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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