Parametric modeling for advanced architecture

Abstract

This paper describes parametric approach in architectural design through elaboration of shift in paradigms in architecture that has brought to the idea of use of parametric modeling with emphasis on two different groups of parametric software and presents the possibilities of generative algorithms in modeling architectural form and development of cities and urban design.

Full text

Abstract—
Computer simulation of evolutionary processes is
already well established technique for the study of environmental,
biological and economic dynamics. Use of algorithms for generation
of virtual entities that will develop its functional and formal
properties within the non-linear process of adaptation of complex
system is a foundation for new point of view in understanding
architecture and urban environment. This paper describes parametric
approach in architectural design through elaboration of shift in
paradigms in architecture that has brought to the idea of use of
parametric modeling with emphasis on two different groups of
parametric software and presents the possibilities of generative
algorithms in modeling architectural form and development of cities
and urban design.
Keywords—g
eometry, parametric design,
generative algorithms
urbanism, architectural design.
I. INTRODUCTION
ESCRIPTION and explanation of a natural phenomenon
within abstract mathematical framework has become very
successful with introduction of calculus in 17th century.
Physical phenomena of world around us have become
reproducible without direct reference to physical reality. It was
achieved with use of codes and equitation that represent the
underlying order and regularities of represented phenomena.
The use of code in architecture as a formal and design
convention has a long tradition. The transformations of those
codes and constraints have determined development of
architecture throughout history. With introduction of
computation, codes in architecture could be understood as a
set of instructions determining certain attributes of the formal
entity or instructing a process of manipulation of the same.
The formalization of the design process and use of
computation has opened an endless range of generative power
of algorithms. This has enabled architects of today to create
new environments with a system of codes that is coherent with
the nature of the phenomena and in the same time to be
creative. It is a moment of revelation in a sense of newly
M. Stavic is a researcher at the Graz University of Technology, Faculty of
Architecture, Institut of Architecture and Media, Austria. Inffeldgasse 10/2,
8010 Graz, Austria ( phone: +43-316-873-4738, e-mail: mstavric@tugraz.at).
O. Marina is Assistant Professor at Faculty of Architecture, University “Ss.
Cyril and Methodius”- Skopje, Republic of Macedonia, blvd. Partizanski
odredi 24, 1000 Skopje, Macedonia (phone: +389 2 3116367, e-mail:
ognenmarina@gmail.com)
released power of codes and algorithms that contemporary
architect can use to breed new forms rather than to specifically
design them.
Digital modeling and visualization of architectural
buildings has become the benchmark in the work of architects
and is unavoidable in architectural education [19][24]. From
the original 2-D programs used for drawing architectural
designs, the software used for computer-aided design has now
turned into intelligent 3-D software packages based on
parametric modeling. These new possibilities have led to new
movements in architecture and defined the field of non-
standard architecture.
Judging by the latest trends, the development of digital
design did not end with simple parametric modeling; it has
taken a step ahead by using generative algorithms. Several
software packages offer graphical algorithm editors (e.g.
Coffee, Grasshopper), which are directly linked to 3-D
modeling tools and allow interactive parametric modeling.
These editors do not require any previous knowledge of
programming or scripting, and yet they make it possible for
designers to generate a broad range of non-standard designs
that can be changed interactively. This new parametrically
based approach in architectural design enables architect to
search for a completely new level in form generating process.
It is possible with design of non-standard objects that can be
dynamically transformed to achieve a strong interaction and
integration of design process with fabrication of architectural
elements, or in the scale of urban plans with development of
semantically enriched elements.
This paper gives a brief overview of parametric design
using two distinct types of parametric software packages and
presents the possibilities of applying of generative algorithms
in modeling architectural form and development of cities and
urban design.
II. SHIFT IN PARADIGMS IN ARCHITECTURE
Dominant typologies that have served to legitimized the
production of architectural and urban form since 18th century
were either based on the idea of return of architecture to its
natural origins – a model of primitive shelter as an imitation of
the order of Nature, or emerging as a result of Industrial era –
architecture as a process of production of functional parts [26].
In these concepts urban form is just an inert receptor of
Parametric Modeling for Advanced
Architecture
M. Stavric
1
and O. Marina
2
D
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externally imposed order and therefore its form is
predetermined by fixed typologies [4].
The order in classical architecture has been determined by
formal tools or techne of composition connected with order
and distribution of matter. The form is predetermined by
formal typology organized and transferred in reality through
canonical system of formal conventions and is encoded by
social conventions through which building obtains social
relevance within the built and social environment. The idea of
architecture and urban form as an inert receptor of
predetermined form originates in part from the dominant
concepts of representation. Formal elements of architectural
form represented in Cartesian three-dimensional space are
determined by fixed coordinates of their points within the
system. With this, elements of architecture are nothing more
than a copy of ideal, platonic forms liberated of any trace of
inherent order [5].
Most of the paradigms were delegitimized with the fact that
the origin of the order of urban form was positioned outside
the system instead to acknowledge the inherent order of the
system as fundamental for form generating process.
With process of revision of Modernism dominant concepts
in architecture are based on phenomenology directly
confronting with functionalism and universal positivistic
models of Modernism [9]. With this shift in paradigms and
transcendence of concepts in architecture the interdependence
of the inherent nature of phenomena of architecture and the
process of its creation has become a new challenge. The nature
of the architecture and urban form is inherently dynamic and
cannot be determined by fixed types regardless of the vastness
of the number of types. Therefore, the existing concepts in
theory of architecture and urban form based on fixed
typologies do not provide solid ground for understanding the
process of creation of form and the phenomenon of urbanity in
general. Solution of this situation can be reach only by radical
change in the viewpoint: the architecture and urban form not to
be conceived as a static system of predetermined ideal forms
but rather as a dynamic system of changes that will generate a
complex result.
The concepts of instability and de-centralization of identity
[7] will be used in architecture to exclude existence of an ideal
form [4] and to determine that the shape is a unique result of
process of morphogenesis. As a result of this, the idea of form
in architecture will shift from a fixed typology toward a
historically convergent result of a form generating process in
time, shaping unique and historic result that is coherent to the
nature of the phenomena that we recognize as architecture.
The emerging form will be a result of a process of
morphogenesis as a historically embedded process of creation
and adaptation [11].
With this shift in paradigms a theoretical ground for novel
design tools and methods in architecture has been established.
Within this theoretical framework the creation of a form can be
understood as a process of individualization where every
particular property of a distinctive element is a result of
accumulation and interaction of different influences,
conditions and restrictions, a process that is completely
dependent on specific and historically contingent details.
Adjacent to this concept is the topological paradigm where
identity and position of each of the elements or parts of it
within the system are determined exclusively through its
relation with all other elements within the system. Since there
is no centre to dictate the predetermined form of elements of
the architectural and urban form, formal order is established
only by locally defined relations between the elements. This
decentralized order generating process is distributed within,
and in the same time dependant on a population of elements.
So, instead of thinking in terms of a form defining centre the
system should be understand in terms of population of
elements. This multiplicity [6] of elements and local relations
that create the order of the system are the source of a
morphogenesis process. In a situation where a system of
architectural forms is defined as a population of elements, we
always have to specify the process of creation first, in order to
have the idea of the overall form of the system. This process is
inherently historic and it is based on the existence of
differences between the elements. Without the existence of
these productive differences that raise the process of
adaptation and differences leveling within the system and the
diffusion of novel and creative solutions within the population
of formal elements there would be no morphogenesis.
These are the new paradigms and new concepts that should
help us to construct a model of dynamic development of
architectural and urban form. Therefore, in the next chapter we
will introduce some of the concepts and softwares that are
enabling the creation of form as a dynamic and parametrically
determined non-linear process.
III. PARAMETRIC DESIGN
During the past fifteen years digital media in architecture
was used in different ways and influenced the whole field of
construction and design. At the beginning digital media was
applied only as a representational tool. With emerging digital
technology architecture has found a new tool for conceptual
design in digital media [22].
On the one hand architectural design was inspired by the
various possibilities of digital technology itself. On the other
hand many topics from different fields influenced the design.
Former “invisible” mathematical and geometrical algorithms,
forms and structures are now visible and spatial
understandable for architects and, therefore, usable. Using new
technique architectural design has established computational
concepts such as: topological space (topological architectures),
isomorphic surfaces (isomorphic architectures), motion
kinematics and dynamics (animate architectures), keyshape
animation (metamorphic architectures), parametric design
(parametric architectures), genetic algorithms (evolutionary
architectures) or fractal geometry (fractal architecture) as
discussed in Kolarevic [14].
Generally in parametric design form is shaped by values of
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parameters and equations are used to describe the relationships
between the forms. Hence, interdependencies between forms
can be established and their behavior under transformation can
be defined (mathematically and geometrically). Since about
1990 parametric design has influenced the development of
digital architectural design, where we can distinguish between:
- architectural CONCEPTUAL parametric design and
- architectural CONSTRUCTIVE parametric design.
IV. CONCEPTUAL PARAMETRIC DESIGN
In conceptual parametric design, it is the parameters of a
particular design that are declared, not its shape. By assigning
different values to the parameters different objects or
configurations can be easily created. Rosenman and Gero,
Prousalidou [18] analyze parametric and generative
representations of buildings, whether based on orthogonal or
curvilinear geometry (DeCOi [3]). They are powerful owing to
their ability to capture a high degree of variation in a few
numerical values. Software like Maya or Rhinoceros (with Mel
or Rhino Script) offers such script editors for parametric
design. Maya is software developed for film industry
(primarily for animation and capturing) but lately many
architects (Fig. 1) have used it for conceptual design.
Fig. 1 Mel scripting, student Martin Schnabel, Institute of
Architecture and Media, Course DM2
This design method requires knowledge of programming or
scripting and it is inherent of the mathematical algorithms
whereby interactive design is not possible.
V. CONSTRUCTIVE PARAMETRIC DESIGN
Constructive parametric design refers to data embedded
within a predetermined 3D object. This parametric concept is
realized in various CAD packages like Autodesk Revit, Soft
Plan, Nemetschek, ArchiCAD or Chief Architect. Instead of
drawing lines, arcs, etc. designers can insert pre-drawn
components, doors, windows, load elements, stairs or roofs
etc.
This results in 3D models instead of 2D drawings, which is
already standard in ship-building industry. The objective of
such technology is to reduce the drafting time and corrections
to 2D drawings. We detected some limitations in such software
tools. First, it is not possible to consider a wide range of
different building materials to make one standard for all
manufactures of building materials and components with the
aim to provide an “intelligent” model. Second, these software
tools are originally designed for standard building elements,
whereas non-standard elements of contemporary digital
architecture cannot be implemented [15].
In contemporary architectural practice there are some
successful examples of using parametric design and we will
discuss some of the projects.
Nicholas Grimshaw & Partners used parametric design for
the arched roof of the train shed at the international terminal at
Waterloo Station in 1993. Each arch and its related cladding
are different as the roof width changes along the curved track.
In this project only a single parametric model of one arch is
modelled and different parametric controlled variations define
the whole roof.
A bigger-scale project is the Hessing Cockpit Building
within the alliance of the Acoustic Barrier in Utrecht, Holland
(Fig. 2).
Fig. 2 Oosterhuis/Boer, Hessing Cockpit Building, Utrecht 2005
Kas Oosterhuis and Sander Boer proposed one
parameterized universal detail for the whole structure, One
Building – One Detail [2]. Oosterhuis/Boer provided a digital
control model to the contractors, which allowed them to build
all constructive details on top of this control structure. All
steps are described as an Autolisp routine. The Swiss Federal
Institute of Technology has realized three projects of complex
forms: Swissbau Pavilion, Inventioneering Architecture,
Libeskind’s Futuropolis (Fig. 3) in timber by implementing
parametric design as early as at the beginning of the design
process [21].
Fig. 3 Libeskind’s Futuropolis
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Frank O. Gehry went one step further using fully parametric
support for a whole building – from design to manufacturing.
Frank Gehry and Associates formed 2002 Gehry Technologies
(GT) [9] to provide integrated, digitally driven constructions
and methodologies for the building industries. Frank Gehry
starts projects by sketching and manipulating physical models.
Using inverse engineering physical models are translated into
Catia and projects are controlled and manufactured using
computer-generated construction plans. At GT it is known
what it will be, how it will be made and who will build it right
from the beginning of the project. Teams of architects,
engineers, and consultants work together in the same Catia
database. The accuracy of the information and the elimination
of middlemen reduce everyone’s cost and risk, and make non-
standard objects buildable. Gehry Technology is serviceable
for big project teams working with the same database. This
oversized technology is not useful in the case of standard
architectural practice.
The whole projects were geometrically well elaborated and
this enabled their realization within a digital chain process
(from CAD to CAM). All three of them are very different in
design and building strategies but they show the advantages of
using parametric design methods.
VI. GENERATIVE ALGORITHMS
Generative programming is a style of computer
programming that uses automated source code creation
through generic frames, classes, prototypes, templates, aspects,
and code generators to improve programmer productivity. It is
often related to code-reuse topics such as component-based
software engineering and product family engineering. In the
field of architecture such editors are tightly integrated with
modeling tools that require no knowledge of programming or
scripting, but still allow designers to build form generators
from the simple to the awe-inspiring [12].
In order to explain the concept of generative algorithms in
architecture, let us remind ourselves of the conventional
method of digital design. Digital modeling involves the
definition of spatial elements (solid or plane/surface), their
transformation and modification. Each change in the design
leads to modifications in the geometry, making it extremely
complicated to intervene on every single element, which is
directly interdependent with the other elements. With any such
changes it is necessary to adapt, scale and reorient each
individual element, which is very time consuming.
Generally speaking, two basic principles may be singled out
when it comes to this type of design process. The first
principle is associated modeling, i.e. the synthetic building of a
structure based on the hierarchical functioning of objects and
their interdependencies. The second is the generative principle,
where one solution is selected out of many 3-D spatial
configurations offered representing the optimal configuration.
The selection criterion for the optimal configuration may be
technical or aesthetic.
It is precisely these two basic principles of conceptual
design that may be described by means of mathematical
models and are contained in associated and generative
modeling.
A. Associated modeling
Associated modeling refers to a method where elements are
connected in a fixed order, which produces a result creating a
basis for building a new order. Let us draw a curve and
quadrilaterals at its beginning and end whose dimensions will
depend on the curvature of the line at its initial and final
points. If we change the form and position of the curve, the
associated quadrilaterals will change their positions and sizes.
This method of design extracts the required parameters from
the designed structures and manipulates them using the right
algorithms.
B. Generative modeling
Instead of drawing a structure, generative modeling uses
numbers as the input data. Designs are generated by means of
mathematical operations, dependencies and functions. Any
structure designed in this way contains a great number of
variables within its internal structure, which may be used as
the next step in the design process. This kind of modeling
allows maneuvering in the development and generation of the
design which is not possible when using standard 3-D
modeling tools.
For example, let us take the range of integers 1-10 and use a
random number configurator to generate three different
numbers representing the spatial coordinates of three distinct
points in space. The generated spatial points define a NURBS
geometry. Every time the spatial coordinates of any of the
input points x, y or z change, the generated surface
automatically changes its geometry and adapts to the new
variables.
C. Generative algorithms in architectural design
Modeling which uses associated and generative modeling is
called generative algorithm modeling. This process has the
term algorithm in its name because objects are generated using
algorithms in this type of design and their output for the
further stages of design is also generated by means of
algorithms. When it comes to architectural design,
Grasshopper is one of the most commonly used generative
design editors [13][16]. This editor is connected to Rhino 3-D
objects and offers a range of mathematical tools for generative
modeling such as operators, conditional statements, functions
and trigonometric curves (Fig 4).
Fig.4 Grasshopper mathematical operators
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There are operators from the branch of analytic geometry
for vectors, points and planes. The list and data management is
a very important segment as it allows extensive database
manipulation. In terms of advanced modeling options, it is
possible to use scripting in VB.NET, rhino. NET SDK (it
allows access to OpenNURBS geometry) and C#.
The operations and analysis of associated elements make it
possible to select from a number of options for NURBS
geometry and somewhat fewer options for mesh objects.
D. Parametric urbanism
Contemporary urbanism tends to embrace a dynamics of the
material and social process that are shaping contemporary
cities [8][23]. It is based on form finding process organized by
networks of interrelated systems. This novel paradigm and
theoretical ground determines the city form as dynamic, non-
linear and mostly parametric phenomena. However, the
ramification of these new paradigms and concepts and their
application in novel design and production tools for urbanism
have widely remained untheorised and have not been exercised
in practice.
The foundation for application of general theory of
computing in urbanism is in the effort to formalize the
dynamics of development of urban form as a procedure, a
sequence of logical steps. By shifting the focus from the matter
toward the organization of the system of urban form in general,
the essence of this process will be determined as a set of rules
regardles of materiality of the phenomenon. This abstraction of
the phenomena to a level of abstract organizational structure
enables us to think of it as a complex system based on simple,
locally determined rules.
Parametric approach to urbanism addresses the ways in
which associative design systems can control local dynamic
information to effect and adjust larger urban life-processes by
embedding intelligence into the formation, organization and
performance of urban spaces, uses, activities, interfaces,
structures and infrastructures [25]. Built environment is the
biggest and most complex creation of mankind. Its complexity
and vastness comes from a process of continous creation of
urban form not only as a physical objects but as a proces of
creation of spatial, social an cultural relations. Dependance of
form creation process on these configurational aspects of
urban form determines the importance of understanding the
same. By this proces of transformation of preexisting condition
and creation of new order within the physical reality and new
configurations of space social meaning and relevance is added
to an act of construction and form creation. With this
architecture becomes socially relevant and meaningful. With
this system of architectural form becomes the spatio temporal
manifestations of configurational order realised througs
physical elements.
With creation of a basic element of architectural form –
spatial cell the elementary configurationally relation between
inside and outside is created. Through process of addition
more discreet elements are created that generates complex
configurations of physical and spatial structures.
These elements and their spatial relations and configuration
of the system in general are represented through system of
cellular automata (Fig.5).
Fig. 5 Cellular automata model
The condition of each of the cells will be determined as
result of interaction and accumulation of different locally
embedded rules rather than by an exterior, order imposing
centre. In this model use of cellular automata is additionally
justified with spatial and representational similarity between
elements of urban form (buildings, lots, streets, squares and
others) and discrete cells as elements of the model [17].
Furthermore condition of each of the elements of urban form
that is beyond its formal aspect (property rights, legal status
and others) can be represented with binary determined
condition of the system of cells (Fig.6).
Fig. 6 Cellular automata model of development of architectural form
The complexity of the system comes from a locally driven
set of simple rules that induce continuous adaptations and
changes on local level, but with an impact on the overall
condition of the system. It enables us to generate complex and
novel shapes and configurations as a result of a dynamic,
nonlinear and locally driven morphogenetic process (Fig. 7).
Fig. 7 Cellular automata model of development of urban form in
residential area in Skopje
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These new structures are more than a sum of their parts and
are not predetermined or preconceived by any means. They are
a result of a historically embedded process of creation, which
is driven by locally conditioned simple rules and constrains.
To breed new designs of the city form these rules need to be
manipulated and to contain principles of growth [1]. These
rules reflect a genetic code in that they orchestrate the
response of the parameters and elements of the system (lines,
surfaces, objects, cells or even a single attribute determined
entity) to the influence of diverse agents and conditions within
the system, creating an emergent order. The result is surprising
in the way that final shape is a result of a bottom-up emerging
order and is dependent on sequences of random, interrelated
and local interactions.
The digital tools used to model cities with parametric
approach and to generate different urban forms are widely
available as packages that use cellular automata, agent-based
models, associated or generative modeling and other systems
in digital urbanism. These are the tools that give us the
potential to understand, update and improve the process of
creation of cities where non-standard methods coherent with
the nature of the phenomena of city can be conceived to
confront the banality of repetitive, arbitrary and pre-
determined form production on the city scale.
The following case may serve as a quick explanation of how
to use the generative algorithm method in urbanisms.
Task definition: Generate a surface based on the given
topological coordinates and determine the optimal conditions
for the location of the principal thoroughfare (the conditions
are technical: inclination and curvature by means of osculating
circles). Based on the results define areas of different housing
quality (conditions: proximity to thoroughfare, terrain
topology). The urban structure was generated using the
graphical algorithm editor Grasshopper. The first step in the
modeling process involved generating the topological
coordinates (x,y,z) which were used to create a NURBS
geometry of the terrain (Fig. 8).
Fig.8 Surface definition with u,v parametar
The advantage of using the NURBS geometry in
comparison with the mesh geometry lies in the fact that
significantly less data is used and the modification of the
existent geometry is simpler as uv parameters are used. At Fig.
9, NURBS surface is defined with the set of points and uv
value is extracted from the final form.
Fig.9 Space coordinates and uv values of the points
This is possible because spatial coordinates are reduced to
parameters located in the 0-1 domain- uv domain. Note: The z
coordinates of the points are scaled for the purpose of better
visualization of the terrain morphology.
The next step involves generating the horizontal contours.
These contours are obtained as the given surface intersects the
planes running parallel to the xy plane. Depending on the
complexity and intricacy of details in the terrain generated in
the further stages, various horizontal distances between the
contours are also defined by means of parameters. All the
contours are generated as a 3rd-order spline curve (Fig.10).
Fig.10 Parametric definition of intersection plane and results for
two intersection distances
The generated horizontal contours are used to determine the
optimal route location in relation to the position of the selected
coordinates. All coordinates are associated to Rhino geometry
and the proximity to the principal thoroughfare is analyzed,
used to differentiate between different housing quality zones
(Fig. 11 and Fig. 12).
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Fig. 11 Visualization location of urban elements based on housing
quality standards; parametrical and virtual model
Fig. 12 One of the infinite options in generating parametric design
VII. CONCLUSION
In the age of digital parametric non-standard architecture,
mathematics and geometry represent the core of the
architectural design process. It has a central role from the
initial stage of finding form, shaping form, generating form, to
the process of manufacturing architectural elements.
Contemporary computer technology allows the application of a
number of tools for the design, analysis, simulation and
manufacturing of complex architectural forms. In the process
of design, today’s leading architects as well as leading schools
of architecture use different software packages and digital
technologies, thus contributing to the formation of a new
aesthetics of digital architecture. On the one hand, technical
possibilities open up new horizons in architecture, while on the
other, they give rise to new issues related to the disciplines of
mathematics and geometry.
ACKNOWLEDGMENT
This work is supported by the Austrian Science Fond under
grand T440-N13 and COST Action TU0801.
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Faro 2010, in Advances in Visualization, Imaging and Simulation,
2010, pp. 86-92.
[25] Verebes, T, “Experiments in Associative Urbanism” in Architectural
Design, Digital Cities, Ed. Neil Leach, July/August, John Wiley &
Sons, London, 2009.
[26] Vidler, A, “The Third Typolgy”. Alexander R. Cuthbert. Ed.
Designing Cities. Oxford, Blackwell Publishing, 2003.
Milena Stavric,born in Belgrad (1969), BA in
Architecture and Urbanism, (1993), MSci in
Architecture and Urbanism (2000), PhD in
Architecture and Urbanism (2002) at Faculty of
Architecture, University in Belgrada, Serbia. 2006,
PhD nostification at the Graz University of
Technology, Austria
She holds position of Researcher at the Graz
University of Technology, Faculty of Architecture,
Institut of Architecture and Media, Austria. She is
lecturer at the Faculty of Applied Science
Johanneum, Graz, Austria and visiting professor at the Faculty of
Architecture and Civil Engineering in Banja Luka, Bosnia. She is involves in
several scientific researches: Austria Scientific Fond (WFW), “Non-standard
architecture using ornaments and plane elements”(2009-2012) and
„Geometric Processing in Architectural Education“(2010-2013). She had a
scholarship from BMWK (Austrian Federal Ministry for Science and
Research) for projects: “Comparative Analysis of Education of technical
Students in Field of Geometry at TU Graz and University of Belgrade”( 2003)
and Generation of Surfaces of Higher Orders in CAD-systems and its
Applications in Engineering Practice” (2004) - Mach Grand Grant.
Milena Stavric is active participant of COST TU0801 Action: Semantic
Enrichment of 3D City Models for Sustainable Development and she has
participated with her work at several scientific conferences (Bremen, Sydney,
Taipei, Montreal, München, Dresden, Zürich, Chaing Mai, Dresden, Vienna,
Faro…).
Ognen Marina, born in Skopje (1972). BA in
Architecture and Urbanism, (1997), MSci in
Architecture and Urbanism (2006), PhD in
Architecture and Urbanism (2010) at Faculty of
Architecture University “Ss. Cyril and
Methodius”-Skopje, Republic of Macedonia.
He holds the position of Assistant Professor at
Faculty of Architecture, University “Ss. Cyril and
Methodius”-Skopje, Republic of Macedonia.
Faculty Research Associate at College of
Architectural and Environmental Design at
Arizona State University, Arizona, USA, for a period of 2002-2003.
Dr. Ognen Marina is a memeber of AAM-EAAE (1997) and ENHR (2010)
and has participate with his work at several scientific conferences and
meetings ENHR2010 in Istanbul, IABSE 2010 in Venice, PBE 2010 in Brno,
WSEAS 2010 in Faro and others. He is active participant of COST TU0801
Action: Semantic Enrichment of 3D City Models for Sustainable
Development. His core interest is in development of dynamic models of
developemt of urban form, use of digital tools for better understanding the
urban phenomena and interdependance of process, form and materials in
architectural design.
Ognen Marina, besides its research work is active in architectural design and
competitions and has received many awards in the field of architectural
design. He has participated in architectural exhibitions at BIMAS (2000-
2008) Skopje, Belgrade and at the XXII UIA Conference of Architecture in
Istanbul.
Issue 1, Volume 5, 2011
16
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND INFORMATICS