USE OF VORONOI DIAGRAM IN AN ARCHITECTURE DESIGN OPTIMIZATION

USE OF VORONOI DIAGRAM IN AN
ARCHITECTURE DESIGN OPTIMIZATION
A DISSERTATION REPORT
Submitted by
K.KEDHEESWARAN
In partial fulfilment for the award of the degree
Of
MASTER OF ARCHITECTURE IN
GENERAL ARCHITECTURE
RVS SCHOOL OF ARCHITECTURE, COIMBATORE
Affiliated to
ANNA UNIVERSITY: CHENNAI 600 025
DECEMBER 2015

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ANNA UNIVERSITY: CHENNAI 600 025
BONAFIDE CERTIFICATE
Certified that this Report titled “USE OF VORONOI DIAGRAM IN AN
ARCHITECTURE DESIGN OPTIMIZATION” is the bonafide work of
K.KEDHEESWARAN (Roll No - 714714566005) to the RVS School of
Architecture, Coimbatore, Affiliated to Anna University, Chennai who has carried
out the research under my supervision.. Certified further that to the best of my
knowledge the work reported herein does not form part of any other
dissertation on the basis of which a degree or award was conferred on an
earlier occasion on this or any other candidate.
INTERNAL EXAMINER EXTERNAL
EXAMINER
HEAD OF THE DEPARTMENT

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DECLARATION
“Declare that this dissertation has not been previously accepted in substance for
any degree and is not being concurrently submitted in candidature for any degree. I
state that this dissertation is the result of my own independent investigation/ work,
except where otherwise stated. I hereby give consent for my dissertation, if
accepted, to be available for photocopying and understand that any reference to or
quotation from my thesis will receive an acknowledgement”.
……………………………………
K.KEDHEESWARAN
DATE…………………………..

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ABSTRACT
This Dissertation is to find how the voronoi diagram application is used in
optimization of design parametrics.To explore how the voronoi is taken in an
account of process of building a design and the topological parametric used for an
optimization to the different array.
“Buildings can be considered as a flow of bodies and information through space,
over time”. - FAULDERS STUDIO
The constraints/parametric synthesis in this research was facade and spatial
planning problem and evolution through voronoi daigrams.The facade and planning
morphology context through a specific study, i.e. from micro-level to a broad level
by individual building and to urban level With Voronoi diagram rule based system
one can easily determine proximity matrix.

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ACKNOWLEGEMENT
The completion of this Dissertation has been made possible because of the
involvement of many individuals. Whatever I am and whatever I will be in future is
because of love, sacrifice a---------------------------------------------------------------------
-------nd goodwill from my family. My parents have always been a great source of
inspiration for me. Words are just not enough to express my gratitude to my parents
and my family. I thank them for always being supportive.
A word of appreciation also goes to my friends and faculty who have supported
me in this endeavour and to all whose names I couldn’t mention here.

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“I DEDICATE THIS DISSERTATION TO MY PARENTS, WHO GAVE ME AN
APPRECIATION OF LEARNING AND TAUGHT ME THE VALUE OF
PERSEVERANCE AND RESOLVE. I ALSO DEDICATE THIS TO MY BELOVED
ONES AND ALL THE PEOPLE WHO SUPPORTED ME IN THIS JOURNEY.”

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TABLE OF CONTENTS
ABSTRACT.................................................................................................................iii
LIST OF FIGURE.....................................................................................................viii
LIST OF TABLES ....................................................................................................... x
AIM & MOTIVATION .............................................................................................. xi
SCOPE.......................................................................................................................... xi
FRAMING OF RESEARCH QUESTIONS ????..................................................xii
1. What is Voronai Diagram? ..................................................................... xii
2. How complex aesthetics are involved through voronoi architecture? ... xii
3. How these design process and ideology will contribute a designer and
a community? ............................................................................................................... xii
4. How the parametric play a domain to a design development and image
building process? ......................................................................................................... xii
5. Does it have compatibility to a building and in urban development for
sustainable growth vs. issues? ..................................................................................... xii
METHOLOGY..........................................................................................................xiii
CHAPTER 1 - INTRODUCTION............................................................................ 14
1.1 - The primary concept of voronoi diagrams ........................................ 14
1.2 - Voronoi diagram components............................................................ 16
CHAPTER 2 - VORONOI DIAGRAMS NATURE .............................................. 17
2.1 - Parallelism of Voronoi with F.L Wright‟s Usonian house................ 20
2.2 - Dimensional study of voronoi............................................................ 21
2.3 - From two-dimensional to three-dimensional .................................... 22
2.4 - Voroni daigram has space fillers....................................................... 23
CHAPTER 3 - CASE STUDY.................................................................................. 24
3.1 - Voroni daigram has a façade modulators/morphogenis ................... 24
3.1.1 - Tulum museum, Mexico. .......................................................... 25

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3.1.2 - Net lab...................................................................................... 25
3.1.3 - Airspace tokyo designed by faulders studio ............................. 26
3.1.3.1 - Design Approach ....................................................... 26
3.1.3.2 - Overlapping thorough voronoi ................................... 27
3.1.4 - Alibaba headquarters, China................................................... 28
3.2 -LANDSCAPE ECOLOGY .............................................................. 29
3.2.1 - Overview.................................................................................. 29
3.2.2 - Location-case study .................................................................. 30
3.2.3 - METHODOLOGY AND CASE STUDY MODEL..................... 30
3.2.3.1 - The first parametric design........................................ 31
3.2.3.2 - Second parametric model ......................................... 31
3.2.3.3 - Voronoi parametric in waterfront ............................ 32
3.2.3.4.Green space parametric............................................... 32
3.3 - Kaohsiung national centre for the performing arts, Taiwan............. 33
3.4 - Potentiality of voronoi diagram in urban design ............................. 35
3.4.1 -Magok waterfront city ............................................................... 35
3.4.1.1 -Digital parametric process of the project................... 36
3.4.1.2 - The process evolved in the waterfornt development.. 39
3.5 -VORONOI AS STRUCTURAL OPTIMISER .............................. 41
3.5.1 - The National Swimming Centre -Water Cube, Beijing, china.. 41
3.5.2 - Process of design generation.................................................... 42
3.5.3 - Inference ................................................................................... 42
3.6 - VORONOI AS URBAN MORPHOLOGY .................................. 43
3.6.1 - Voronoi skyscraper-Geoffrey Braiman, David Beil ,U S.
3.6.2 - Theme......................................................................................... 44
3.6.3 - Ways and Mean.......................................................................... 45
3.7 - PARAMETRIC URBANISM THROUGH VORONOI .............. 46
3.7.1 - MVRDV Venture – Architect.Denes. ........................................ 47

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3.7.2 - Design process.......................................................................... 50
CHAPTER 4 - INFERENCE .................................................................................... 58
CHAPTER 5 - CONCLUSION................................................................................. 59
BIBLIOGRAPHY ...................................................................................................... 60
LIST OF FIGURE
Figure 1 : Step-1, Defining the finite points as reference........................................................15
Figure 2 : Step-2, joining finite points.....................................................................................15
Figure 3 : Step-3, Bisection of line ..........................................................................................15
Figure 4 : Step-4, Bisection each to create voronoi ................................................................16
Figure 5 : Step-5, Further division to create voronoi..............................................................16
Figure 6: Final voronoi pattern...............................................................................................16
Figure 7: Elements of voronoi .................................................................................................17
Figure 8 : Illustrate of space evolution....................................................................................18
Figure 9 : Different broad application of voronoi...................................................................19
Figure 10 : Layout of Usonian house ......................................................................................20
Figure 11: Fragmentation of layout ......................................................................................20
Figure 12 : Illustration to Voronoi ..........................................................................................21
Figure 13 : Natural forms as a Voronoi diagram....................................................................22
Figure 14: Different voronoi diagram by variation of points..................................................22
Figure 15 : Marc Newson‟s Voronoi Shelf ..............................................................................23
Figure 16: Gourdoukis algorithmic body project....................................................................24
Figure 17: Space filler for........................................................................................................24
Figure 18 : Tulum museum ......................................................................................................25
Figure 19 : Conceptual view of Net Lab..................................................................................26
Figure 20 :Effect through punctured voronoi overlap.............................................................26
Figure 21: The façade randomness as whole ..........................................................................27
Figure 22 : The façade layering through different to form a building cubicle........................28

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Figure 23 : Alibaba headquarters-View, Elevation &Site Block model..................................29
Figure 24 : The topology of Pataua coastal settlement...........................................................30
Figure 25 : Different land use mapping for waterfront development......................................31
Figure 26 : Generation land use through points ie through site parametrics.........................31
Figure 27 : Parametrics of voronoi used for visual opportunity.............................................32
Figure 28 : Green and blue space development ......................................................................33
Figure 29 : Topologial force, Kaohsiung national centre for the performing arts,
Taiwan......................................................................................................................................34
Figure 30 : Right: the in Layout. Left: the stages of generating the layout starting
from the points to the final form...............................................................................................34
Figure 31 : Visual generated from the form ............................................................................35
Figure 32 : View.......................................................................................................................35
Figure 33 : Conceptual view of Waterfront Magok.................................................................36
Figure 34 : Over design process for Magok waterfront city ...................................................38
Figure 35 : The different phases of voronoi optimization for water surface
development..............................................................................................................................39
Figure 36 : The Site for Waterfront developement ..................................................................40
Figure 37 : Final master plan for Magok waterfront ..............................................................40
Figure 38 : Illustration from Weaire-Phelan structure to Voronoi structure .........................41
Figure 39 : Voronoi form developed in rhino to water cube...................................................41
Figure 40 : Final out of Water-cube........................................................................................42
Figure 41 : Voronoi Skyscraper...............................................................................................43
Figure 42 : structure of Daigrid in skyscraper........................................................................43
Figure 43 : Design development .............................................................................................44
Figure 44 : Plan typology ........................................................................................................45
Figure 45 : Voronoi particle development in section ..............................................................45
Figure 46 : Voronoi in Skyscraper...........................................................................................46

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Figure 47 : Form and Space that is derived from the interaction beaten urban
conditions. Zaha Hadid............................................................................................................46
Figure 48 : Form and space derived by Schumacher through Voronoi..................................47
Figure 49 : Urban form & topography of Switzerland City ....................................................47
Figure 50 :Patterns created through Voronoi for urban design of Switzerland City..............48
Figure 51 : A layering system in order to understand complex relationships.........................49
Figure 52 : Proposed final Voronoi assimilated Design for Switzerland city by
Ar.Denes...................................................................................................................................49
Figure 53 : Process of Design developement ..........................................................................50
LIST OF TABLES
Table 1 : Façade & spatial planning-core analysis process ................... 51

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AIM & MOTIVATION
 My hypothesis of subject is to find how and the factors of voronoi is used in
the design optimization.
 In depth on functional the various analysis and method to in applied nature
to space planning parameters. For example for comparing areas covered by
different space planning, building morphogenesis etc.
 With Voronoi diagram rule based system one can easily determine proximity
matrix from micro to macro level planning (broad level i.e. GIS) by voronoi
diagrams
 Sustainable approaches in urban and landscape planning issues
 To break the conventional design process in contrast.
SCOPE
 Way to subdivide/organize space, based on proximity/closest neighbour.
 Expansion in three dimensions organizes a constructive expansion toward
infinity in all directions without any gaps.
 To create clear proximity matrix in urban scape zoning and also for
landscape ecology for sustainable development as in MAGOK
WATERFRONT in Korea.
 Voronoi diagram can be used as plugin with other program to have better
design solution for structural optimization, form, shape and urban design.
 It used as tool used as space filling.
 It used as surface modulator to create an interest and an image in a building
for local attractors.
 It is a self-organization parametric which goes with a rule based system
which is parametric in nature.
 Diversity of design alternatives in a balanced hierarchy system.

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FRAMING OF RESEARCH QUESTIONS????
1. What is Voronai Diagram?
2. How complex aesthetics are involved through voronoi
architecture?
3. How these design process and ideology will contribute a designer
and a community?
4. How the parametric play a domain to a design development and
image building process?
5. Does it have compatibility to a building and in urban
development for sustainable growth vs. issues?

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METHOLOGY
UNDERSTANDING THE CONCEPT
&APPROACH BEHIND THE VORONOI
DIAGRAMS BY STUDY BASED ON
NET, ARCHITECTURAL JOURNALS
PARAMETER BEHIND THE DESIGN
PROBLEM AND SOLUTION
THROUGH VORONOI DIAGRAM IN
BUILDINGS
FRAMING OF PARAMETER
WHICH INTERCONNECTS TO
THE DESIGN AND APPROACH
TOWARD THEM.
SYNTHESIS OF
INFORMATION
CONCLUSION

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CHAPTER 1 - INTRODUCTION
Nowadays architects, more often than it was before, look at the branches of
science like mathematics, biology or physics for inspiration and for tips on how to
solve problems they are trying to tackle. The idea taken from mathematics and
applied to architecture design. To be more specific – about the Voronoi diagram.
Voronoi diagram is being used so often by architects because it produces very
organic looking patterns.
The primary concept of Voronoi Diagrams: “The Given a set of a finite
number of distinct points in the 2-D Euclidean space, a Voronoi diagram of
the point set is a collection of regions that divide up the plane, and all
locations in one region (exception the region boundary) are closer to the
corresponding point than to any other point”.
1.1 - THE PRIMARY CONCEPT OF VORONOI DIAGRAMS
A Voronoi diagram of the point set is a collection of regions that divide up the
plane, and all locations in one region (exception the region boundary) are closer to
the corresponding point than to any other point”.
Voronoi diagram using any CAD software or pen and paper. For start you need
set of points on the plain.
Step1: is to draw a line connecting adjacent points.
Step 2: is to draw a perpendicular line to the one you just drew in the midpoint of it.
Step 3: is to connect lines, drawn in the second step, into a network.

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Figure 1: Step-1, defining the finite points as reference
Figure 2: Step-2, joining finite points
Figure 3: Step-3, Bisection of line

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Figure 4: Step-4, Bisection each to create voronoi
Figure 5 : Step-5, Further division to create voronoi
Figure 6: Final voronoi pattern
VORONOI DIAGRAM COMPONENTS

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A simple voronoi diagram has the following elements.
Voronoi diagram of a point is just made of the same point.
 Voronoi Vertex
 Voronoi Cell,
 Voronoi Space,
 Voronoi Foam.
Figure 7: Elements of voronoi
CHAPTER 2 - VORONOI DIAGRAMS NATURE
WAY FINDING-NAVIGATION
1. The Voronoi diagram was implemented as the background navigation,
especially way finding mainly in GIS.
2. The shortest way/ proximities as physical displacement.
OCCUPATION ANALYSIS
1. The centre of Voronoi cells becomes the search agents that receive information
of the surrounded cells during the searching process.
2. When the information from the surrounded cells fits their inherent
requirements, the agent holds the space.

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SPACE EVOLUTION
1. The Voronoi diagram activates a process of generating and evolving spatial
forms interacting with all entities of a system, the self-organization.
2. In the context of the architecture, it would be referred to the co-adaption which
generates a space out of complex relationships and needs among disorganized Sub-
systems of the environment
Figure 8 : Illustrate of space evolution

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Figure 9: Different broad application of voronoi

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2.1 - PARALLELISM OF VORONOI WITH F.L WRIGHT’S
USONIAN HOUSE
Charles E. Aguar and Bernard Aguar found this drawing of layout plan for
Usonian II housing estate by Frank Lloyd Wright.
Method used here is not exactly a Voronoi diagram but it is very similar to it.
Drawing below should give an idea how Voronoi diagram could be used for
space planning and what sort of design it can produce.
Figure 10 : Layout of Usonian house
Figure 11: Fragmentation of layout

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Figure 12 : Illustration to Voronoi
2.2 - DIMENSIONAL STUDY OF VORONOI
Voronoi tiles have been created by a series of points.
A cellular pattern that each of these cells includes the space surrounding the
point. Place of the rest of the shapes created with these pattern fits into a close
system. They form a collection of shapes that look like squares, honeycombs,
crystals or boulders.
The personal space of each point is separated by a neutral zone lines from its
neighbourhood.
These lines are equidistant from both the surrounding area i.e. optimum proximity
matrix

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ONE-DIMENSIONAL
Figure 13 : Natural forms as a Voronoi diagram
 Voronoi diagrams include patterns called Dirichlet Tessellation.
 These irregular tessellations on a plane occur spontaneously in nature at
every scale.
 They are used in the studies with space making problems such as computer
science, growth of crystalline structure, biology, anthropology and etc.
2.3 - FROM TWO-DIMENSIONAL TO THREE-DIMENSIONAL
Figure 14: Different voronoi diagram by variation of points

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The minimal enclosure system of these bubbles and cells shows that tilings are a
simple system, rather their thickness in three dimensions expands constructive
toward infinity without any gaps.
Geometry and topology of polygonal cells, such as size, proportion and number of
edges is sensitive to the slightest change in position of each point anywhere in the
neighbourhood.
The relationship between the cell nucleus and the resulting geometry is complex
in nature.
2.4 - VORONI DAIGRAM HAS SPACE FILLERS
The Voronoi diagram has become a ubiquitous motif in recent generative
architecture and design.
Voronoi diagram is a way of dividing up space into regions so that, for a given set
of sites within that space, each region contains all points in the space that are closer
to one site than any other.
The attributes of the Voronoi as a model in this way. It is multiplicities, but in a
different way to the gridline uniformity of the foam models.
The variability of the Voronoi can be phrased another way, as arbitrariness; In
other words, that there is no inherent reason for a given site to be where it is. There
is nothing internal to the model that can generate that differentiation
Figure 15 : Marc Newson’s Voronoi Shelf

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The visual signature carries an association of organic logic: but in formal fact the
cell sites are arbitrary, that is to say, designed. There is no necessary relation of one
to another it can be unique...
VORONI DAIGRAM HAS
SPACE FILLERS
Figure 16: Gourdoukis algorithmic body
project
In Gourdoukis Algorithmic
Body project, the locations of the
voronoi sites are specified by a
second generative system, a
cellular automaton; Here the Voronoi acts as a geometric filter, interpreting and
interpolating one set of spatial data into another.
Figure 17: Space filler for geometric
CHAPTER 3 - CASE STUDY
3.1-VORONI DAIGRAM HAS A FAÇADE MODULATORS/MORPHOGENIS
1. Tulum museum, Mexico.
2. Net lab

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3.Airspace Tokyo designed by “Faulders studio”
3.1.1. TULUM MUSEUM, MEXICO.
Museum is design by Andrew Kudless for a competition. This Archaeological
museum is outside of devastation of Mayan in Cancun peninsula.
Researchers in this project used Voronoi system for organizing cells (Spaces).
The walls and roof of the museum is formed from a three dimensional Voronoi
tiling. That examines the nature of the structures through holes instead of mass.
Structure is directly related to the Tulum’s site rock walls. This structure can be
considered a fulfilment of the empty spaces between separate rocks.
Thus, structure of the museum refers to the available tectonic and at the same time
it is lightweight
Figure 18 : Tulum museum
3.1.2. NET LAB:
The project is 16 months research of a person called G Nome. The purpose of this
research is the use of parametric algorithms, in forming of cell spaces in relation to
certain criteria which express different social systems, scale and needs of the users.
This design includes a set of computational methods based on Voronoi algorithms
summarized in a plugin created during the investigation.
This plugin gives access to an iterative process of feedback, adjustment and
optimization of the design. In addition, the project by integrating designs, analysis
as a formal process, provides a redefinition of the role of the architect with the use
of algorithms in real terms…

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Project explores the redefinition of the architect’s role by integrating design,
analysis, and production manufacturing as a whole formal process by applying
algorithms in real contexts.
Figure 19 : Conceptual view of Net Lab
3.1.3 - AIRSPACE TOKYO DESIGNED BY FAULDERS STUDIO
3.1.3.1 - Design Approach
Digitally-generated overlapping voronoi pattern that represents the biomorphic
cells of vegetation, suits our preferred digital technique exploration.
At night, the interior lightings passing through the perforations of overlapping
voronoi make a mysterious feeling as it seems to move as we move…
Figure 20 :Effect through punctured voronoi overlap

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3.1.3.2 - OVERLAPPING THOROUGH VORONOI:
Taking the concepts from our matrices exploration, we came up with a
technique to produce an overlapping voronoi by generating random points and
outcome is similar to that of our case study, Airspace Tokyo.
Figure 21: The façade randomness as whole
The 2-dimesional facades into a cube would be the easiest approach to achieve
“the stereoscopic sense of voronoi brought by clubbing overlaps and randomness as
a whole”.
Playing with light, the façades of the cube create shadows that overlapped each
other and further fragmenting the voronoi.

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Figure 22 :The façade layering through different to form a building cubicle
“Buildings can be considered as a flow of bodies and information through space,
over time”.
The programmatic elements were modelled as attractors on the site. Visitors,
information and exchanges were modelled as particles.
Once the particles attracted, they started forming varying degrees of
concentration. A halo of particles was floating over the site, suggesting an eventual
architectural space.”
3.1.4 - ALIBABA HEADQUARTERS, CHINA.
Alibaba is China’s leading e-commerce company and operates the world’s largest
online marketplaces for both international and domestic China trade.
The dynamic campus accommodates approximately 9,000 Alibaba employees and
has been designed to reflect the interconnection, diversity and vitality of the
company.

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Figure 23 :Alibaba headquarters-View, Elevation &Site Block model
3.2 - LANDSCAPE ECOLOGY
3.2.1 - OVERVIEW
The voronoi algorithm used urban coastal development.
Voronoi parametric is used for mapping/surveying through GIS for finding
various issues as topology growth pattern and the flood plain etc.
There have been many interpretations of the voronoi diagram across architecture,
urban design and landscape architecture. One particular example is a waterfront
development named the “Majok Project”.

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Figure 24 : The topology of Pataua coastal settlement
Urban design is the profession of shaping the physical setting for life in cities,
towns and communities;
In recent years, landscape architecture becoming more involved, urban design has
become a diverse and multi-disciplinary profession.
The design process in general terms is seen by a lot of professions as – a brief, a
need, a demand - a solution.
3.2.2 -LOCATION-CASE STUDY
Coastal settlement to the west of Whangarei, New Zealand - Pataua North figure:
24.
3.2.3 - METHODOLOGY AND CASE STUDY MODEL
Pataua North is about a 31km drive from Whangarei, and there are just over 100
houses. These houses are made up of holiday beaches and some that have
permanent residents
GIS data the site was mapped, including contours, hydrology, land-use, slope,
aspect, viewpoints and built form.

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Mapping gave an insight into the spatial characteristic structure of Pataua, which
helped determine site constraints and opportunities.
Figure 25 : Different land use mapping for waterfront development
3.2.3.1 - THE FIRST PARAMETRIC DESIGN.
Experiment followed the mapping and analysis.
The goal was to explore variations of road layouts, generated using Voronoi
diagram around points of interest.
The points included flood plains, road intersections, knolls, and landscape
features…
Figure 26 :Generation land use through points i.e. through site parametric
3.2.3.2 -SECOND PARAMETRIC MODEL

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Then created for various parts of the design using attract and repel notions to
create different patterns.
All the models were incorporated together and a series of generations were
created. Keeping record of the results enabled reflection and evaluation of the
designs.
3.2.3.3 -. VORONOI PARAMETRIC IN WATERFRONT
The waterfront is a key component of Pataua, with one of the main attractions
being the surf beach. Several points were located along the beach representing
coastal features.
One of the points was a knoll and another was a depression in the sand dunes,
which opened up a view to the beach. This depression opened up the opportunity to
locate a green corridor from the floodplain to the beach, creating a visual
connection. These points were then used to influence the geometry of the road.
Figure 27 : Parametric of voronoi used for visual opportunity
3.2.3.4 - GREEN SPACE PARAMETRIC
The green space design definition a visibility rule was added. This meant that the
road (shown in red in figure could deform only if the deformation increases the
visibility of the green space (in green).

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Figure 28 : Green and blue space development
INFERENCE
The parametric models developed collectively proved how the interdependencies
between various elements of the settlements fabric (road network, open spaces,
plot sizes, etc.) can be explored and evaluated in order to overcome the challenges
in coastal settlements’ growth for sustainable communities.
3.3 -KAOHSIUNG NATIONAL CENTRE FOR THE PERFORMING ARTS,
TAIWAN
 The building was designed by Zaha Hadid in a competition.
 She used Voronoi diagram to analyse the relationship between the
environment and site data.
Visitors’ access points are controlled using data on the site such as trees,
monuments and borders-Topological & Forces
The area around points, which is created by the analysis of the relationship
between space and the site, is connected to the main flow of human traffic, so that it
becomes a tool for space traffic control.
„Deformation of visual data and canopies, roofs and facades designs is derived
from the Voronoi diagram‟

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Figure 29 : Topological force, Kaohsiung national centre for the performing arts, Taiwan
Figure 30 : Right: the in Layout. Left: the stages of generating the layout starting from the
points to the final form.

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Figure 31: Visual generated from the form
 In this project, the architect distributed points in the main envelope to create
the main form.
 The overall form of the building itself seems to grow out of the voronoi
patterned landscape, merging at the top, to form a canopy that shades the
public plaza below.
 The main form was created by the Nurbs geometry then it was divided by the
voronoi algorithm
Figure 32: View
3.4 - POTENTIALITY OF VORONOI DIAGRAM IN URBAN DESIGN
3.4.1 -MAGOK WATERFRONT CITY
The project which uses the Voronoi system for dividing the given district of Seoul
city
The main concept of this project, the International Design Competition for the
Magok Waterfront City, is to merge the flow of the landscape with the logic of the
Voronoi diagram.

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The designer becomes increasingly interested in the efficient use of ecosystem
and water flow.
Using Voronoi diagram, this problem can be solved by breaking the physical
limits of the urban grid. Moreover, it accepts the numbers of information and needs
from the architectural environment.
Figure 33 :Conceptual view of Waterfront Magok
Process of overlapping preliminary design with voronoi diagram
Space should accept various activities and events reflecting the concept. And
through the analysis, we reach the conclusion that we should make a reservoir space
for the safe city in case it gets a flood. Therefore, we make a condition based on the
data from we investigate, and extract two main concerns from our analysis; The
relationship and the volume of spaces
3.4.1.1 - DIGITAL PARAMETRIC PROCESS OF THE PROJECT
The process which applies the Voronoi diagram for dynamic cartography, and
modifies it in order to fit our project’s concept. In addition, we use the Voronoi
diagram plugin offered as Rhino script….
VORONOI DIAGRAM Fragmentation of land

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FIRST STEP:
The project is to set up the axis of the site drawn from the parameter of landscape,
water, and traffic in order to create the grids of the site. These grids are optimized
by offsetting by from the axis and are used as the limitation of the block size.
The intersections between these grids and the preliminary sector design, and are
set in array i.e. finite points according to the flow of the whole space.

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Figure 34 : Over design process for Magok waterfront city

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3.4.1.2 -THE PROCESS EVOLVED IN THE WATERFORNT DEVELOPMENT
Figure 35 : The different phases of voronoi optimization for water surface development.
Attractors and Repellors1
The segments cannot be eliminated, but can only be expanded or shrunk, since
collision detection and topology maintenance are based on the primary input points
Project is directly editable due to the parametric system of the geometry creating
system.
1
Attractors: Zones of compatible nature are termed as Attractors…
Repellors: Zones of conflicting types are termed as Repellors.

P a g e | 40
Figure 36 :The Site for Waterfront development
Figure 37 :Final master plan for Magok waterfront

P a g e | 41
3.5 - VORONOI AS STRUCTURAL OPTIMISER:
3.5.1 - The National Swimming Centre -Water Cube, Beijing, china
The internal steel frame of The National Swimming Centre „Water Cube is based
on the unique geometry of water-soap bubbles known as the Weaire-Phelan
structure.
Figure 38 :Illustration from Weaire-Phelan structure to Voronoi structure
Building design that employs polyhedral derived from so-called Voronoi
cells.
Figure 39 : Voronoi form developed in rhino to water cube

P a g e | 42
3.5.2 -PROCESS OF DESIGN GENERATION
STEP 1:
Establishment- using guiding points.
STEP 2:
Exploration- using dynamic findings.
STEP 3:
Refinement, using repelling/attracting fields and particles. These three stages
process produced two irregular, topologically cylindrical surfaces and were
continued by two more stages
STEP 4:
Generated voronoi cells around these points.
STEP 5:
Created cell-walls and cell-skins.
STEP 6:
Prepared the cell components for robotic i.e. CNC manufacturing.
Figure 40 : Final out of Water-cube
3.5.3 -INFERENCE:
 The structure commutation and less material consumption are proved.
 The pattern of voronoi structure creates a surface modulator to
aesthetical image to building (water cube).

P a g e | 43
3.6 -VORONOI AS URBAN MORPHOLOGY
3.6.1 - VORONOI SKYSCRAPER-Geoffrey Braiman, David Beil ,U S.
Figure 41 :Voronoi Skyscraper
This is the typical example of tall building architecture structure always use
Diagrid which moment resistant frame.
Similar Diagrid pattern is developed by use of Voronoi pattern
Figure 42 : structure of Daigrid in skyscraper
So rather than conforming to column and slab construction techniques a skyscraper
based on nature results in a streamlined structure that:
1. Minimizes materials.

P a g e | 44
2. Accommodates variable programs.
3.6.2 -THEME
 Introverted style stacked of world.
 The unending array of floor slabs.
 The city of the future is a multivalent hybrid reliant on strong infrastructure...
 The most common solution to densification is to stack volumes, insert a
circulation core.
 This approach repeats the ineptitude of the street grid by rotating its vector
perpendicular and extruding the form.
 The resultant tower to grow and change over time. In order to adapt, we must
look for alternative organizing strategies to accommodate our changing
needs which tangible in nature
Figure 43 : Design development

P a g e | 45
Figure 44 : Plan typology
Figure 45 : Voronoi particle development in section
3.6.3 -WAYS AND MEAN
1. Created - rectangular box
2. Generate/import point cloud – random
points or import data cloud from structural
analysis
3. Generate voronoi cells from point cloud.
4. Cells for subtraction/Addition ……

P a g e | 46
Figure 46 : Voronoi in Skyscraper
3.7 - PARAMETRIC URBANISM THROUGH VORONOI
Parametric Urbanism can understand “the dynamic and real time relationships
within mass amounts of information found in quantifiable data and social issues
through the use of parameters, which can then be used to create reflexive pattern
and form that give architects a much more knowledgeable, although more
complicated, starting point to design from resulting in the slow morph of sterile
cities into flexible living environments.”
Figure 47 : Form and Space that is derived from the interaction beaten urban conditions. Zaha Hadid
Traffic, in efficient living space, environmental issues, poverty, crime, and poor
use of networking are some of the major problems seen in today’s sterile cities.

P a g e | 47
Many have tried to solve these issues independently because the human mind
cannot comprehend the amount of information needed to correct multiple large-
scale problems.
Figure 48 :Form and space derived by Schumacher through Voronoi.
“Parametric Urbanism” through which he shows some interesting progress through
his and Zaha Hadid’s entry for the Urban Istanbul Competition.
Schumacher has taken a stance that says,
“Everything must resonate with everything else to understand parametric
urbanism we need to locate the beginning...”
3.7.1 - MVRDV Venture – Architect.Denes.
Intelligence of the urbanism can be found in two forms:
1. Practical knowledge (quantitative)
2. “Military type” knowledge (qualitative).
Switzerland‟s city design- MVRDV
Figure 49 : Urban form & topography of Switzerland City

P a g e | 48
Swiss Cross Urban Study MVRDV says traffic is the major issue of Switzerland’s
city design. In order to show” the effects of increased or decreased traffic flow on
city function”, MVRDV developed “sliders
2
” that control the level of traffic flow
through the city.
Matei Denes, a senior architect at Mahai Radu Architects, performed a complete
urban design using parametric that begins where MVRDV left off.
The site of Denes’ intervention is Sao Paulo Brazil. Denes’ study is so
informative because it is much more specific than anything MVRDV focused on.
Figure 50 :Patterns created through Voronoi for urban design of Switzerland City
“Denes” first selects a type of pattern known as a “Voronoi”.
 The voronoi pattern is reflexive in nature because it is based off of a system
of points that are governed by parameters- Space-Filling.
2
Quantitative mechanisms that have the capacity to transform numeric values into quantities.

P a g e | 49
 If points are added, moved, or altered in any way, the voronoi pattern adjusts
itself to the new layout-Self-organising
 What is so appealing about the voronoi is that its primary objective is the
most efficient use of space and distance from one point to any other point in
the field. space fill-Minimum proximity Intervention
Figure 51 : A layering system in order to understand complex relationships
Denes then locks in three specific parameters to inform the voronoi: “traffic flow,
program, and landscape”
Each parameter is then broken down into its component parts. For example,
program is broken down into housing, commerce, and parks.
Figure 52 : Proposed final Voronoi assimilated Design for Switzerland city by Ar.Denes

P a g e | 50
3.7.2 -DESIGN PROCESS
1. Fixing of problem/parameter-points in voronoi
2. Development of the point
3. Customization through voronoi diagram
4. Assimilation
Figure 53 : Process of Design development

P a g e | 51
Table 1 :FAÇADE & SPATIAL PLANNING-CORE ANALYSIS PROCESS

P a g e | 52
PARAMETER FAÇADE SPATIAL PLANNING
PROJECT
MICRO LEVEL MACRO LEVEL
Airspace Tokyo
designed by
faulders studio
Voronoi
skyscraper-geoffrey
braiman,david beil
, US
The National
Swimming Centre
-Water Cube,
Beijing ,China
Kaohsiung national
centre for the
performing arts,
Taiwan-Zaha hadid
Magok Waterfront
City, Seoul, Korea.
Switzerland‟s city
design
MORPHISM
LOGICS
SURFACE MODULATORS
SPACE EVOLUTION/SPACE
FILLERS
PARAMETRIC
CONCEPT
USED
Overlapping of skin
by generating voronoi
random points
Customisation
Topological &
Forces w.r.t the
relationship between
the environment and
site data.
Refinement, using
repelling/attracting
fields Topological
cylindrical surfaces
Using data on the site
such as trees,
monuments and borders
Topological parameter
The intersections
between these grids
and the preliminary
sector design, and are
set in array i.e. finite
points
Reflexive in nature
because it is based off
of a system of voronoi
points that are
governed by
parameters

P a g e | 53
PROJECT
Airspace Tokyo
designed by
faulders studio
Voronoi
skyscraper-geoffrey
braiman,david beil
, US
The National
Swimming Centre
-Water Cube,
Beijing ,China
Kaohsiung national
centre for the
performing arts,
Taiwan-Zaha hadid
Magok Waterfront
City,Seoul,Korea
design
PROCESS
1. The 2-dimesional
facades into a cube
would be the easiest
approach to achieve
the stereoscopic sense
of voronoi brought by
clubbing overlaps and
randomness as a
whole.
2.Once the particles
attracted, they started
forming varying
degrees of
concentration
3. A halo of particles
was floating over the
site, suggesting an
eventual architectural
space.”
1. Created -
rectangular box...
2.Generate/import
point cloud –
random points or
import data cloud
from structural
analysis
3. Generate voronoi
cells from point
cloud.
4.cells for
subtraction/Addition
1. Establishment
using guiding points.
2 Exploration- using
dynamic findings
3. Refinement
, using
repelling/attracting
fields and particles
4.These three stages
process produced
two irregular,
topologically
cylindrical surfaces
and were continued
by two more stages
The area around points,
which is created by the
analysis of the
relationship between
space and the site, is
connected to the main
flow of human traffic,
so that it becomes a tool
for space traffic control.
2.Deformation of visual
data and canopies,
roofs and facades
designs is derived from
the Voronoi diagram
1. Location of cell by
fixing finite point for
initializing voronoi.
2. Mapping of water
flux gradient.
3. findings of water
flux gradient
4.Optimization/custo
mization by
attraction/repulsion
Matrix are developed
5.Final output
6.Water surface
1. Fixing of
problem/parameter-
points in voronoi.
2.Devolpement of the
point
3.Customization
through voronoi
diagram
4.Assimilation

P a g e | 55
PROJECT
Airspace Tokyo
designed by
Faulders studio
Voronoi
skyscraper-geoffrey
braiman,david beil
,US
The National
Swimming Centre -
Water Cube,
Beijing ,China
Kaohsiung national
centre for the
performing arts,
Taiwan-Zaha hadid
Magok
Waterfront City,
Seoul, Korea.
design
OUTPUT/
FINDINGS
1. Playing with light,
the façades of the cube
create shadows that
overlapped each other
and further
fragmenting the
voronoi.
2.Fragmentation is
brought by voronoi
overlapping
3. The voronoi pattern
imitates the trees‟
foliage and is not just
decorative it‟s
functional.
4. The façade
functionally works as
a screen (Jalli‟s) to
provide a sense of
privacy; this has been
achieved by layering
voronoi façade.
1. The vertices of the
Voronoi are of
triangulation in
nature in which base
geometry consume
less area.
2.A scatter of points,
it is based on the
packing of spheres in
the space.
3.The packed
program according to
common requirements
such as adjacencies,
access to sun, views,
etc.
4.Three dimensional
array of irregular
planar polygons using
Voronoi
(cont.)
1. The structure
commutation and less
material
consumption are
proved.
2. The pattern of
voronoi structure
creates a surface
modulator to
aesthetical image to
building (water
cube).
3. Voronoi systems
have a useful and
structural logic
where they can
produce stable yet
irregular structures.
1. The architect
distributed points in the
main envelope to create
the main form.
2. The overall form of
the building itself seems
to grow out of the
voronoi patterned
landscape, merging at
the top, to form a
canopy that shades the
public plaza below.
3. The main form was
created by the Nurbs
geometry then it was
divided by the voronoi
algorithm.
4.Deformation of visual
data and canopies, roofs
and facades designs is
derived from the
Voronoi diagram
1. Project is directly
editable due to the
parametric system
of the geometry
creating system.
2. Matrix are
formed for the
tracing of water i.e.
by attractor/repel.
3. At simple
recursive point
voronoi diagrams
where voronoi
concepts are used to
tessellate space with
respect to a given
set of generator
points.
1. The voronoi pattern is
reflexive in nature
because it is based off of
a system of points that
are governed by
parameters. (Space-
Filling …)
2. If points are added,
moved, or altered in any
way, the voronoi pattern
adjusts itself to the new
layout. (Self-organising)
3. Each parameter is then
broken down into its
component parts. For
example, program is
broken down into
housing, commerce, and
parks.
(cont.)

P a g e | 56
PROJECT
Airspace Tokyo
designed by faulders
studio
Voronoi
skyscraper-geoffrey
braiman,david beil ,
US
The National
Swimming Centre -
Water Cube,
Beijing ,China
Kaohsiung national
centre for the
performing arts,
Taiwan-Zaha hadid
Magok
Waterfront City,
Seoul, Korea.
design
Output/
Findings
skyscraper based on
nature results in a
streamlined structure
A matter of necessity,
natural systems
continually
reorganize until the
best possible solution
is realized
3. What is so appealing
about the voronoi is that
its primary objective is
the most efficient use of
space and distance from
one point to any other
point in the field. (Space
fills).
4. Changes in the
landscape have dramatic
effect on how traffic is
able to flow through the
city if founded out.

P a g e | 58
CHAPTER 4 - INFERENCE
In the following voronoi studies reveals these criteria is observed evidently…
1. In building facade modulation and shading elements-exterior morphism
2. Spatial planning parameter is evidently seen from micro planning to
macro level.
In micro level voronoi points are taken as finite points with respect to some
parametric is seen.
Architecture is increasingly becoming a simulation through Voronoi
Diagrams. Therefore the study of architecture should assume the simulation
as a powerful design tool to understand and implement complex
relationship factors of environment.
Voronoi diagrams on macro level are a way of dividing spaces which
formed based on a series of points.
The voronoi developed facade are perceived as aesthetic surface
articulators and functionally as a screening (i.e. as Jalli’s) element meant
for privacy.
In Urban contexts the large scale spatial segregation and land use pattern are
taken as layers for proximity constraints for minimum adjacency master
planning parameters such as zoning, parking and qualitative open space
generation.
Voronoi concepts are used to tessellate space with respect to a given set
of generator points

P a g e | 59
CHAPTER 5- CONCLUSION
The use of parameter in spatial & facade design by voronoi allows us to
design not just a piece of art but rather a building with a context that fit into
culture and social realm…..
Town and urban planning in Architecture may be simplified by assigning the
site as a nodal point and generating the Voronoi diagram…
Creating a systematic design process for urban design using parametric
system.
Balancing of forces and tensions in the design.
Variety of design options in the design of a balanced hierarchical system.
Today this method is available as a command in software’s such as
Grasshopper and Rhino.
The result of this unique process in a city zoning creates a natural structure
of urban space, not like a random shape that we usually understand forms, But
as a balance between entities relations.
-It is an “EMERGENCE”

P a g e | 60
BIBLIOGRAPHY
 http://matsysdesign.com/category/projects/tulum-site-museum
 http://www.gnome-netlab.com,
 http://issuu.com/diegosuareztraverso/docs/adda
 http://faulders-studio.com/proj_airspace.html
 Ben Pell, „Airspace Tokyo‟, in The Articulate Surface : Ornament and
Technology in Contemporary architecture (Basel, London: Birkhäuser
;Springer distributor, 2010), pp. 86 - 89
 http://www.archdaily.com/
 http://www.Wikipedia.com/Voronoi
 http://www.dysturb.net/2007/associativedesign-berlage/,
 www.patrikschumacher.com/index.html,
 http://matei23.wordpress.com.
 http://www.designbuildnetwork.com/projects/watercube/
 http://www.pierpaolomaggiora.com/pdf/citylife_eng.pdf
 http://cumincad.architexturez.net/system/files/pdf/caadria2008_49_sessi
on5a_399.content.pdf
 http://www.issue.com,Magazine
 http://www.designbuildnetwork.com/projects/watercube/
 http://teemingvoid.blogspot.in/2010/08/uniformdiversityspacefillingand.
html
 http://www.evolo.us/architecture/voronoiskyscraper/
 http://www.snibbe.com/digitalart#/projects/interactive/boundaryfunctio
ns/
 https://tomaszjaniak.wordpress.com/2012/01/15/voronoi-diagram-in-
arch
 http://www.evolo.us/architecture/voronoi-skyscraper

P a g e | 61
 https://en.wikipedia.org/wiki/Voronoi_diagram
 http://digiarchi.blogspot.in/2010/03/application%ADof%ADvoronoi%A
Ddiagram%ADinto.html
 Architectural Design-Digital cities -Magazine
 http://www.archdaily.com/8277/alibaba-headquarters-hassell.
 Architecture design studio: air journal-adriana d‟amico
 Studio Air Journal

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