting through the city, highly visible whileapproaching the city thus making it a recognizable landmark.
The project consists of five different crystal-like volumes organized arounda central courtyard, embedded in the landscape, engaging the visitorsboth through indoor and outdoor areas. The differentiation of theexhibition spaces is amplified by very specific daylight conditions relatedto different programmatic needs.
PARAMETRIC DESIGN
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The computational techniques used for the form finding process, define a
multiplicity of light shafts oriented and shaped according to the studies of the
sun circulation on the site on a year-round cycle.The museum offers exceptional environment for manifestation of
contemporary art, where light and atmosphere are constantly changing
throughout the whole year
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Development of the project consists of different analytical stages:
1) a simulation developed in Processing, distributing different
programs and light openings along the site, depending on their
requirements in terms of factors like noise, sun exposure, accessibility
and views
PARAMETRIC DESIGN
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2) parametric studies in Rhinoscript investigating geometrical potential of positions for the light
shafts
3) environmental studies in Ecotect and Radiance analyzing light conditions in different times of
the day throughout the whole year
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The excel database which stores the data in a numeric array correspondingwiththe generated execution drawings and 3d segments is bundled together andfurther communicated to the manufacturing units as a concise productionschema. This assists in speeding up the production process and hence resultsinaccomplishment of complex projects within the specified timeline. Theassemblyphase (Fig. 06 right) is hence reduced to an exercise of connecting preciselynamed/numbered parts (more like a kit of parts scenario) in asequential mannerto produce a holistic topological marvel.ConclusionThe design-informatics Informed-Design technique, while promoting aparametric mode of operation, which enables one to communicate smoothlywith three dimensional models and the project database, inherently involves acollaborative design approach, entailing derivation and appropriation ofdiversetools and techniques (programming/scripting, graphic design, architecture,engineering and CAM) towards manifesting spatial constructs.
PARAMETRIC DESIGN
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For A given project ( GP2- OR ANY DESIGN STUDIO PROJECT)
1. Analyze geometrical rules.
2. Identify Parametric elements.3. Compose Parametric equation for a certain form.
4. Draft in an appropriate scale the parametric modified form
from the original form.
Deliverables:
3 A2 sheets to trace the needed process described above.
3 A4 sheets reporting the process by calculations.
Deadline: 4 Weeks project. Group work ( same GP2)
Midterm: Next Week 1 Hour on Thursday No Tuesday .
Assignment