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Preliminary Study in non-linear Parametric Design
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國立成功大學建築研究所
Ecological Pattern---Preliminary Study in Non-linear Parametric Design
研究生:
碩士論文
Submitted to the Department of Architecture,College of Planning &DesignIn partial fulfillment of the requirement for the degree of Master of Architecture
National Cheng Kung University, Tainan, Taiwan
生態胚騰---初探非線性參數化設計
Thesis Supervisor: Graduate Student: Chen, Nai chun
Jeng, Tay Sheng
陳乃君 指導教授: 鄭泰昇教授
中華民國一百零一年七月
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Certificate.National Architect License (No. 6221) / Ministry of the Interior R.O.C, March. 2012(4000 candidates, 4% are accepted annually)
Work Experience.Lecturer, Shi-Li Architectural Educational Institutions July 2012 - Dec. 2012 Taught Architectural Design and Urban Design --- Teaching members how to conduct architectural and urban design in National Architect Exam
Speaker, National Taipei University of Technology Taught Architectural Design --- Teaching students who have full-time jobs, this rare opportunity was commissioned by professor, for I possess not only women’s careful and positive attitude but also man’s ambition; Moreover, I constantly did excellent work, which was beyond professor’s imagination.
Teaching Assistant, Dept. of Architecture, National Cheng Kung University Sep. 2009 – Sep. 2012 TA of Modern Architectural History Sep. 2009 – Jun. 2010 --- Assisted professor prepare lessons and research project, with meticulous and active attitude. TA of Construction Sep. 2010 – Jun. 2012 --- Assisted professors prepare lessons and took undergraduate students to visit practical site, for I am a cooperative teaching assistant, professor wishes me stay and study in Doctor program, however, I would like to go back U.S and do research in the top graduate program, MIT SMArchS program.
Honors & AwardsFirst Prize in Architectural New Talent Award / Taiwan Architects Association, Jul. 2009 --- Participants as national new graduates, 230 candidates, including China, Taiwan, Hong Kong graduatesFirst Prize in Excellent Architectural Graduate / Jointly organized by the Architecture Institute in Taiwan, Aug. 2009 --- Outstanding Architectural graduates in Taiwan almost participated, namely, I won the first prize in national graduate design. 3rd Prize in D3 Natural System Competition / Columbia University, June 2009 --- Candidates from all around the world, including Asia, Europe, America, jury were professional professor in U.S.A.2nd Prize in The Wuku Industrial Area Urban Renewal / Industrial Development Bureau R.O.C), Aug. 2011 --- 36 professional architects participatedFirst Prize in The Kaohsiung Old warehouse district urban renewal /Kaohsiung City Urban Development Bureau), June 2011Excellent work in International Takao Station Urban Design / Kaohsiung City Urban Development Bureau Apr. 2011 --- 105 International architectural groups around the world, including AGER, .First Prize in The Hua-shan Graduates Design Award / Hua-shan cultural creative organization, July 2009 --- Candidates from all Architecture Institute in Taiwan4th Prize in The Rural Residential Competition / Construction and planning Agency), Apr. 2008
Chen Naichun +886 911503027 | [email protected]
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PublicationThesis Ecological Pattern—Preliminary Study in non-linear Parametric Design ---Written in English, exploring the new possibility in CAAD and conducting integrated design. Study Workshop “Chinese traditional architecture workshops”/ Tsinghua University in Beijing, July,2011 “Forshan Urban design Workshop” / Chinese University in Hong Kong, Aug. 2010 “Dusseldorf Urban Design Workshop” / Stuttgart University in Germany, Aug. 2009 “Cinemetric Workshop” / Chu Hai College in Hong Kong, Feb. 2008
Extracurricular ActivitiesMedical Service Corps, Mar. 2008 – Aug. 2008NCKU Badminton Team, Sep. 2005 – June 2007
AdditionalCountry visited: France (following the traces of Le Corbusier), India (Exploring Indian culture) Netherlands & Germany ( Workshop and Exploring Architecture of ZAHA and OMA) China (Exploring Traditional and contemporary architecture in Taiwan, Hong Kong, Beijing, Tianjin, Guangdong, Shanxi) Japan (Adventure of Ando and Sejima’s Architecture)
Training courses"3D Max certification courses" in Taiwan 2009"Rhinoceros Architectural Advanced training course" in Beijing 2012
Certification of Architect
Certification of Master Degree
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key words.parametric design, non-linear, form finding, digital fabrication, algorithm
Abstract The objective of this research is to explore the ecological pattern of non-linear parameter design. Although computer-aided design has been merged into the mainstream of architectural education and design practice, most of the research works are focused on the relationship between modeling, visualization, and digital fabrication. This thesis explores the implicit logic of algorithm-based digital design in the form-finding process. The thesis provides a research method that is consisted of three parts. The first part investigates the role of the role of non-linear parametric design before modernism and in digital era by applying literature analysis .The second part sorts out t the commonly used parametric software and computational mechanism which can generate form. The third part implements algorithm which are mentioned in the previous chapter as design method to generating three experimental parametric design. Three experimental design embedded scripting, fabrication and digital technology, each of them address non-linear parametric design in computer-aided architectural design in design process. The major finding of this research shows that algorithm-based design is an exploration-based approach to architectural design, yet requiring embedded design logic associated with computation. To find a satisfactory architectural form, it is necessary to refine the digital model and transform it into a more appropriate design solution. The experimentation of digital tools and algorithmic processes of creating forms have given architects the opportunity to generate increasingly complex visual forms in emerging design practice.
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Thank you for your companionshipI have power to move forwardYou give me to love and help me to find the sunlightWhenever I am upset hour you always make me again strong nearby at me
Appreciate all of you
Naichun, 2012,
Acknowledgement
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ContentsChinese AbstractEnglish AbstractAcknowledgementContentsContents of figure
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Chapter 1 Introduction 1.1 Research Background & Motivation1.2 The objective of the research1.3 Research Framework and Method
Chapter 2 Non-linear related theories and works2.1 Non-Linear Science2.2 Concept of Non-linear Architecture 2.2.1 The definition of non-linear architecture 2.2.2 Non-linear architectural concept from Deleuze2.3 Non-Linear Architecture in History 2.3.1 Gothic Architecture 2.3.2 Baroque and Rococo Style 2.3.3 Art Nouveau and Antoni Gaudi2.4 Non-Linear Architecture in Digital Era 2.4.1 The characters of Non-Linear Architecture 2.4.2 Non-linear architectural design theories BLOBS FOLDS Fractal Emergence 2.4.3 Non-Linear Mimic Nature Landscape 2.4.4 Non-Linear Working Process
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Chapter 3 Non-linear related parametric software3.1 Parametric Design 3.1.1The definition of Parametric Design 3.1.2 Non-Linear Parametricism 3.1.3 Non-Linear Parametric Urban Design 3.1.4 Non-Linear Parametric Architecture3.2 NURBS Modeling vs. SUB-D Modeling3.3 Software Related to Architectural Parametrics 3.3.1 Revit Architecture and BIM 3.3.2 Parametric Software and Second Platforms 3.3.3 Parametric Analytic Software 3.4 Non-linear Integrated Design 3.5 Non-Linear Parametric Fabrication
Chapter 4 non-linear related mathematics4.1 Mathematics and Algorithms 4.2 Mathematic Logics and Geometric Orders in Algorithms 4.2.1 Cellular Automata 4.2.2 Dynamic Relaxation 4.2.3 Voronoi 4.2.4 Hyperbolic Geometry 4.2.5 Homology 4.2.6 Weaire–Phelan structure 4.2.7 Fractal 4.2.8 Minimal surface 4.2.9 Metaball
Chapter 5 Ecological Pattern---Non-linear parametric form-finding design5.1 Ecological surface form-finding 5.1.1Ecological Pattern---Surface Form Finding 5.1.2 Squama 5.1.3 Ecological Pattern--- Folding and unfolding5.2 Pavilion ---Ecological pattern in fabrication5.3 Psychedelic Rhapsody---Ecological pattern in architecture design5.4 Bio-digital Renaissance---Ecological pattern in Tainan Main station urban design5.5 Conclusion
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ReferenceAppendixResume
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figure 1.1 important publications on computer-aided architectural design
figure 2.1.1 Chaos mathematical modeling
figure 2.1.2 Soliton mathematical modeling
figure 2.1.3 Linear mathematical function
figure 2.1.4 Linear proportional relationship between geometries
figure 2.1.5 sketch primative geometry from Lecorbusier
figure 2.1.6 BLOBS advocated by Greg Lynn
figure 2.3.1a,b Animal's skeleton-like structure
figure 2.3.2.a,b,c Baroque dynamic plan and carving by Borromini
figure 2.3.3.a,b The development of microcosmic inspired Gaudi
figure 2.4.2.a,b FOLDS, Staten Island Institute of Arts and Science
figure 2.4.2.c FOLDS, Staten Island Institute of Arts and Science by Peter Eisenman
figure 2.4.2.d,e Competition for a Virtual House
figure 2.4.2.f,g Peter Eisenman applied Fractal theory to architectural design
figure 2.4.2.h,i Emergence theory applied in city
figure 2.4.2.j Emergence theory applied in Taipei Pop Music Center
figure 2.4.3.a Aquatics Center in Olympic Park
figure 2.4.3.b Guangzhou Opera House
figure 2.4.3.c Performing Arts Center
figure 2.4.4.a Grotto and Excavation by Cecil Balmond
figure 2.4.4.b Experiments:Subdividing Space
figure 2.4.4.c Experiments:Subdividing Space
figure 3.1.d The function of parameters, and the application from parametric modeling
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Contents of figure
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figure 3.1.2 a,b,c Parametricism as a style applied in cities
figure 3.1.3 a Wool-thread model to comppppute optimised detour path networks
figure 3.1.3 b digital breeder for designing cities
figure 3.1.3 c non-linear integrated urban design
figure 3.2The difference between NURBS and Polygon Modeling
figure 3.3.2 a grasshopper interface,convas
figure 3.3.2 b the icon of code made designer generate form easily
figure 3.3.2 c the design process of Generative Component
figure 3.3.2 d the design process of Generative Component
figure 3.3.2 f,g,h Marks Barfield used fractal theories generating structure in Digital Project
figure 3.3.3a CFD Simulation in Rhino
figure 3.3.3b Immediately solar radiation analysis feedback
figure 3.3.3c best orientation
figure 3.3.3 d,e,f FEA in GSA,
figure 3.4 a Integrated different softwares
figure 3.4 b, Non-linear integrated archietctural design process
figure 3.4 c,traditional linear archietctural design process
figure 3.5 a, Customization of BLOBS in CAM
figure 3.5 b,Robot CAM with brick wall
figure 3.5 c, Sectioning
figure 3.5 d,Folding, C-wall
figure 3.5 e, Tessellating,Puppet theater
figure 3.5. f,Forming,P-wall
figure 3.5. g,Contouring,bone-wall
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figure 4.2.1,Cellular Automata
figure 4.2.2,Dynamic relaxationform finding method
figure 4.2.3.a,the relationship between voronoi and nature
figure 4.2.3.b,three dimension voronoi
figure 4.2.3.c, relationship between woronoi and delaunay
figure 4.2.3.d, the formation of voronoi
figure 4.2.4, Hyperbolic Geometry with homology in grasshopper
figure 4.2.5, homology in digital sub-D modeling
figure 4.2.6.a,Digital fabrication with Weaire–Phelan
figure 4.2.6.b,generating Weaire–Phelan with code
figure 4.2.6.c,Weaire–Phelan table created by Haldane Martin
figure 4.2.7.a,L-system phisical model
figure 4.2.7.b, cantor set figure
figure 4.2.7.c, peano curve
figure 4.2.7.d, Sierpinski triangle
figure 4.2.7.e,Koch snowflake
figure 4.2.8.a Helicoid-Catenoid
figure 4.2.8.b Catenoid
figure 4.2.8.c Planar Enneper
figure 4.2.8.d Costa
figure 4.2.8.e, Schwarz PD Family Surfaces
figure 4.2.9.a, metaball generated by grasshopper
figure 4.2.9.b, a series of metaball, generated by grasshopper
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Chapter 1. Introduction
1.1 Research Background & Motivation1.2 The objective of the research1.3 Research Framework and Method
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The manifest form---that which appears---is the result of a computational interaction between internal rules and external (morphogenetic) pressures that, themselves, originate in other adjacent forms (ecology). The (pre-concrete) internal rules comprise, in their activity, an embedded form, what is today clearly understood and described by the term algorithm. ----by Sanford Kwinter (Computational Design Thinking, 2011)
1.1 Research Background & Motivation This thesis is motivated by the rapid development of Computer- Aided Architectural Design. Nowadays, Computer- Aided Architectural Design is not only a design tool but also a way of design thinking . In 1951, UNIVAC emerged as the first generation of computers. The emergence of computer embarks the revolution of designs and leads to many inventions and innovations in architecture. With the rapid development of digital media and new technologies, architectures are constantly delivered or created in different forms. We could sense the message of change via forms, spaces and materials in digital era. Nicholas Negroponte, the founder of MIT Media Lab, said “Computing is not about computers any more. It is about living." In the book “Being Digital" on the relationship between computers and architectures, Nicholas Negroponte depicted a blueprint for computers. [ Negroponte,1995]. Our life is dominated by technological advances and surrounded by computers, hence, architecture, a science closely related to our life, opens up a new era of digital technology . The book, "Computer-Aided Architectural Design", written by William Mitchell in 1977 , introduced the function of data structure and shape language of form in computer-aided drawing. This rarely seen book became a very important masterpiece at that time. In William's later work," e-topia", mentioned an notion," Form follows Function, Function Follows Code" [William,2000]. This notion was compared to the notion in the Modernism, "Form follows Function", which was advocate by Louis Sullivan, became a significant opinion in computer-aided architectural design. The concept "BLOBS" was created from Greg Lynn who tried to challenge the primitive geometry advocated by Le Corbusier. Non-linear architectural form was generated by computer to replace the traditional architectural form of the Euclidean. It was constructed from virtual space to real life and emerged from the cocoon with the evolving technology.
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The Guggenheim Museum Bilbao, designed by Frank Gehry, was once questioned for its incongruousness but is now hailed as the new landmark about digital manufacture. This signals meant the arrival of digital era. Digital forms have become real architecture in our life, rather than computer graphics. Computers were no longer just for graphics in the implementation stage. Instead, they were far-reaching aides and indispensable tools for designers in the conceptualization process. The logics and thinking behind architectural designs also . According to Peter Eisenman, another master architect in deconstructionism, also said, "hands generate what you already know. However, if you enter these images into a computer, it may open up some possibilities you never knew before."[Peter,2001]. Mao-Lin Chiu also argued that human brains are a type of computers, and our thinking is a complex computing process. [Chiu,2003].
figure 1.1 Important publications on Computer- Aided Architectural Design, (drawn by the author) The time of the publication showed the change of influence in compuer-aided architectiral design
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With the progress of computer, the scope of application in computer-aided architectural design had become increasingly wide, and the range of discussion extended from computer-aided drawing to more aspects, such as simulation, prediction, evaluation, artificial intelligence, analysis, interactive architecture, and digital fabrication. The architectural works were created by computers rather than by hand because of the advancing technologies and the arrival of digital era.
Although the computer has brought many possibilities for the design of architecture, the criterion of modernism, “Form (ever) follows function” was deeply believed in most of the architects in Taiwan. The tedious repetitions of drawing tasks were eliminated by computer-aided design. Meanwhile, the traditional thinking in architectural design was still clung. The Euclidean rules and linear pattern dominated the pattern of the city from architectural to urban design. Linear pattern should not be the desired pattern in any organized city. The city was developed rapidly and life was changed by the modulus and mass production. The paradigm of labor-based manufacturing was shifted to industrialized production by industrial revolution. The process of manufacturing and production was sped up by shifting from manual labor to machinery utilization. The process of building constructions was altered by focus on mechanical and modularization.
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1.2 The objective of the research
The objective of this research investigated the possibility of creating non-linear form-finding parametric design by using algorithm. In the title, “Ecological Pattern – Preliminary study in non-Linear Parametric Form-Finding Design”, ecological Pattern could be divided into two words, ecological and pattern. Ecological is quoted two definitions from Merriam-Webster's dictionary, the two definitions which are the noun of ecological are as follows. One definition is the totality or pattern of relations between organisms and their environment, and another definition is environment, climate <the moral ecology>[Merriam-Webster's online,2012]. Algorithm generating design and non-linear ecological form were being applied and formed by the author to represent first definition, and analysis and form-finding software was integrated by the author to create environmental-friendly architectural form to represent second definition.
The term “pattern” quoted from "Pattern language" was written by Christopher Alexander. The Pattern consisted of a language-like rule system during the time which was on the demand for rapid economic construction after World War II and resolved the conflicting forces of a group but still not a language was proposed by Alexander. Many decisions about how to solve problems in designing stage had to make by designers. The product after sloving the conflict was the pattern. The computer aided architectural software in digital era was applied by the author to look for ecological pattern.
Digital architecture was condemned by some architects as being impractical. Research in methods and theories behind the digital architectural was scant in the professional field while most of the theses were in Computer Aided Manufacture and digital fabrication. The relationship among architecture, mathematics, computer, and ecology were examined by this research. They were considered independent in their effects on design, but have been combined with each year over the recent years as evidenced with the emergence of biomathematics, biomimetic-architecture and CAAD. In fact, computer was a technological product on the basis of mathematical theories. Architectural design with mathematic and logical algorithms was attempted by many researchers. Even though algorithms were fallen in the realm of computer science, unlimited design possibilities could be brought by algorithms. In the past, programming languages were tedious and prone to errors. Algorithms were difficult to work with for designers without the knowledge in programming languages. Since the development of Grasshopper plug-in by Rhino, the visualized 3D second platform was created. Programming languages were packaged into visual components and made them easier to learn by designers. Meanwhile, the interface became flat because of the components, which became the common language among designers all over the world. National discussions were made in the same platform and the boundaries of nation were broken by the graphical programming language in Grasshopper.
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1.3 Research Framework and Method Literature Analysis Method is being used in this research. Theories and manipulation were inextricably bounded together. Related literatures were extracted by the author by reading various documents about non-linear parametric design. The feasibility of applying theories and methods to architectural design was analyzed through practical operation. Three stages were included in this research. Related literatures review to find non-linear architecture and theories in architectural history was conducted at the beginning of this thesis. Commonly used parametric software and mathematical methods in algorithm were recommended and sorted out by the author in the second stage. Apply the theory to architectural design was attempted in the third stage. The factors and details of the non-linear parametric design were discussed in each chapter in different prospective. The ecological pattern in architectural form which was implicated in the architectural history was discussed in Chapter Two. Non-linear architectural was included not only before modernism, but also in digital age. Finding the mathematics and the industrial technology included in non-linear theories and architecture were the main purposes. Parametric design software and integrated design software which used in computer-aided architectural design regularly was sorted out in Chapter Three. Designing with integrated software would have an impact in the early stage of architectural design was proposed. Mathematics-related algorithms which used frequently in computer-aided architectural design were collected and analyzed in Chapter Four. The mathematical and logic behind the sorted out algorithms were described in detail. Apply the methods and theories which discussed in the previous chapters to practical architectural design were attempted in Chapter Five. Therefore, the relationship in between digital models and physical models in computer-aided architectural design through using algorithms were analyzed and acknowledged by the author.
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Research Framework
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Chapter 2. Non-linear related theories and works
2.1 Non-Linear Science2.2 Concept of Non-linear Architecture 2.2.1 The definition of non-linear architecture 2.2.2 Non-linear architectural concept from Deleuze2.3 Non-Linear Architecture in History 2.3.1 Gothic Architecture 2.3.2 Baroque and Rococo Style 2.3.3 Art Nouveau and Antoni Gaudi2.4 Non-Linear Architecture in Digital Era 2.4.1 The characters of Non-Linear Architecture 2.4.2 Non-linear architectural design theories BLOBS FOLDS Fractal Emergence
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figure 2.1.2 Soliton mathematical modeling(Important developments in soliton theory, 1993)
2.1 Non-Linear Science In 1980, the concept of non-linearity was published by Jules Henri Poincaré, the great mathematician of France at all times as well as a theoretic scientist and scientific philosopher at the turn of the 20th century. In the study “Non-Linear Dynamics & Complex Systems, Physics” by D.K. Campbell, the director at LANL (Los Alamos National Laboratory), the US, non-linear science was defined as the science that examine non-linear mathematical systems and natural phenomena. The abbreviation of linear functions in mathematics was linear science. The classic science from Newton onward was also linear science. In the past, natural phenomena into the Cartesian coordinate system and the world through the simplified straight lines was simplified and learned respectively by scientist. However, dynamic, complex and constantly changing would be the natural world. Non-linear relationships did not exist but approximations only. Scientists group all the problems not addressed by linear science as non-linear science. Non-linear science deals with non-linear relationships where inputs and outputs were out of proportion. In such relationships, linear functions did not hold because the relationship between variables was not a straight line. Non-linear relationships were described with a parabolic or quantified simply was not possible. Complex, dynamic and non-linear were common in many natural phenomena. The chaos status at the beginning of the universe was an example. In fact, non-linear science was still at its infancy and has limited explanatory power over many phenomena. However, in a non-linear world of complexities and changes, life was also non-linear. In that case, should architecture be linear?
figure 2.1.1 Chaos mathematical modeling(Elegant chaos,2010)
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linear theoryemphasized the following attributes: 1. Linearity: Straight lines produced by Linear functions. 2. Proportional relationship: The slope was consistent in a linear function f(x)=mx+b. 3. Perfect geometry: The geometry produced by linear functions followed a linear proportional relationship. 4 Interconnection: A variety of shapes could be created by accumulation or eliminations.
Le Corbusier, a master of modern architecture, mentioned that modern architecture basically consists of a number of geometric forms in different permutations and proportion relationships. The most prominent feature of modernism was linear geometry. The era of industrialization signaled a beginning of new period with a new spirit was indicated. From economics and took the lead of mathematic formulae were drawn by Engineers, aiming to align the law of nature and the great harmony. “The house is a machine for living in” and “Primary forms are beautiful forms” were developed in the era of industrialization and contributed to the creation of modernism such as simple and linear geometric forms.
figure 2.1.3 Linear mathematical function( Wiki website, 2012)
figure 2.1.4 Linear proportional relationship between geometries( drawn by the author)
figure 2.1.5sketch primative geometry from Le Corbusier(Versune architecture,1923)
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Non-linear thinking refers all the thinking falling outside the scope of linear thinking. Non-linear theory was in contrast with linear theory, Non-linearity works in the opposite direction was known for the following key features: (1) graphic elements were curvy or in irregular broken lines; (2) a lack of specific proportion between elements; (3) disobedience of traditional proportions and rules in the section of lines and composition of building blocks; (4) a lack of relationship between elements. In contrast with linearity was non-linearity. Linearity and non-linearity were often used to describe the relationship in the context of independent variable x in the function y=f(x). In a non-linear relationship between the independent variable x and other variables, the relationship was not a straight line. Rather, it could be a curve, parabolic or simply could not be quantified. If the output and the input of a system were out of proportion, it would be regarded as non-linear. It was defined as “bound thinking”, such as system thinking and fuzzy thinking. Logical thinking or linear thinking might not be followed. Intuitive was the key as well as a summary without the analysis of large amount of data. In fact, virtually all the known systems in natural sciences or social sciences were non-linear if sufficiently large inputs were existed. Therefore, the number of non-linear systems was significantly higher than linear systems. The objective world was non-linear. Linearity was an approximation. In a non-linear system, a small disturbance or a tiny change of initial conditions might lead to huge differences in the system at a later time. The three most frequently theories in non-linear science were chaos theory, fractal theory and soliton theory. A new philosophy about of the universe was and new thinking and concepts were formed by the three interconnected theories in natural sciences, social theories, medical science and ecology. The world was irregular and chaotic. The universe was not closed but expanding.
figure 2.1.6 BLOBS advocated by Greg Lynn in digital era, which are the forms generated by computer (Folds,blobs+boxes,2001)
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Non-linear architecture, led by the complexity of science, will become the next architectural millennium. ----- (Charles Jencks,1997)2.2 Concept of Non-linear Architecture
2.2.1 The definition of non-linear architecture Charles Jencks, an architecture critique, stated in his book “The Architecture of the Jumping Universe” that non-linear architecture would become the next architectural millennium.[Charles Jencks,1997]. The concept of non-linearity was used to describe the pattern of modern architecture. Non-linear architecture was the building with continuous and flowing patterns. These irregular patterns were stemmed from the interactions between all the influencing factors on the basis of the analysis on the environment and architectural elements. In fact, patterns was reflected the relationships between factors. If these relationships were non-linear, the ultimate pattern of architecture would also be non-linear. The following characteristics were mentioned in the non-linear architecture: (1) the use of natural vocabulary; (2) the reflection of the nature of the universe; (3) complexity and layers; (4) timeliness and dynamics.
Although his concept of non-linear architecture was fuzzy and not completely accurate, new perspectives in the reading of contemporary architecture and new possibilities of future architecture were opened and created respectively. Non-linear architecture, led by the complexity of science, was indicated to become the next architectural millennium. New design processes and methods were created by new architectural thinking combined with the concepts of dynamics and thermodynamics.Neil Leach stated, ”Non-linearity brings about changes and effects to our architectural thinking. We no longer focus on the forms of the architecture. Rather, we emphasize the process and use the computing technology as a way of designing architecture.” Linear space refers to the modernism which was created in the Cartesian system where architecture vocabulary, i.e. proportions, modulus, balances and axes, were centred in the tradition of Euclid. The pure forms and proportions in such architectures were fixed, precise and repeatable. The classical aesthetics was formed. Nonlinearity, in contrast with linearity, was free from the constraints of the Cartesian system and Euclid geometry. The flowing, smooth, landscape-like complex patterns were created by drawing from non-geometry, ecology, biology, technology and art. The non-linear complex scientific theories were followed by non-linear architecture. The non-linear philosophical thinking was anchored, particularly the ideas of Gilles Louis René Deleuze, and applies relevant theories in the exploration of architectural concepts, processes and methods, in order to create rich, complex and dynamic architecture with new scientific perspectives. The ideas of the philosopher Gilles Louis René Deleuze, i.e. folds, smoothness, diagrams and becoming, were the new blood in the thinking of modern architecture. Folds and smoothness have profound effects on the thinking of non-linear architecture.
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2.2.2 Non-linear architectural concept from DeleuzeFolds Folds were developed on the foundation of “monads” created by Gottfried Wilhelm Leibniz. Deleuze, was influenced by the twisting and dynamic style of Baroque, which examined the world of folds. In this world, time and space was folded with mattes, unfold and fold again. Monads were bended and formed into crushed, fractured and curly surfaces. Objects were come into existence by the double bending of inward out and outward in. Hence, no boundary between inside and outside was existed. The embodiment of object organization was appearance, in the same way as the continuous curves in Baroque. This concept was a breakthrough of the idea about space in Euclid’s geometric tradition. Flowing world was opened where time and space coexist in a dynamic movement.
Nomadic Space and Smoothness A free, flowing, smooth, borderless and smooth space for human activities was defined as nomadic space by Deleuze. All the key features of nomadic space were in contrast with striation space. National space was an example of striation space. State laws and regulations governed human behavior, in the same manner as straight lines were made from one dot to another. However, nomadic space, the space where nomads lived was known for no boundary. Nomadic space was decentralized, de-ordered, de-integrated and objective to metaphysics. Non-linear architecture was the freeze-frame of nomadic space. Nomadic space was the opposition of the space in a vector status where movements were drawn by forces and only between fixed points. On the contrary, nomadic space was open, with movements happening at any point and variables constantly changing. Smoothness was pursued in non-linear architecture. It was an expression of nomadic space.
Diagrams When writing about Michel Foucault, the concept of diagrams was discussed by Deleuze. Diagrams were interpreted as an abstract machine, which all kinds of relationships were considered in the diagramming process. This function relationship might be tangible, or abstract. Diagrams were used by Leonardo da Vinci in the Renaissance to explain the human body. A nine-square grid was used by Peter Eisenman to illustrate the creation process of architecture. The computer was used by Rem Koolhaas to analyze environmental phenomena and examine the society with diagrams. The analyzed diagrams were also converted into architecture. In the era of digital architecture, digital diagrams were the abstract machine in the words of Deleuze. They were imported and generated with description functions and abstract function relationships after the analysis of environmental phenomena. These function relationships were in a mutual check-and-balance, forming hidden rules and patron-client relationships. Shapes were formed and simulated through such function relationships.
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Linearity is frozen music. Nonlinearity is flowing musical notes. ------- (Yao Qiang,2009)
2.3 Non-Linear Architecture in History
Non-linear architecture was not a product of the digital era. Before Industrial Revolution and modernism, non-linear architecture was once at the forefront of architectural design. Architecture was the representation of technology, humanity and social values. Non-linear architecture was the combination of human pursuits and natural forms. The architectural patterns associated with non-linear architecture in history was examined in this chapter.
2.3.1 Gothic Architecture Gothic architecture, a breakthrough from ancient Roman style, was prevalent in the Medieval Time. The structural parts of the building was ceased to be solid walls (to resist the thrust of stone-made fire-proof roofs), and became a stone skeleton comprising clustered columns, free from the horizontal shove of vaults. The surrounding structure and the supporting structure were hence separated. Open windows were allowed in the non-linear structural design. In essence, Gothic architecture was like a sculpture of windows and supporting walls. Pointed arches, flying buttresses and ribbed vaults, these elements of Gothic architecture were all functional, structural and ornamental at the same time. Roman or Romanesque architecture was known for turtle-shell like arches; whereas Gothic architecture was supported with mammal-like skeletons, a tense structure consisting of organic combinations of ribs and spines. This structural change set the three dimensions free and natural elements began to walk in. The burden with supporting walls was shared by rose windows and the mysterious light of Heavens was created by telling religious stories on the rosy panels. The organic changes of traceries, such as Butter Tower of Rouen Cathedral, expressed the craftsmen’s yearning for the nature.
figure 2.3.1a,b Animal's skeleton-like structure and the integration of column and plates. Plants-like pattern represented in the hollow wall. (Gothic architecture,1985)
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Baroque is so often characterised in contrast with the Renaissance by its excess and drama. This artful style of subversion, tension, movement, gravity-defying feats and freedom was really one of whimsical frivolity or subversive disquiet. Exuberance in Baroque architecture is often expressed as defiance of gravity. ----- (Robert Harbison,2010)
2.3.2 Baroque and Rococo Style The term “Baroque” was derived from the Portuguese word "barroco", i.e. distorted pearl. The exaggerative and dynamic tensions of Baroque architecture were one of the characteristics non-linear architecture pursues. Baroque style was challenged the flat, monotonous, horizontal/vertical, regular, harmonious and proportional architectural patterns sought after in the Renaissance. A large number of deformed and out-of-shape lines were used to create non-linear structure with strong, dynamic and ornamental curves. Following Mannerism in the late years of the Renaissance, Strong emotions were transformed in Baroque architecture into dramatic, flowing and moving lines. Wavy curves and cymae spell out the architectural tensions. The architectural space was consisted of a large amount of surfaces and oval rooms. Sculptures became in motion, no longer static or in repose. A deeper understanding of the nature and changes in aesthetical definitions were reflected in Baroque architecture and Rococo architecture. Architects were started to learn from the nature and created the dynamics and layers of Baroque style with natural elements. In terms of spatial layers, the mould of classicism was broken in Baroque architecture. Its free style was a break from the traditional geometric patterns and an experiment in space, pattern and structure. In Architectural Design Magazine’s special edition “Exuberance”, Baroque architecture was approached by Robert Harbison with new perspectives “New Era of Exuberance in Digital Design”. Baroque architecture was turned against the fixed, sturdy, stable and harmonious style of the Renaissance. It used the transient fireworks, curves and edges to create luxurious but asymmetric décor. Liquid, unstable geometric shapes and broken gable walls were given a sense of freedom and wildness. The elaborate designs were changeable but contrived. Borromini architecture was always twisted and twisting. Columns of varying heights, bending gable walls were embedded in trainable gable walls, swirling patterns forming into flowing waves, all created a dynamic, unstable form of architecture.
figure 2.3.2.a,b,cBaroque dynamic plan and carving by Borromini(Baroque architecture 1600-1750,2008)
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"Those who look for the laws of Nature as a support for their new works collaborate with the Creator.""Paraboloids, hyperboloids and helicoids, constantly varying the incidence of the light, are rich in matrices themselves, which make ornamentation and even modeling unnecessary." -----Antoni Gaudi2.3.3 Art Nouveau and Antoni Gaudi Art Nouveau was a rebel against classical rationalism. It was sought to break away from the Euclidean geometry. However, the industrial technologies at that time were not sophisticated enough. New technologies and sciences were available now to allow us to view the world with new perspectives and explore natural patterns. The wild-and-free expression in architecture was possible in the Ernst Haeck’s study in morphology of fauna and flora. The inspiration for lively and beautiful lines was lent by Flora, as well as flowing waves. The list of the three factors that influence architecture the most were listed as follows:
1. Study in biology: Kelps, grass and insects, were examples of organic forms and curves. Flowers and other plants were the source of creative ideas. 2. Application of mathematics and microscope: The invention of microscope and other equipment made it possible to observe the small tissues and cells of animals and plants. Meanwhile, the creation of lively, moving, wavy and elegant lines was allowed in the mathematical/logical relationship, structural relationships and proportional relationships. 3. Emergence of video media: Objects were documented by cameras and video recorders in a dynamic fashion. Experiment dynamic curves were also started by Creative professionals.
figure 2.3.3.a,b The development of microcosmic inspired Gaudi to create nature-like structure(Scripting culturies,2011)
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Antoni Gaudi was the key advocator of Art Nouveau. Learn from the nature was proposed by him. No pure straight lines in nature was believed by him. He stated, “The straight line belongs to Man. The curved line belongs to God". Organic and anarchic patterns were examined and applied by Gaudi to architecture. First, his study of nature into ruled geometrical forms was transformed, such as hyperbolic paraboloids, hyperboloids and helical cones. Second, hyperboloid vaults were used as an influence form Gothic architecture. The supporting systems were revisited by Gaudibut but the relationship between beams and columns was believed to be a vague one. Ornamental structural elements were applied to create structured nature and blend the whole architecture into unity. Lines and organic patterns constituent buildings were curved lively, like living organisms. Dynamics to architecture was reflected on the load-bearing walls.
figure 2.3.3.c,d The paraboloid logic was implied behind organic form. These mathematical and geometric inspired Gaudi(Scripting Culturies,2011)
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"Non-linearity affects and changes our architectural thinking. We focus not on the forms, previously emphasized by architects. Rather, we focus on the process and use computing as a technology to design architecture.” -----(Neil Lynch,2009)2.4 Non-Linear Architecture in Digital Era 2.4.1 The characters of Non-Linear Architecture The direction of world architecture and the computing power of computers was explored and exploited in non-linear architecture to assist designers in modelling, synthesis, simulation and evaluation. Designers were started to experiment the application of complex scientific theories to architecture designs and computer technology was used to resolve complicated issues. The expressions in the form of architectural designs were non-linear objects and irregular, dynamic bodies of volume. The goal was to integrate with the nature. This type of architectural designs was broken down away from the domain of drawings, pens and models. Designers were empowered by the simulation over computers with new imaginations, who could easily twist, revolve, Boolean and repeat space in the virtual world. Designers could simply change parameters to create the complexity of virtual patterns in the digital realm. The architecture was not only a body of volume, but also a spatial existence was suggested by Xu Weiguo, a professor in Tsinghua University. Three elements were consisted in the spatial existence: human behavior, natural environment and architectural body of volume. Architectural designs were tailed for the needs of human activities by being dynamic, irregular and organic. They should not be rational, square boxes. The natural environment surrounding architecture should be organic and irregular. Buildings should also be dynamic, irregular and organic in order to interact with other factors and create a harmonious union. In contrast with rationality of Euclidean geometry, the complexity of non-linear architecture was more optimal. When people were tired of the architectural forms dominated by Euclidean geometry, starters was sought to break the restrictions of Euclidean geometry by drawing aesthetical inspirations from topological geometry and fractal geometry. Architecture was begun to flow and became plastic. Non-linear architecture, a response to the non-linear world, was dynamic and complex. The plethora of concepts and techniques was provided in non-linear architectural thinking to enable to diversity of architectural creations. Xu also believed that,""Non-linear architecture breaks away from the limitation of traditional architecture and gives architecture the freedom of forms. Non-linear architecture allows designers to think beyond the dreariness and monotony of linear, geometry architecture. It explores the possibilities of architectural patterns and gives a new lease of life to architecture. This new architecture is flowing and changeable.”[Xu,2009]The following characteristics were showed in the non-linear architecture: 1.Organic forms: Architecture and the environment were interacted with each other and blended into an organic form of landscape. 2.Dynamics: The application of surfaces and curves were presented with the tension of flowing dynamics, as if framed in time and in motion. 3.Follow Natural rules: There were logics behind natural forms and bionic architecture.
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A folded mixture is neither homogeneous, like whipped cream, nor fragmented, like chopped nuts, but smooth and heterogeneous.
Folding employs neither agitation nor evisceration but a supply layering. Likewise, folding in geometry involves the sedimentation of mineral elements or deposits which become slowly bent and compacted into plateaus of strata. ---------(Greg Lynn,1999)
2.4.2 Non-linear architectural design theoriesBLOBS Computer-aided design and irregular, bionic architectural forms were studied and produced by Greg Lynn. In “Animate", he mentioned that architecture was subject not only to vertical/horizontal forces but also the effects of other force fields. The concepts of monads developed by Leibniz, a mathematician was used. Monads were the smallest, indivisible units in mathematical and physical structure. They were the smallest unit in the world of matters. BLOBS (Binary Large Object Balls) were the digital basis transformed from the concept of monads. BLOBS were affected by each other. Computer graphic software, metaball, was used to create blob architecture. The smallest unit in the digital era, such as BLOBS, were attracted and gathered under the momentum of internal forces. In the past, BLOBS were only for the architectural creation over digital media, but it was no longer the case due to the development of CAM. According to Greg Lynn, bricks and mortars were the smallest unit of building blocks. However, BLOBS, under the CAM technology, have become the smallest unit in the digital era. Louis I. Bricks was used by Kahn, the smallest architectural unit, to express the poetry of architecture. Now, digital tools were applied by Greg Lynn to create flowing poetry.
figure 2.4.2.c FOLDS, Staten Island Institute of Arts and Science by Peter Eisenman(Greg Lynn,2001)
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FOLDS Deleuze, a philosopher, indicated that there were folds everywhere in nature. Mountains, rivers, forests, brains were all fold issues. Folds constantly specialized and matters became indefinitely small, spongy and empty tissues with holes inside. The concepts of folds and the idea of nomadic thinking were applied by Greg Lynn in the architecture forms of the digital era. Folds and unfolds, progression and regression, the relationship between the interior and the exterior of architecture was no longer fixed or clear-cut. Rather, it was in a constant status of energy exchanges. Internal folds were complex and indirect; whereas external folds were bends of matters, flowing and borderless. The Flowing, moving and complex aesthetics were expressed in the decentralization in the nomadic concept of Deleuze and the liquidity modernity in the words of Zygmunt Bauman. Peter Eisenman illustrated the concept of folds and states that the world was irregular and chaotic. The universe was not enclosed but expanding. A dynamic, continuous, fuzzy, intertwined, integrated and smooth space was created. Architecture should be wavy and curly, twisted and folded. The contrast between horizontal floors and vertical walls was disappeared. The space was liquid and continuous. Folded space was free from the constraints of the Cartesian coordinate system. The non-Euclidean geometry was created by eliminating the opposition between the environment and architecture, the internal and the external, the horizontal and the vertical.
figure 2.4.2.c FOLDS, Staten Island Institute of Arts and Science by Peter Eisenman(Greg Lynn,2001)
figure 2.4.2.d,e Competition for a Virtual House. (c)1997, Peter Eisenman. (Peter Eisenman,2006)
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Fractal Fractal theory is a new science of mathematics. It is able to process irregular, fluid and complex graphs, such as tree branches, coastal lines, river forks, mountains, snails & shells, tree leaves and lightning. These irregular and complicated forms cannot be explained with the Euclidean geometry but can be dealt with by fractal theory. Fractal geometry was first developed by Beniot B Mandelbrot in 1975 and is known for the following key characteristics: 1.Fractional dimension: Fractional dimensions, unlike the Cartesian coordinate system, do not have to be in integers. They can be fractional. 2.Self-similarity: Fractal structures repeat the same graphs in each level of the hierarchy and create highly complex forms by repeating simple rules. 3.Scale irrelevance: The same fractal graph in different scales shares the same level of complexity. 4.Unlimited structure of limited areas: Fractal graphs constantly repeat themselves. 5.Relativity: In the example of coastal lines, the exact length cannot be measured as the lines repeat in the same rules. 6.Unity: Large scale of graphs can be obtained with small-scale fractal ones due to self-similarity.
Peter Eisenman covers Chao’s Theory, fractal theory and Big Bang Theory in his study of digital design. To him, computers are used not just to generate graphics. Eisenman utilizes the computing power to create spatial forms. Designers are the creator of algorithm rules. When they start, they start not with abstract ideas about spatial forms, but with algorithm rules and generators. Computers perform highly complex computing processes and generate a set of virtual graphs for the choice of designers. Eisenman expresses the abstractness of architectural concepts with physical buildings and constructions. As a master in deconstructionism, Eisenman elaborates the relationship between deconstructionism and non-linear architectural thinking. The computing power of the digital era transforms complex sciences into tangible design elements for designers.
figure 2.4.2.f,g Peter Eisenman applied Fractal theory to architectural design (Peter Eisenman,2006)
figure 2.4.2.f
figure 2.4.2.g
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City as a manifestation of emergence. The city operates as a dynamic, adaptive system, based on interactions with neighbors, informational feedback loops, pattern recognition and indirect control. "Like any emergent system." ------Steven Johnson(Digital Cities,2009)
Emergence Birds, fishes, termites, are all interacting with each other in a bottom up manner. Birds know no leaders. They follow a certain but simple rule, influencing each other and forming a feedback system from bottom up. Single entities have their own behavioural traits. The individuals of the same group follow the same but simple rules. They organize themselves into a highly complex group. Scientists describe this phenomenon with swarm theory or emergency theory. Steven Johnson refers to this phenomenon in his depiction of traditional urban developments. He argues that it did not stem from the theories associated with urban designs and provides a critique in “AD Digital City” that urban designs are jammed with straight lines of the Euclidean geometry. Neil Lynch refers to the multi-agent system, developed on the foundation of emergency theory. Kokkugia,a studio had a software program, was able to mimic the workings of emergency theory in the virtual space.[Digital Cities,2009]. Fractal, L-system and Cellular automata all follow a bottom-up approach but they are constrained to their own internal logics. However, kokkugia is a multi-agent system that transcends all these theories because it contains artificial intelligence. The interactions of varying input factors generate different relationships and form different spatial forms via self-organization. They continue to extend with simple rules and exhibit irregular appearances on the basis of rational thinking. In the bidding for the project “Taipei Pop Music Center”, the design team applied the agent system and coded the spatial requirement into programs. They sought to strike a balance between topology and structural efficiency by leveraging the characteristics of materials. The result is a complex system with vein-like networks. The roofs and lattices collectively form a semi-automated agent system through these networks. Swarm intelligence can actively self-organize by following the network and topological structures. This allows the interaction between specific designs and multi-agent systems. This process opens up the internal communications within the agent system between topology and geometry and generates the connecting forces between systems of material behaviors. This self-organization is the characteristic of swarm theory.
figure 2.4.2.h,i Emergence theory applied in city(Digital Cities,2009)
figure 2.4.2.j Emergence theory applied in Taipei Pop Music Center
(Digital Cities,2009)
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2.4.3 Non-Linear Mimic Nature Landscape Inspiration was emphasised in the mimic nature landscape from nature and creates abstract but organic patterns. Zaha Hadid was a leading architect in this field. Zaha Hadid was born in Bagdad and majored in mathematics in Lebanon. She was fascinated with the complex designs of Persian rugs and wondered how the craftsmen weaved the realities into a rich tapestry when she was young. Inspiration from nature was discussed with her non-linear exercise. Her architecture reminded people of how plains cut through hills, how caves expand and open up, how rivers curl along and how mountains show directions. She was learnt from the nature and applied bionic techniques to create a flowing and liquid world. A variety of topological patterns were leveraged and extracted by Zaha Hadid into a manmade natural landscape. The technological advances and graphic software upgrades were reduced the complexity for non-linear architecture to create bionic buildings and structures. Zaha Hadid stated, “I have no idea what my next piece will look like. I constantly experiment with all kinds of media variables. Each design is like a re-invention. Architectural design is like art creation. You do not know what is possible until you have worked on it. Once you have mobilized a set of geometric graphs, you can sense a building is starting to move.”[Digital Hadid,2004] Non-linear architecture was opened by digital media to all kinds of possibilities through attempts and experiments. Architectural designers were enabled by the digital sketches to seek for inspirations and creative ideas. The Guangzhou Opera, designed by Zaha Hadid, was like a pair of heavenly boulders of the Pearl River from a distant past, carrying a touch of poetics. Some of the plastic forms were reached out for the skies, and some was formed into roomy shapes. The interior and the exterior were consisted of juxtaposition. In fact, all forms were echoed with each other. Zaha Hadid’s architecture was a string of bionic patterns generated with parametric software. These forms did not exist under the traditional thinking of linear geometry. Complex, organic and dynamic architectural forms were allowed and enabled in non-linearity for a harmonious coexistence of architecture and the environment.
figure 2.4.3.a Aquatics Center in Olympic Park(Zaha website,2012)
figure 2.4.3.b Guangzhou Opera House (Zaha website,2012)
figure 2.4.3.c Performing Arts Center(Zaha website,2012)
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2.4.4 Non-Linear Working Process Non-linear working process was the research topic carried out by Cecil Balmond in the Nonlinear System Organization, University of Pennsylvania. In the past, design prints were handed out by designers to structural technicians for calculations and then the designs were submitted to architects for modifications. However, Cecil Balmond believes that structure and architecture should be considered at the same time in the architectural design process. Powerful computing capability could handle the bionic structures and systems and process the rules behind. Bionic architecture was the structural creation of algorithms in the context of mechanics of materials. Cecil Balmond, was influenced by swarm theory and fractal theory and applied the algorithms of structural systems in his architectural design and structural analysis. Each piece of architecture was a unique living being. Serpentine Gallery, the interwoven white lines and glass structures, was a product of systematic algorithms developed by Bauman. Cecil Balmond was indicated that the structures of all beings, as well as tissue insides, were the product of ancient algorithms and carrying the memories of survival laws. Since the distant past, the nature and the universe have been constantly evolving its rhythms and workings. This was how the order of structures comes into existence. These concepts were underpinned in Cecil Balmond’s philosophy. Captured the stable status amid disabilities from lattices, mathematics, extended lines and the power of two and created many novel structural forms with amazing dynamics were his primary objectives. Structure was architecture in the view of Cevil Balmond. Geometric patterns were generated with some rules of lower levels. The above concepts were converted by those non-linear shapes and forms of non-right angles into corresponding pattern algorithms. The architectural space was generated by the powerful computing capacity by connecting units (cells and modules). In this process, structure and space were interrelated. The computed patterns were like organic bodies.
figure 2.4.4.a Grotto and Excavation by Cecil Balmond
(Tooling,2006)
figure 2.4.4.b Experiments:Subdividing Space(Tooling,2006)
figure 2.4.4.c Experiments:Subdividing Space(Tooling,2006)
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Chapter 3. Non-linear related parametric software
3.1 Parametric Design 3.1.1The definition of Parametric Design 3.1.2 Non-Linear Parametricism 3.1.3 Non-Linear Parametric Urban Design 3.1.4 Non-Linear Parametric Architecture3.2 NURBS Modeling vs. SUB-D Modeling3.3 Software Related to Architectural Parametrics 3.3.1 Revit Architecture and BIM 3.3.2 Parametric Software and Second Platforms 3.3.3 Parametric Analytic Software 3.4 Integrated Design 3.5 Non-Linear Parametric Fabrication
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"Parametrics is more about an attitude of mind than any particular software application." ---Hugh Whitehead,(Elements of parametric design,2010)“Parametric design is such that it is the parameters of a design that are declared, not the shape… Equations are used to represent the relationships between objects. The ability to define, determine and reconfigure geometrical relationships is of particular value.” ----- Mark Burry, (Paramorph’, 1999)3.1 Parametric Design 3.1.1The definition of Parametric Design In 1963, changeable parameters into a Sketchpad system and the exploration of parametric were placed and embarked by Ivan Sutherland in his PhD thesis in computer-aided design. Parametric was a broad concept. A series of parameters was used in parametric design and relations between parameters in creative design. Parameters were the objects that define three dimensions, such as height and diameter. They could also be stored into variables or equations, rather than assigned fixed values. All influencing factors were included in parameters. Some were changeable variables, but others were constant. Parametric models might be about properties, could be names or containing schema. The relationships were defined in between parameters, various conditions and factors. Different virtual models were generated with differing parameters and variables as inputs. Parametric design was defined as the treating of the factors that influence architectural design as parameters and the identification of certain relations. These parameters were organized together with the help of computer programming and software and structured into a parametric model. Some of the factors were changeable such as parameter variables and other parameters were constant. Different outcomes were derived by the change of parameter variables. Parametric design was focus on the illustration of design parameters, rather than design patterns. The relationships in between objects were expressed in equations. Design was no longer the only outcome of one-to-one relationships.Parametric design was a tool and a new thinking method. Unexpected forms were generated and made up the insufficiency of traditional design tools. It could be an extension of traditional design methods, with some crossovers and expansions. Overrule was not necessary for the conventional approach to design.
figure 3.1.a Deformation and parametric changing(after on growth and form,1942)
figure 3.1.b The function of parameters(Drawn by author)
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The defining of parameter rules and relationship process was the parametric design as the foundation. The traditional approach was different where designers determined the forms directly according to specific design criteria. Parametric design was to control the parameter relationship factors that influence design in a dynamic fashion, in order to simultaneously produce, assess and adjust geometric forms in the design process. The greatest potential of the parametric design was the capability to instantaneously process a large amount of repetitive data and attribute relations with computers. In this way, the workflow of architectural design was a dynamic feedback mechanism. The input of changing design criteria was converted directly into the visualized outputs of architectural forms. The criteria of performance could be followed to evaluate and adjust architecture in a real-time manner, rather than simply dictated design forms on the priori factors such as aesthetic constituents. The similar characteristics in between effects and patterns were clearly represented in the derivative systems of the natural phenomena and expressed with the harmonious interactions between bio-mechanisms and environmental changes. The hexagonal unit of honey bombs were an economic and sturdy form-resistance structure. The survival efficiency was supported by individual bees working together in nest building and food storage. The workings of bionic mechanisms were examined and developed by scientists for many functional applications. In the domain of architecture, it was not until a few years ago when the maturing of the tools supporting parametric designs and productions made it possible to integrate the natural modelling concepts, parametric rules and structural generations. The best method to change forms, qualities and quantities was to operate a parametric model. Various thinking patterns and development processes were exhibited in different parametric models. In the design process, designers were able to use a variety of software tools and interfaces to define parameters in different ways. It would be both an opportunity and restriction to designers. Designers were constrained to decide which parameters need to be defined. The definition and change of parameters could be achieved through the design patterns desired.
figure 3.1.c The relationship between primitive and modeling (Digital design media,1995)
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The advantages and the characteristics of parametric design were the systems and parametrics in the design model. Parametric design was a new trend in the wake of post-modernism and deconstructionism. Currently, the applications of parametric design in architectural design could be divided into (1) traditional designing thinking: the input of design results into a computer to create a parametric model; (2) introduction of non-linear thinking: the combination of design tools and moulding tools to create variable parametric models. The former one has been widely used in Taiwan. Design products were inputted into Revit or 3Ds Max for simulations. Parameters could be adjusted and modified. This approach was suitable for architectural drawings that need to be modified frequently. The latter was classified as an algorithm method by some scholars. It was being used by many firms overseas but not popular in Taiwan.
The parametric design application was studied in four categories in this research: 1.Computer graphics Parametric was a tool to identify the appropriate mathematic models. Archetypes without architectural scales were generated with topological relationships. Architects were able to translate abstract mathematic models into spatial ones with graphic expressions of mathematic concepts. Objects were created with mathematics and geometric logics. The mathematic parametric relationships in between geometric elements in the parametric model were controlled by geometric variables to meet with the design requirements. Mathematic equations were deployed and generated by parametric modelling for parametric design for the patterns of mathematic/physical logics. Geometric theories and computer aided modelling were able to work together by parametric design works. The process was simplified to create non-linear patterns and break away from the traditional forms of the Euclidean system. Free curves and surfaces were used by architects in design. 2.Customization of digital fabrication In the past, the inputs were fixed values. However, three-dimensional relationships were defined in parametric design. Different models were generated with adjustment of parameters. As parametric modifications simplified, it was possible to customize industrial products in the information era. In the digital age, customers were no longer satisfied with mass production of modernism. Many industries have started to apply parametric techniques to create personalized products. The attempts in digital fabrication were to apply the principle of parametrics to convert building blocks into architectural units of different patterns. Even though, the design to construction was an integrated process, different appearance of architecture could be customized by the same algorithms.
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3.Data-based design--- evaluation and optimization In the past, parametric design was limited to resolve technical issues or design complex styles. However, new functions such as analysis, simulation and processing of quantifiable factors were built in the parametric models. These parameters were transformed into design. The rules, cases and parameters were included in the parametric design. The simulation function of computers could convert any factor that influences architectural patterns into parameters and transform data into statistics for calculations. Abstract parameters were converted into architectural forms with visual effects. Parameters were integrated for simulations, analysis, evaluations and optimizations. Human brain was superseded by computers to process a large amount of complex data. Parameters were the inputs to facilitate the definition, determination and allocation of geometric relationships in the internal computing mechanism. Another attempt in parametric design was to use morphology of parameters and patterns as a research tool to study design. The fundamental pursuit of architecture was remained the same. However, climates issue was a challenge to both traditional design and parametric design. The solutions and logics were basically identical. Intangible elements such as sounds, light and heat could be converted into parameters and constructed parametric models by computers. Design conditions were built on the basis of inputs and architecture was generated by computer.
4.Visualization of form-finding The concept of “abstract machine” was proposed by Deleuze. The machine was a system in its own right, not subject to the effect of any external forces. Changes could be made with system adjustments. The description function was performed by the input side while the visualization contents were produced by the output side of the machine. The process of architectural design could be converted into an abstract machine to process the relationships in between elements. The variables that influence architectural design were entered into one end of the machine. Architectural forms were generated automatically by the other end of the machine after processing these variables. Parametric models were the “abstract machine” in the words of Deleuze. Parametric design was about rule setting or logic defining. It was translated from architectural issues into logic problems, or issues describable with programming languages. It was a new way of thinking to code logics into computing languages. Algorithm language and variable parameters was used in parametric design to convert the modeling process into programming languages by architect. In other words, the traditional “black box” process of form finding was describable programming languages now. The description of computing languages sheds light to the hierarchical relationships of factors that were under consideration of designers. Parametric design was the process with which architects used to leverage power computing as an abstract machine to process massive and complicated issues. Parametric was defined relationships and form derivative ones. It focused on relationships and rules about forming, rather than forms themselves.
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figure 3.1.d The function of parameters, and the application from parametric modeling(drawn by the author)
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"Parametricism "as a new global style for architecture and urbanism. Challenging Le Corbusier's celebration of the orthogonal. " ----Patrik Schumacher (Digital Cites,2009)
3.1.2 Non-Linear Parametricism Patrik Schumacher, a partner in Zaha Hadid’s firm, published his statement of parametricism as a style after years of research and experiments in the Architectural Association School of Architecture. It was a geometric structuring method based on non-linearity and relations. Digital tools and scripts were applied, and parametric operations with logics were performed in order to generate design prototypes in time. Modernism was about the forming of modern architectural language with basic geometric shapes, such as cubes, spheres and cones, advocated by Le Corbusier as architectural prototypes. Design forms were determined by experience. However, parametric was transformed from basic geometry into BLOBS, NURBS, and other parametric units, and redefined aesthetics of the parametric era. Modernism was anchored on the foundation of straight lines; whereas parametric was transformed into irregular forms. The irregular patterns could be the next millennium under the guidance of complex sciences. Modernism of the 20th century was about heroes. It was the era for masters such as Le Corbusier, Louis Kahn and Frank Lloyd Wright, to purse the architecture of balance and harmony. At the end of the 20th century, post-modernism was emerged as criticism against modernism by emphasizing asymmetry, non-harmony, fractions and segmentations. De-construction was redefined architecture from a philosophical point of view. Non-linear parametric architecture was an extension of post-modernism and de-constructionism. Non-linearity was a new thinking. Complex sciences and new perspectives were described and provided. In the past, it was difficult to visualize non-linear architecture. However, computers became a new platform and provided a new technology for designers to apply new design techniques. Parametric would be a new tool for designers when computing technology advanced further. Computers were the platform for designers to realize non-linear concepts.
figure 3.1.2 a,b,cParametricism as a style applied in cities,such as Kartal-Pendik Masterplan,SineCity(Digital Cities,2009)
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3.1.3 Non-Linear Parametric Urban Design Urban design of modernism was primarily on automobiles. A square network was formed with both vertical and horizontal lines. The arrival of digital and information age were contributed to two design models. First, data of the information age was used but urban design was performed in the traditional manner. Second, design tools and thinking were integrated, starting from conceptualization. The orthogonal model was challenged.
Xu Weiguo, was attempted to parametric urban design. The parametric variables were examined in urban design such as environment, climate, traffic of people and vehicles, functionality and organization.[Xu,2009]. A feedback mechanism was established. Scripts were written with programming languages. The relationships between parametric variables were reflected in the mechanism. Design was optimized with changes to parameters or design adjustments. Design concepts and software tools were integrated. A dynamic equilibrium was achieved through the check-and-balance among parametric variables. This process produces a virtual model by articulating abstract logic relationships.
Neil Lynch, in his design of swarm urbanism, multi-agent systems were allowed to change the nature of urban hierarchy. The hierarchy in the design process was left out. All the elements in urban organization were treated as process agents, interacting with each other in a continuous system without design hierarchy. Swarming was tending to happen spontaneously from the macro level. [Neil Lynch,2009]
figure 3.1.3 a Wool-thread model to comppppute optimised detour path networks (Digital Cities,2009)
figure 3.1.3 b digital breeder for designing cities(Digital Cities,2009)
figure 3.1.3 c non-linear integrated urban design(Digital Cities,2009)
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3.1.4 Non-Linear Parametric ArchitectureNon-linear architecture was a trend and architectural pattern. Parametric was a technique and methodology. Non-linear architecture was a liquid form, based on the analysis of architectural functions and surrounding environments. The process of architectural design was the study of all the factors that influence architecture. These factors were extracted and synthesized, in order to develop images from concepts, and ultimate generated architectural forms. As these factors were highly complex, architectural forms were expected to be irregular. In fact, architectural forms were the outcome of design and research, as well as the product of analysis and development. Such forms should offer the required functions and adapt to the environment. Liquid, non-linear forms were generated with the help of computer software. In other words, a solid foundation for the creation and development of non-linear architecture was laid by the computers. The exploration of non-linear architecture was a reflection on the non-linear scientific theories (complex scientific theories) starting in the 1960s. It was inspired by fuzzy theory, Chao’s Theory, dissipative structure theory and non-standard mathematic analysis, and armed with the decentralization theory and philosophy developed by Deleuze, a philosopher in the 20th century. However, the most critical technique was to resolve a variety of complex issues with computing power, such as the analysis of parameters, the examination of graphic systems and the generation of architectural forms. Non-linear parametric design made the traditional black-box of conceptualization a tangible process. An analysis was performed on the list of factors that influence architecture in order to identify relationships and rules. The relationships and rules were described in computers in order to construct parametric models. Changes to variables would affect the relationships in between variables and derive multiple solutions. This leads to structures that were dynamically stable. The designed pattern, at any given juncture, was the frozen frame of a dynamic pattern in certain stages of the process. It was a reflection of the relationships in between factors. As such relationships were non-linear, the patterns would have been liquid, complex and non-linear. The non-complexity of architecture was mirrored by architectural prototypes. Non-linear parametric design was mainly on the generation of process design such as the interactions of parametrics that influence design. Architectural forms were emerged in the process of analysis and research. The resulting architecture was the transformation of this process. It was a bottom-up design approach. The results were unique and no imitation or duplication was existed. Non-linear parametrics were known for richness, diversity, openness, dynamics and imbalance. In the early days, a lack of sufficient technologies made it difficult to achieve non-linear architecture. Powerful computing and forming capability of the latest development of computers was able to gernerate non-linear architecture. New aesthetics were created by decentralised, relevant, layered, learned from nature and bionic, and non-linear architecture. Parametric design was the transformation of the black-box of conceptualization and form-finding into describable computing languages. The relationships between parameters were established with design software via information inputs, analyses, form generations and rule mimicking. A system consisting of a series of complex rules was established by following a bottom-up logical framework. The construction of rules-based parametric models was the form-finding process for designers. In the 1960s, complex sciences were established, the theories were applied by some architects to change design methods. However, such efforts did not bear fruits due to a lack of effective computing tools. It was not until the late 1990s, the scientific approach to architectural design was engulfed quickly around the world due to the development of computer technologies.
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3.2 NURBS Modeling vs. SUB-D Modeling
Digital surface modeling is closely related to and modeling logic. The most widely way used to describe model is Polygon and NURBS. Both model ing methods have advantages and disadvantages. The development of polygon modeling is longer than NURBS, and Polygon used more frequently in 3D modeling software, especially in the CG field. The NURBS modeling use mathematical geometric principles, it can describe surface or brep which created from curves precisely, so it always applied to the analysis and CAM system. There are several reasons for why NURBS will be conducive to CAM, as follows:
1 The way NURBS calculated is more stable.2 The flexibility of adjusting one point can adjust the entire form.3 Precisely function of the mathematical and geometrical calculation tool.
figure 3.2The difference between NURBS and Polygon Modeling(drawn by the author)
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3.3 Software Related to Architectural Parametrics
Parametric software was existed for a while. However, Alias and CATIA were targeted at industrial design in the early days. Architectural design was still about two-dimensional software. Digital architectural development and digital design software were highly related. Recently, architectural parametric software has been developed. With constantly evolving software, the possibilities of new forms of architecture were explored by architectural designers. It was a new platform for digital designers to work with. This section was divided parametric software into parametric modelling software and parametric analytic software as follows:
Parametric Software and Second Platforms
Parametric SoftwareParametric modelling software could be further divided into two types: one was equipped with parametric modelling features and the other was able to address parametric design on a second platform. Generative Component, Digital Project and Revit were included in the former one. 3Ds Max+Maxscript, Maya+Mel, Rhino+Rhinoscript and Rhion+Grasshopper were included in the latter one. This research was focus on its discussion on Rhino+Grasshopper, a graphic and open platform, and examined its influence in the following section.
Second Platforms Second platforms were in relation to modelling software. They were parametric relation platforms developed for modelling software. Scripts were used for modelling edits to improve design efficiency and logics. In fact, script instructions were used to create models frequently in parametric models. Most under development second platforms were targeting at graphic editing software. The modelling process and the relationship between parametric variables and models were able to be recorded. It could be achieved with two methods. The first method was to generate digital drafts in the process of model scripting over second platforms of the modelling software. Different models could be created by using differing parametric variables. The second method was to build the model with the modelling software and import data to second platforms for detailed design. Surface could be decomposed to generate surface design in details. As a result of the growing popularity of modelling software, the integration between second platforms and modelling platforms was also increasing. It was able to help designers to create more digital forms. Parametric design was no longer a tedious programming but a valuable and user-friendly tool for most architects.
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3.3.1 Revit Architecture and BIM Revit Architecture was the Building Information Model (BIM) three-dimensional parametric design software developed by Autodesk for the architecture industry. It was three-dimensional digital modeling that gathered all the information concerning engineering aspects and allowed for an integrated approach from design to construction. In other words, it was about coordination within a three-dimensional model. In Revit, all the information required by designers was saved on the .rvt file. Floor plans, elevation drawings, section graphs, materials and other information were generated simultaneously in the model. Any adjustment to a single parameter would change the information in the model. Manpower costs were reduced from modifications. BIM was a revolutionary method and a new design technique. The way people think was changed. Five features were provided by BIM: (1) it boosts productivity of firms. (2) It facilitates learning. BIM solutions work in the desired way for architects and engineers. (3) It enhances high-efficiency workflows and consolidates low-efficiency workflows. (4) Project owners, subcontractors and designers benefit from BIM. (5) It reduces design errors and supports the communication and coordination between project members. Parametric design was also the important feature of Revit Architecture. Parametric graph elements and parametric modification engines were the two components. In Revit Architecture, all the graph elements were components, defined with a series of parameters. All the information of graphic elements was preserved as the components of digital architecture. Users were allowed to make changes with the parameter modification engines to any part of architectural design by changing other information at the same time. For example, if the location of stairs was changed on the floor plan, the relevant information regarding the stair location would be changed in the section graphs and detailed design charts. Two-way communication was a very important feature of Revit. Meanwhile, the concept of families in Revit Architecture was marked a start contrast with other modeling software. Basic graphic units was called as graph elements in the design process for Revit Architecture. Walls, doors, windows, texts and sizes were all graph elements created under families. Families were the fundamental concept of modeling. They could be stored together with project documents, or independently and shared with other projects. Many parameters of the families could be adjusted freely. The information of graph elements regarding sizes, materials, and locations were recorded as parameters in a given project. The greatest advantage of Revit Architecture was the developer Autodesk owned many software packages. Revit Architecture was their current product specifically catering to the architecture industry. In the past, 3Ds MAX or MAYA could not yield accurate outcomes. The useful features of other software program were incorporated into Revit Architecture by Autodesk. For example, the analytical function for environmental physics in Ecotect was being duplicated in Revit Architecture. Meanwhile, the company was also developing parametric platforms similar with grasshopper. The Revit Architecture was expected to become even more powerful.
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3.3.2 Parametric Software and Second Platforms
1. 3Ds MAX and MAXScript The modeling of 3Ds MAX was used for both NURBS and Polygon, but Polygon was considered to be more powerful and popular. Polygon was being used by many Taiwanese firms for modeling, rendering and animation. Polygon and AutoCAD were developed by Autodesk. It was also a tool for graphic presentations in later stages in the process of architectural design. However, it was known as a powerful tool for rendering and animation. MAXScript was the embedded script language in 3Dx MAX. According to the official website, the following functions were provided: (1) script-ability of different commands such as modeling, animation, materials and rendering; (2) cross-control over 3Ds MAX with commands over shell windows; (3) software packages to write scripts in self-defined tool bars or modeless windows and provide standard 3Dx MAS interface; (4) use embedded documents I/O to build import/export tools according to definitions; (5) scripting of program controllers for the status of the entire sites such as the deployment of batch tools and batch rending scripts; (6) the use of OLE automation and real-time links with external systems. However, its interface for scripting and programming was not considered friendly for architects without programming skills. The majority of MAXScript users were engaged in the modeling for animations.
2. MAYA and MEL MAYA, developed by Alias, was renowned for powerful functions in modeling and rendering mainly for special effects in movies and animations. In architectural design, MEL was often used in parametric design, in addition to model production and rendering during later stages. MEL, the built-in programming language of Maya, was the corner stone of Maya. Virtually all the features over the Maya interface were built with MEL instructions and script programs. As full support to MEL was extended by Maya, users could scale or assign Maya. It was possible to further develop Maya with MEL to be a unique and innovative environment for projects. Master MEL was not required for users to effectively use Maya. However, the familiarity of MEL could improve professional skills with Maya. MEL could be handled by users with little or no programming experience. Fans of MEL did not necessarily enjoy programming. There were ways of leveraging MEL without worrying about programming details. If generate MEL scripts was attempted by the user, MEL could provide the most advanced digital graphic methods. (1) MEL instructions were used for Maya interface to quickly generate hot keys and delve into issues. (2) The interface of MEL in MAYA was complicated for architectural designer to transform design thinking logic to parametric model. (3) The definition of the specific scenes was to change the setup of a missing device. (4) MEL programs were generated to execute the scripted programs for modeling, animation, dynamics and rendering.
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3.Rhinoceros/Rhinoscript or Grasshopper Rhinoceros was a NURBS 3D modeling software program developed by Robert McNeel& Assoc. It was frequently used for industrial design. However, it was being used as a platform for software sharing and a major program for architectural design. Rhinoceros was the first program to introduce NURBS modeling into CAD. Although it was positioned as an industrial design tool, Rhinoceros has been widely used in architecture. This was because it offered a large variety of plugs for architectural design, such as Grassshopper and RhinoBIM. Rhinoceros was known for its capacity in surface shaping and RhinoScript as a parametric design platform. It was regarded as a powerful tool for the expression and exploration of new architectural forms. Various large firms such as Zaha Hadid, Peter Cook and Foster+Partner, were leveraging the great surface shaping capabilities and key features of the parametric design platform to create unique designs.
Characteristics of Rhinoceros:1.NURBS modeling accuracy: Rhinoceros modeling was backed up with precise data, and regarded as ideal for industrial design. In the context of architectural design, the generated model could be interchanged with other software programs or sent to vendors directly. NURBS’s features in dealing with curves such as SWEEP, REVOLVE, LOFT and BOOLEAN, could create many bizarre surfaces. 2.Simple modifications: History was able to be recorded in Rhino. Undo and Redo features were included for an unlimited number of times. It was combined with Rhino modeling function to make model modifications quick and easy. Work in conjunction with other plug-ins was possible to enable model modifications. 3.Format interoperability: Rhino was considered as a great platform for compatibility with various file formats. Many large firms were used it to leverage the format interoperability of Rhino for file transfers and modifications. Interchange work with other software was simple. 4.Parameters and platform scalability: Even though Rhino was not considered powerful, designers were allowed to develop different plug-ins to customize the parametric software. Rhinoceros was regarded as the most convenient platform for parametric design. For example, The rendering function of Rhino was limited, but many plug-ins such as VRay and Flamingo were available to enhance the features. Thus, Rhino was provided with great rendering support.
Rhinoceros and RhinoscriptMany scripts for choice were offered in Rhino. Rhinoscript was a programming platform based on VBScript. It was a VBScript-based modeling method. There were pros and cons in Rhinoscript and Grasshopper. Rhinoscript was difficult to use without language knowledge. In fact, commands were written to offer greater flexibility than applying cells. Scripting was highly relevant to strings and built-in commands of Rhino. Compared to MEL, the programming language of Maya, VBScript was not complicated.
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Grasshopper As an important editing plug to Rhinoceros, Quest3D was used in Grasshopper, a virtual realization program as a visualization editing tool. The hard-to-learn programming languages were converted into an arithmetic unit. It was connected linearly with editing arithmetic units by logical inferences in order to generate relatively complex models. Although Rhino opens up the scripting function of Rhinoscript, the scripting was complicated, particularly for those who have no knowledge in programming. Many logic and programming codes were tedious and challenging. The complexity of programming languages was reduced and considered an important parametric tool in META-design by Grasshopper.
1.Visualization of node logics: The programming languages were packaged into arithmetic units, the linear arrays of these units were highly related to the logics behind them. The thinking in a black-box was visualized with the connections of arithmetic units. The complexity thinking of the designer was clearly presented. 2.Real-time and dynamic adjustments: In the process of making adjustments to arithmetic units in SLIDER, any changes with inputs would lead to visible results to outputs throughout different stages over the RHINO interface. Different from script writing model, the most updated calculation result was presented by Grasshopper atomically in the event of changes to any given parameter. 3.Statistical modelling: Grasshopper was used statistics as center, by converting modeling thinking into observable mathematic expressions. The unlimited possibilities were provided by accurate computations and efficiency power. 4.Proposal reviews: The logics behind design were clearly stored and feed-backed with complete statistics. Designers would be able to access digital drafts and explore all possibilities by changing parameters. 5.Developability: Grasshopper was a plug developed with high-level programming languages. Users were allowed to define and expand functions with high-level languages. Meanwhile, arithmetic units for users to work with VB.net or C＃ languages were provided by Grasshopper. Rhinoceros was a software platform, whereas grasshopper was a platform for programming. They were worked together to make borderlines design possible.
figure 3.3.2 a grasshopper interface,convasfeedback from other software immediatedly(drawn by the author)
figure 3.3.2 b the icon of code made designer generate form easily(drawn by the author)
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f igure 3.3.2 c the design process of Generat ive Component(https://workshopsfactory.wordpress.)
f igure 3.3.2 d the design process of Generative Component(https://workshopsfactory.wordpress.)
5.Generative Component Generative Component, often abbreviated as GC, was the computer-aided design software developed by Bentley System. A three-dimensional model was enabled in parametric process to become an architectural model. It could be stored in any format. For example, DWG files into Autodesk or, Rhino, BIM model into Revit. With the help of powerful computing capability, the creativity of designers would be able to present their idea precisely into sustainable architecture. Various shapes and experiment were able to generate with innovative materials and components. GC could convert information quickly, even in a complex model. Designers were allowed to make edits in an intuitive manner, and explored all kinds of possibilities, without the hassle of programming languages or scripts (as in the case of a second platform). It was possible to deform a control unit such as cell by air pressure manipulations and result in a cross-the-board change of shapes in the prototype system. The cells were implanted to the sites according to different context conditions. Basically, shapes were varied along with the changes in the environment and applications. Parametric design in this project was mainly on the geometric layout of prototype units. It was a popular way of breaking the whole into units for the processing of complex surfaces. The relationships between parametric were maintained through the mesh of surfaces and sketchup of units. In other words, the shapes were adjusted automatically by the units of prototype based on the varying sizes of individual frames and meshed surface to fill up all the frames. In this process, a series of restrictive conditions were able to incorporate into control the rules regarding surface meshing by designer, or simply standardized prototype units to a certain degree. The parametrics were possible to set up the parametric relationships between inputs and outputs in the processing of complex forms. Designers were given an accurate control platform for modeling to bring design from visual and intuitive to rational, quantitative and economical. GC was a second platform with many embedded parametric setups. GC parametric could be divided into two parts generally. The first part was about surface creation with dots and lines. The second part was detailed meshing of surface. It was fairly similar with the working of paneling tool, as Rhino’s second platform. After surfaces were generated by Rhino, the surfaces could be changed on a paneling tool or grasshopper. Also, the visual interface of Rhino was user-friendly compare to GC.
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6.Digital Project Digital Project was the software program developed by Gehry Technologies Building Information Modeling (BIM) on the basis of CATIA. It was used by many top-tier architects and engineers, such as Zaha Hadid and Frank Gehry were adapted in fluid architecture for the most complex and creative design. The CATIA functions not required by architects were eliminated and optimized the features by the Digital Project needed by architectural designers. The powerful BIM functionality was boasted but cost a lot less than CATIA. Sub-D function was provided to enable the production of a rough model. Crease, filter, and streamline a model were included in the divide-into-pieces function. The complete life cycle was covered from project management to construction. The proposed Marks Barfield Architects was based on the concept of the design team. The main feature was the surface and structure generated with Digital Project. A master model was generated by sketch-up first.Main branches were divided into sub-ones and further separated into twigs. The ends were reached out to the roof and converted into the fences of the rooftop garden. The shortest line between two points was represented by the curve components on the surface. Meanwhile, the information required for the evaluation of traffic, evacuation and exhibition space was fed into the master model. The patterning parameters were adjusted and divided into eight individual units. Parametric relationships were assured that all the surface lines automatically update along with pattern changes. Next, the reasonable size of the structural members was calculated and fed the information to the master model by structural engineers for further improvement of the curve components. However, the overall scale has to cut back due to budget overruns. At this juncture, structural principles were modified and façade components were ornamental. These changes were simple because relevant control parameters were already pre-determined in the model. The design task was completed in Digital Project by offering powerful modelling functions. The modeling logic of Digital Project was similar with 3Ds MAX and MAYA.However, powerful BIM functionality was offered to make model modifications quick and easy by manipulating parameters. The CAD graphics were accurately produced, in order to making engineering and construction being completed at the same time. As CATIA was the operating system, it was difficult for architects to maneuver the modeling interface. This was a challenge in Asia where projects were scheduled for completion in a short time. As a result, Digital Project was used in large international projects only.
figure 3.3.2 f,g,h Marks Barfield used fractal theories generating structure in Digital Project (http://www.marksbarfield.com)
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3.3.3 Parametric Analytic Software Architectural analytical software can help designers to simulate and analyse physical environments and building structures. This type of software programs is relatively weak in modelling but strong in simulations. It allows designers in decision making by tapping into physical information.
Autodesk Ecotect Ecotect is a software program focused on design in the context of energy efficiency. It analyzes multi-dimensional and intuitive graphs. In addition to a friendly interface for three-dimensional modeling, Ecotect also provides a wide range of analytical and simulation functions. Ecotect, an eco-building evaluation software program, explores green design by experimenting with light, sounds, heat, air and visibility. Its user interface is friendly, and compatible with SketchUp, AutoCAD and Revit Architecture, modeling software frequently used by designers. Computational fluid dynamics, usually abbreviated as CFD, is one of the most important branch of fluid mechanics in twenty-one century. CFD uses numerical methods and algorithms to solve and analyze fluid flowing problems. CFD most basic consideration is how to deal with continuous fluid with a discrete manner in computer. The solution is discretizing space region into a small cell to form a three-dimensional grid or lattice for applying the appropriate algorithm to solve the equations of motion. In the past, engineers used experimental methods and theories to assist in the analysis and correction, the way they used is not only time-consuming but also expensive. Now CFD methods have been widely used in the design and the development of technology. Compared to the traditional way, using computer simulation to aid design is more efficient. Computer simulation system can quickly report the information CFD produced, designer can improve performance according to the response. In urban design, CFD simulation provides the designer a new basis to arrange building configuration. The beginning of the space layout in urban design will determine the building ventilation in the ultimate. In parametric model, data will transfer from modeling software to analysis software immediately,
figure 3.3.3a CFD Simulation in Rhino(http://www.a-ngine.com)
figure 3.3.3b Immediately solar radiation analysis feedback(drawn by the author)
figure 3.3.3c best orientation(drawn by the author)
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Structure Analysis System and FEA Finite element analysis (FEA) is often known as The finite element method (FEM). Finite-element analysis is an experimental and analytical method in algorithm ,which is an approximate solution of boundary value problems for engineering. FEA is a numerical technique for solving numerical solution of differential equations or integral equations. Take flexural of Beam for example, boundary condition is associated to the equation.[Lee,2009]
I
In structural systems,we use FEA to analyze stiffness, truss structure system, flexure elements. In mechanical engineering, design drafting has already combined with structural analysis. FEA plays an important role in CAD. But in architectural design, architects gave architectural modeling to structure engineer for FEA analysis after designing. Now, we can transfer parametric model data to structural analysis software such as GSA immediately. According to the value in feedback, designer can take structure system into consideration in the design process. In FEA system, we need to we need to follow three steps,1 Pre - treatment 2 Solving 3 Post-processing. Pre - treatment is defining the analysis model three condition, Geometry, Load and Boundary condition, then the function of automatic mesh generation will generate mesh. Solving are establishing model system according to the definition of analysis and responding. Post-processing is graphically outputting the results, in order to facilitate the designer read directly.
figure 3.3.3 d,e,f FEA in GSA,
Immediately structural analysis feedback with different radius and shape of column(drawn by the author, followed the tutorial on Geometry Gym website.)
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3.4 Non-Linear Integrated Design Software EcosystemMany software programs, such as 3Dx MAX, CAD and Maya, were incorporated parametric design. Advantages and irreplaceable features were built-in in the program. In fact, it was difficult to rely on a single program to meet all the requirements of parametric design. The design process was covered with analysis, design, and simulations, and it was encompassed with statistics, computing and digitalization. Statistics were calculated by different programs to assist and evaluate the realization of design. Multiple programs were used at the same time for majority of the firms such as Rhino, Grasshopper, 3Ds Max, Ecotect, SAP, Geometry Component and CATIA. Excel, as an intermediate tool and a database program, facilitates data exchanges and collaboration across different software programs. The software ecosystem was consisted in the program to provide data to another program for analyses or simulations. Feasibility and accuracy were enabled in the design.
Traditionally, architecture design consists of six steps: (1) planning & design; (2) drawings; (3) initial design; (4) detailed design; (5) site drawings; (6) construction. In Taiwan, computer graphics were frequently used for steps (4) and (5), but rarely for other steps. In other words, computers were used often when the design has been decided. Computers were generated graphics and presentations which resulted in two phenomena. (1) Capacities of computers were not maximized. Graphics and presentations were a small part of their functionality. Majority part of the computing power and analytical ability was left out. (2) The discontinuity of digital design was observed. As computers were used to generate graphics and presentations only, the whole design process was disconnected.
figure 3.4 a Integrated different software’s,finding possibilities for evaluating the performance of a design (http://www.utos.blogspot.tw/)
figure 3.4 b, Non-linear integrated archietctural design process(drawn by the author)
Integratedarchitecturaldesign
CFD
SOLAR
MATERIAL
FORM
STRUCTURE
BUDGET
FLOOR AREA
SOUND
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Non-Linear Integrated Design The era of BIM was the integration of architectural information systems by combining all the architectural information into one file. All the relevant information was changed when any modification applied on any single parameter, but the integration was not affected until the architectural information at later stages. Since the ancient past, architects were required to take into account all the relevant factors in architectural design. Architecture was the synthesis of all interrelated sub-disciplines such as architectural structures, environmental control of building physics, architectural design and site planning. In the era of digitalization and information, integration was not only gone beyond the information within architectural models, but also encompassed architectural thinking. A platform was offered in the Grasshopper for designers to create plug-ins as required by tapping into the knowledge base of all the users around the world. Different plug-ins was created for the analysis of structures, light and shadows, or transmission of parameters to relevant software like Ecotect, GSA and SAP200.
Algorithms were more than just enabling forms not manageable with human hands. Calculate the parameters were considered by designers from conceptualization and detailed design to form-finding. They were parameter inputs and outputs with a form of artificial intelligence to create desired forms by designers. It was more than just about modelling. It was covered design thinking to construction. A closely knitted network was formed by multiple software programs combined together. Parametric was travelled in between programs in various formats. Non-linear integrated design was strived to convert a long list of design considerations into changeable parameters.
figure 3.4 c,traditional linear archietctural design process(drawn by the author)
site analysis
concept+diagram
preliminary design
detail design
Working drawing
Structural system
Environmental Control
Practical construction
Equipment System
conceptual design
architectural design
evaluationsimulation
construction
feedback
Architect
Architect
Professionalengineer
Linear Construction system
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3.5 Non-Linear Parametric Fabrication Building fabrication was an issue of importance since distant pasts, for nomadic tribes and agricultural settlements. Natural materials were used by the ancestors for shaping and forming, and building shelters from rain and wind. As a result of scientific advances, fabrication techniques and methods were evolved from random stones to modularized brick work, and to large-scale precast concrete. Materials were modularized and mass-produced. Fabrication was being a procedural. Computer-aided design (CAD) was started to influence design. CAD was faster and more efficient than traditional process. Architecture was redefined as a profession with a history of thousands of years.
Tools were closely related to thinking. Impacts were profound on design conditions and methods. CAD was no longer just a design tool. It was being a thinking philosophy and a platform for designers to communicate with computers. CAD could be divided into two aspects: thinking (conceptualization) and doing (operability). Issue clarifications and development of supporting tools were emphasised on the former one. Practical issues of design were highlighted in the latter one such as the application of existing computing theories or tools to stimulate creativity. (Prospects of Digital Architecture, Chiu Mao-Lin)
CAD/CAM was an important tool for industrial design and engineering, particularly in the automobile industry and the aerospace industry. Digital graphics was used by architects for more than three decades. The two-dimensional graphics were faster and more efficient by CAD. Editing was easy and simple. Although the graphics interface was shifted from manual to digital, architectural design was remained basically the same. However, when CAD was being three-dimensional, not only three-dimensional model and rendering features were provided, but also powerful thinking and possibilities of forms and constructions were formed.
With the development of CAD/CAM, digital media was being part of architectural design and fabrication. It was a new method and a new thinking. Designers were given a wide range of tools for assessments. In the past, computers were used to assist in representations of design. This paper examined whether CAD/CAM enables parametric design and empowers new possibilities in fabrication.
figure 3.5 b,Robot CAM with brick wall(Digital Fabrication,2010)
figure 3.5 a, Customization of BLOBS in CAM(Digital Fabrication,2010)
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figure 3.5 c, Sectioning(Digital Fabrication,2010)
Architecture design was relied on computers, throughout each stage of the process, from conceptualization to fabrication. Architects or structural engineers was started to use software such as three-dimensional modeling and visualization, generative form finding, scripted modulation systems, structural and thermal analyses and file-to-factory production. Digital fabrication was often the final step of the process. It was a method to control fabrications by digital data and construct or cut modules with CAD/CAM. Digital media and new technologies were grown rapidly. Architecture was delivered information by representations and constructions. Forms, space and materials were able to convey messages. A design revolution was started and leaded by digital fabrication to many inventions and innovations in architecture. In "Translation from Drawing to Building", Robin Evans indicated that in the traditional approach, architects were required to separate inevitably for the processing of graphs, design materials, construction and structural components. [Lisa,2010].Digital fabrication was presented by a new opportunity, by linking up all these processes. It was a productive media with limitations and possibilities. Reduce the gap between representation and building, and bridges design and fabrication were possible in digital practice. Imaginations and innovation were executed by the new generation of designers with digital design and fabrication. In the past, digital design was mostly on forming and rendering effects. This paper was argued that digital design redefined practice through the design and fabrication process. Do-It-Yourself attitude and experiments were fostered with new technologies and experiences. Digital fabrication was started in a small scale, as a vehicle to apply parametric design and re-think about design. Lisa lwamoto, in “Digital Fabrications”, was divided digital fabrication methods into five categories: sectioning, tessellating, folding, contouring and forming. Sometimes, only one method was used. Sometimes, multiple methods were applied in design.[Lisa,2010] detailed design to form-finding. They were parameter inputs and outputs with a form of artificial intelligence to create desired forms by designers. It was more than just about modelling. It was covered design thinking to construction. A closely knitted network was formed by multiple software programs combined together. Parametric was travelled in between programs in various formats. Non-linear integrated design was strived to convert a long list of design considerations into changeable parameters.
figure 3.5. f,Forming,P-wall(Digital Fabrication,2010)
figure 3.5. g,contouring,bone-wall(Digital Fabrication,2010)
figure 3.5 e, Tessellating,Puppet theater(Digital Fabrication,2010)
figure 3.5 d,Folding, C-wall(digital fabrication,2010)
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Chapter 4 Non-linear related mathematics
4.1 Mathematics and Algorithms 4.2 Mathematic Logics and Geometric Orders in Algorithms 4.2.1 Cellular Automata 4.2.2 Dynamic Relaxation 4.2.3 Voronoi 4.2.4 Hyperbolic Geometry 4.2.5 Homology 4.2.6 Weaire–Phelan structure 4.2.7 Fractal 4.2.8 Minimal surface 4.2.9 Metaball
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“An algorithm is a very specific set of instructions for carrying out a procedure that generally includes an instruction to stop.""A computer always means to activate an algorithmic procedure that transforms input to output. In architecture, this means formalizing the design process a set of procedures and specific instructions. " ---Jane burry+ mark burry(Scripting culturies,2011)
4.1 Mathematics and Algorithms
AlgorithmsAl-Khowarizmi, a Persian mathematician of the 9th century, was the first person that came up with the term “algorithm”. Algorithms were defined as the programs or equations for problem solving. In the field of mathematics and computer science, algorithms were referred as the programs that resolve mathematic cycles. Each computer program could be deemed as an algorithm. Whether algorithm equates to non-linear parametric design was still open to debate. The author believes that parametric modelling was one type of algorithm modelling. However, algorithm was not the same as parametric modelling because parametric modelling was based on algorithms. In fact, algorithm was a new design method in architecture after the birth of computers. Algotecture, algorithms in architecture, was an emerging architectural science in the age of computer. Computers were used by architects in parameter setups by a series of computer programs similar with the process of gene encoding. The process of geometric forms and export relevant graphs were described in algorithms through mathematical formulae. The results were architectural models. The development of algorithms was to generate the rules concerning form generations, and not about the forms themselves. It was created in dynamic and irregular forms not manageable by human brains or hands. Algorithm was also known as meta-design or generative design. Algorithms were referred as the tangible steps and methods to accomplish a task. Given an initial status or data inputs, algorithms was able to produce the final status or outputs as required or expected. Repeated steps or certain comparison/logical judgments were included. Different algorithms might achieve the same task within different timeframes, in different spaces or with different efficiencies. The quality of an algorithm could be measured with spatial complexity and time complexity. In architectural design, Algorithm languages and variable parameters were consisted and generated a set of rules and arithmetics to calculate changeable results. Architects control design was not directly related to results but through the determination and judgment indirectly over rules. They were not only operated with shapes, but also with rules to generate shapes by generation process and description techniques.
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The definition of algorithms was given by Donald Knuth in his book, “The Art of Computer Programming”:
1.Inputs: An algorithm must have one or more inputs. 2.Outputs: An algorithm must have one or more outputs. Outputs are the results produced by an algorithm. 3.Certainty: The description of an algorithm must be free from ambiguity, in order to assure the execution results can accurately meet requests or expectations. Usually, executions are required to produce certain results. 4.Definiteness: According to Alan Mathison Turing, an algorithm is a string of calculations that can be simulated with a complete Turing system. In contrast, the Turing machine only has a definite number of statuses, input signs and transfer functions (commands). Some definitions require that algorithms must accomplish a task with a definite number of steps. 5.Effectiveness or feasibility. Algorithms describe operations that can be executed with a definite number of steps, and can produce multiple outcomes. [ Donald Knuth,2005]
Le Penseur discussed the functions of algorithms in modeling in his book "Parametric Architecture with Grasshopper”: (1) automated processes; (2) definition of geometric statuses with mathematical equations; (3) rapid changes to parametric models at the initial stage of design; (4) capability of generating complex models quickly. Algorithms were used architecture to learn from the rhythms of nature. Inspirations were drawn from the study of biological compositions and natural patterns such as Fibonacci sequence, golden ratio, bifilar helix, and bionic structures such as sea shells and tree branches. Adjust the models of space generation was possible in Design rules. Nature was the teacher of art. [Le Penseur,2011]
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4.2 Mathematic Logics and Geometric Orders in Algorithms The whole universe was regarded as a gigantic computer, with each life was created by continuous algorithms from a molecule to an ecosystem. Mathematic models could be found across different aspects of life. It was remained as a mystery how mathematics control the growth of living beings. The double helix of a DNA, the 20 triangular sides of a poliovirus, the number of petals on a flower often in the Fibonacci numbers, growth patterns of plants in L-SYSTEM, animal stripes, spirals and whorls were expressed with Turing equations and coral reefs in the oceans, mathematical models were everywhere in nature. Mathematic principles and weapons of God was expressed beauty in robust logical relationships by following simple but elegant rules. Mathematics was important throughout human history. It was dictated appropriate proportions and angles. The book “De architectura” was written by Vitruvius in two thousand years ago. Universal formulae and mathematic equations were applied by architect to carry the beauty of mathematical relationships in architecture. In the era of Art Nouveau, the logics behind different surfaces were examined and created by Gaudi for a variety of non-linear architectural works. IT technologies and computers in the digital age have strengthened the role of mathematics and given architects a new opportunity to exercise their creativity. Architects conveyed their design with sentimental languages, as well as with mathematic and geometric descriptions. In addition to the geometric world created with mathematics of the 17th century, the thinking of complex sciences was introduced. Mathematics, logics and geometric relationships were abounded in nature. The impacts brought by computers were well documented. The uncertainty was the role of mathematics in this digital revolution. Architecture, same as mathematics, was a dimension of thinking and experience. A borderline where two dimensions meet was emerged. Abstract mathematic rules were used to create architectural space for experiencing. In parametric design, mathematic, logic and statistical relationships were converted by algorithms into visualized geometric models. robust mathematical logics and geometric orders were contained in the nature phenomena from the textures of inorganic minerals, waves of the sea, to organic structures of plants and surfaces of living creatures. The logical relationships behind ecology were examined and created derivative rules by mathematicians such as Voronoi Diagram, Fibonacci number, Lindenmayer System and Cellular Automata. These natural patterns were explored and analyzed the conditions, parametric relationships and dynamic derivatives of these forms, and understand the algorithmic attributes of self-organization, repetition and randomness, and dynamic equilibriums. The modeling software was controlled the logics of arithmetic components, data stream links and geometric relationships in parametric functions. The algorithmic logics and dynamic geometric relationships required for parametric design were obtained through simulated modeling and pattern transformation techniques. Computers and IT technology were experienced dramatic advances during the past fifteen years. The changes to data exchange rules across databases had profound impacts on architecture. The role of geometry in architecture was redefined and revitalized the wonderful possibilities of topology in the new design software and digital fabrication. Parametric design and mathematics, from scripts to technical aspects, biology, genetics and other sciences were all sources of inspirations. The impacts of computers were widely documented. The role of mathematics was less certain in this revolution. The list below was the mathematic concepts frequently used and discussed.
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4.2.1Cellular Automata Cellular automata such as cellular spaces and tessellation automata were a discrete model. The relevant studies could be located in computability theory, mathematics and theoretical biology. It was consisted of an infinite number of hardened and orderly cells, and each cell was in a definite number of states. Any finite number of dimensions could be the grid. The state of each cell at time t was determined by the state of the definite cell at time t-1 (i.e. the neighbourhood). The neighbourhood of each cell was fixed. At each evolution, the same rule was followed and evolved by each cell at the same time. As far as their forms were concerned, cellular automata were known for three characteristics: (1)Parallel computation: Each cell changes simultaneously.(2)Locality: The change to a cell’s state is subject only to the effects of its neighboring cells.(3)Homogeneity: All cells are governed by the same rule. 4.2.2Dynamic Relaxation Dynamic relaxation was a method to derive solutions to non-linear problems. Day and Bunce were the first persons to apply this technique in cable-net structure. Barnes was embarked on a series of studies in the 1970s and used this technique successfully in the form-finding of the cable-net and membrane structures. Dynamic relaxation was in discretion of the structural systems in time and space. Spatial discretization was referred to the discretion of a structural system into units and nodes and the assumption of its quality centred on the nodes. If a vibration force was imposed to a given note, the note would oscillate. The presence of damping would taper off the oscillation and eventually a static equilibrium achieved. Time discretization was about the oscillation process of a note. In other words, the nodal speed and speed were set at zero in the initial state. The note was begun to oscillate under the impact of a vibration force. The momentum of the system was tracked. When the maximum value was reached, the nodal speed would set to zero. The tracking restarts in the geometry until the disequilibrium force was minimized and a new equilibrium was attained.A total stiffness matrix was not required for structural forming in Dynamic relaxation. In the form-finding process, it was possible to modify the topology and boundary conditions of a structure to calculate the new equilibrium. It was used to derive the solution of an equilibrium surface under given boundary conditions.
figure 4.2. 1,followed the code of Axiom: F Production rule: F=FF/F+F^ Number of generations: 8 Default step of the turtle: 6 Default angle increment of the turtle: 90(http://morphocode.com/work/)
figure 4.2.2,Dynamic relaxationform finding method (http://www.grasshopper3d.com)
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4.2.3 Voronoi Voronoi Diagram was also known as Dirichlet tessellation. Spatial partitioning algorithm was established by the Russian mathematician, Georgy Voronoi. Georgy Voronoi was inspired by the idea of Cartesian space with convex domain partitioning. Voronoi diagram was a special kind of decomposition of a given space in mathematics and widely applied in many fields, such as architecture, geography, meteorology, information system. In architecture and urban design, voronoi would be applied to map in the spatial science, created two-dimension graphic pattern, form three-dimension space in algorithm. There were three characteristics in Voronoi: 1 The feature of Linear: Perpendicular bisectors of the line connecting two neighbor points would be form consecutive polygons. 2 The nearest of neighbor: A group of different points in the plane, each point was associated with the nearest neighbor region according to the principle of the nearest division. 3 Dual graph to the Delaunay triangulation: Voronoi diagram was the dual graph corresponding to the Delaunay triangulation for the same set of points in Euclidean space. Sometimes, Voronoi diagram was pursued by researcher by drawing Delaunay triangulation. Delaunay triangulation was regarded as a popular mathematical algorithm to create graphics.
The characteristics in Delaunay triangulations were listed as follows: 1 Avoid skinny triangles: in computer geometry, Delaunay triangulations were maximized in the minimum angle of all the angles in the triangulation for avoiding skinny triangles. 2 Never intersect with the constrained segments: In the network of configuration, the nearest point was chosen in Delaunay triangulations form a triangle to avoid intersecting with segments. 3 Unique: The same and the unique structures were obtained no matter the location to start the construction network. 4 The circumscribed circle is empty: In Delaunay triangulation, no other points were existed in circumscribed circle of triangles
figure 4.2.3.a,the relationship between voronoi and nature (The new mathematics of architecture,2010)
figure 4.2.3.d,the formationof voronoi (Tooling,2006)
figure 4.2.3.b,three dimension voronoi (drawn by the author)
figure 4.2.3.c,r e l a t i o n s h i p b e t w e e n woronoi and delaunay (drawn by the author)
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4.2.4 Hyperbolic Geometry In mathematics, hyperbolic geometry was part of the domain of non-Euclidean geometry or Bolyai-Lobachevskian geometry. The shape of a saddle such as hyperbolic parabloid was the alluded example. The parallel postulates were challenged by hyperbolic geometry in the Euclidean geometry. According to the Euclidean geometry, the summation of the internal angles of a triangle was 180 degrees. However, Lobachevsky stated that when many parallel lines passed through a single point, the summation of internal angles of a triangle (as assumed by Gauss) would be smaller than 180 degrees. The Euclidean geometry was based on planes. When planes were switched to surfaces, many postulates were challenged. Modernism was inspired by the Euclidean geometry and rarely creates non-linear shapes such as hyperboloids. However, Gaudi, a master of Art Nouveau, examined hyperbolic geometry and placed many non-linear curves in his works. In the digital era, many complex sciences could be described with mathematic formulae and became applicable to architecture. Below was an illustration of how this paper uses grashopper, a parametric tool, and its plus to calculate hyperbolic paraboloids, define the surface patterns and create geometric forms of homological relationships.
4.2.5 Homology Homology is a biological theory. It refers to the presumption that more than two structures sharing similar characteristics come from the same ancestors. It is similar with the theory of evolution. For example, human arms and bird wings share a homological relationship. This concept is frequently in topology and algebra. In digital architecture, there is a relationship between digital modeling and geometry in the context of topology. Algorithms show the homological relationships between models. This paper plots the geometric graphs of homology below. Platonic solids show a homological relationship. Algorithms can sub-divide the surfaces. Many software programs in computer-aided graphics apply the Sub-D principle and create polygons with similar surfaces. Sub-D of differing degrees can create patterns of homological relationships. Polygons are highly related with each other.
figure 4.2.4, Hyperbolic Geometry with homology in grasshopper (drawn by the author)
figure 4.2.5,homology in digital sub-D modeling (drawn by the author)
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4.2.6 Weaire–Phelan structure Weaire–Phelan structure was regarded as a complex three-dimensional structure which has been found by Trinity College Dublin physicist Denis Weaire and his student Robert Phelan. The best solution was proposed to Kelvin problem by using computer simulation system. Kelvin problem was a mathematical problem about "What partitioning of space into equal volumes minimizes their surface area?” or “what was the most efficient bubble foam?" The Kelvin conjecture was based on the bitruncated cubic honeycomb. It was considered as the most efficient foam and the best solution in three-dimensional Euclidean space for over 100 years. If packing was assumed in the same size condition, no higher density than packing would be observed. The difference in between the Weaire–Phelan structure and the Kelvin conjecture would be two kinds of cells were used ( Tetrakaidecahedron, Dodecahedron) in Weaire-Phelan structure, which both have equal volume. Dodecahedron was formed by pentagonal faces with possessing tetrahedral symmetry. Tetrakaidecahedron was formed by two hexagonal and twelve pentagonal faces possessing antiprismatic symmetry. Although the Weaire-Phelan structure was not proven to be the best, that Weaire–Phelan structure was a better solution of the "Kelvin problem" than the Kelvin structure which was considered to the best solution previously, Weaire–Phelan structure. As a result of developing in computer science, mathematical geometry was become part of architecture by computer algorithms. For example, the design of the Olympic Bubbly Aquatics Center was inspired by the Weaire-Phelan structure which makes architectural structure system associated with nature system.
figure 4.2.6.a,Digital fabrication with Weaire–Phelan (Digital fabrication,2010)
figure 4.2.6.b,generating Weaire–Phelan with code (drawn by the author)
figure 4.2.6.c,Weaire–Phelan table created by Haldane Martin (http://www.haldanemartin.co.za/)
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4.2.7 Fractal In 1975,Benoit B. Mandelbrot published a new theory "Fractal geometry" in his book"The Fractal Geometry of Nature". The term of "Fractal" was according to the Latin word" frāctus " which means fragments and irregular graphics. He mentioned that "Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes." Many theories in complex nonlinear science were explained by the fractal theory and chaos theory. The followings were the characteristics of Fractal:
1 Self-similarity: Repeat the same pattern in every scale and layer again and again . 2 Fractal dimension: Dimension of the fractal geometry is not necessarily integer, unlike the Euclidean geometry is an integer system3 Infinite of the structure: In specific region, repeated structure form unlimited length of the curve.4 Irrelevant to scale: The approximate patterns appear in different scale. Regardless of zoom in or out, complexity is the same.5 Integrity: The fractal theory reveals the intrinsic link in between the whole and partSnowflake-like designs, which noticed by Albrecht Dürer, cantour set, Peano curve, Koach curve, Sierpinski Gasket, L-system were the examples of Fractal.
figure 4.2.7.a,L-system phisical model (drawn by the author)
figure 4.2.7.b,cantor set (Fractal geometry,1975)
figure 4.2.7.d,Sierpinski triangle (Fractal geometry,1975)
figure 4.2.7.e,Koch snowflake (Fractal geometry,1975)
figure 4.2.7.c,peano curve (Fractal geometry,1975)
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figure 4.2.8.a,,Helicoid-Catenoid (http://xahlee.info/surface)
figure 4.2.8.cPlanar Enneper (http://xahlee.info/surface)
figure 4.2.8.bCatenoid (http://xahlee.info/surface)
figure 4.2.8.dCosta (http://xahlee.info/surface)
figure 4.2.8.e, Schwarz PD Family Surfaces (http://xahlee.info/surface)
4.2.8 Minimal surface In mathematics, minimal surface was defined as a surface with a mean curvature of zero and meet some smallest constraints surfaces. For example, if closed curve-shaped copper wire was being put into soapy water, and this frame of wire was immersed in soapy water. A dazzling membrane was formed on the frame when pull it out from the soapy water. The dazzling membrane was named as minimal surface in physics which meets the surrounding air conditions and bubble blowing shape. The smallest surface area was formed. The reason why minimal surfaces was particularly important in mathematical problem would be the physical effect of surface tension was reflected by the minimal surface. Minimal energy surface was also represented by minimal surfaces. In nature, minimize the energy and minimum bubble area was preferred according to this logic. There were some mathematical surfaces according to minimal surface theory, such as helicoid, Catenoid, Enneper surface, take Enneper surface for example,[ Denis Weaire,1996]
"Enneper's surface, was defined in 3-dimensional Cartesian coordinates as parametric surface. While this surface has self-intersections in three-dimension space, it's minimal because it has the property of minimizing surface area." extracted from the paper" Construction of Surfaces by Patches of Standard Curves and Minimal surfaces" In digital era, curved space was able to create from mathematical equation and parameters which was behind nature system.
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4.2.9 Metaball In 1980,Jim Blinn proposed every Metaball is a function in N-dimensions, and Metaball surface is the implicit surface .The Metaball based technique is a emerging technique in computer aided geometry design and computer graphics design field. The implicit surface is one of the description of geometric objects. Parameterization is a bridge for implicit surfaces and algebraic surfaces to connecting surface modeling techniques.[Jim Blinn,2003]
The function most often applied to Metaball are as above, the concept of Metaball function is similar to universal gravitation, gravity is inversely proportional to the distance, but proportional to the radius. Thresholding value which related to energy field defines a solid volume. Metaball three-dimensional model describe the liquidity between volumes more natural than NURBS. We can use this features to depicting simulation of natural form, such as fluid motion volume, liquid surface, organic surface.
figure 4.2.9.a, metaball generated by grasshopper (drawn by the author)
figure 4.2.9.b, a series of metaball generated by grasshopper (http://madeincalifornia.blogspot.)
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Chapter 5. Ecological Pattern---Non-linear parametric form-finding design
5.1 Ecological surface form-finding 5.1.1Ecological Pattern---Surface Form Finding 5.1.2 Squama 5.1.3 Ecological Pattern--- Folding and unfolding5.2 Pavilion ---Ecological pattern in fabrication5.3 Psychedelic Rhapsody ---Ecological pattern in architecture5.4 Bio-digital Renaissance ---Ecological pattern in Tainan Main station urban study5.5 Conclusion
5.1.1Ecological Pattern---Surface Form FindingSkin was given different meanings in different periods: skin, surface, enclosure, envelop, interface and façade. Le Corbusier defined surface in spatial terms in his book, “Five Points of Architecture” [Le Corbusier ,1923]and regarded architecture skin as the element of spatial form expressions. Since then, skin became an independent architectural element, and façade was no longer part of structural load-bearing. Peter Eisenman indicated that skin events were social events and building skin was like the third skin of humans. Architectural skin was an important media to express the relationship in between interior space and external environments. In the information age, new types of building skin were created in parametric design by skin structures and patterns. Self-expression was enhanced in the independence and parametric of skin .
Parametric surfaces, information controllability, surface tabularization and optimization and engineering information integration were the current issues for skin parametric. The most prominent feature of was the ability to mathematically describe NURBS surfaces. It was more precise than Polygon modeling. The creation of NURBS surfaces by Rhino and the parametric editing over Grasshopper could generate logics of varying surfaces and hence different patterns. The internal organization of skin patterns was examined in algorithms. Parameters ware delved into the effects of skin over spatial structure. Skin generation was a process from needs to form creations. It was a response to the environment via skin changes.
Three methods were offered in Rhino to create ecological patterns of building skin and these methods were related to Rhinoso modelling. 1.Algorithms are used to generate ecological patterns. The function of “flowalong surface” is switched on for building skin.2.The function of “divide surface” is used to define the surface, before the application of “bounding box” function to create ecological patterns. 3.Parameters are extracted and connect to create polygons. Statistics are analysed and feed-backed to generate different ecological patterns.
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figure 5.1.1 flow along surface (drawn by the author)
figure 5.1.2 sub-division with different scale(drawn by the author)
figure 5.1.3 statics are analyzed and feed-backed to generate ecological pattern(drawn by the author)
5.1.2 Ecological Pattern---Squama Squama was referred as the structure shaped like the scale. In most biological nomenclature, a scale (Latin squama) was a small rigid plate that grew out of an animal's skin to provide protection. In Lepidopteran species, scales were plates on the surface of the insect wing, and provide coloration. Scales were quite common and have evolved multiple times with varying structure and function. Scales were generally classified as part of an organism's integumentary system. There were various types of scales according to shape and to class of animal. By using of parametric program,surface is subdivided in to different pieces, and fitted with similar pattern,just like scales of animal,every scale is similar but identical.We can apply mathematical principles behind program,and the relationship between the equations and data createecological pattern.
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figure 5.1.4 squama by algorithm(drawn by the author)
figure 5.1.5 squama by algorithm(drawn by the author)
5.1.3 Ecological Pattern--- Folding and unfolding
In the "Folding and Unfolding" section, the relationship in between physical model and virtual model of the folded plate was examined. The system of folded plates could tessellate along horizontal or vertical axes of growth to produce horizontal or vertical forms was mentioned by Farshid Moussavi in the book “The Function of Form”. If folding plates could decompose to base units and describe logically in different systems, the parameters and generate form in virtual system would be defined. [ Farshid Moussav,2006] The physical models of folded plate and parametric models in virtual world were folded and represented at the beginning. In this process, look for the logical relationship in between mathematics and logic in three dimensions space was the main purpose. The virtual form and unfolding virtual model into units were generated by the parameters. The units were folded and combined into folded plates in real world. In conclusion, patterns in traditional architecture including implicit relationship in between mathematic and space could be analyzed. Parametric model and non-linear ecological pattern were converted and generated respectively by them.
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figure 5.1.8 (drawn by the author)
5.2 Pavilion ---Ecological pattern in fabrication This section is the continuation of the previous one; the relationship of the algorithms and digital manufacturing were explored in the experimental design. First of all, the algorithm and minimal surface were applied, which created hyperboloid in the previous chapter. Without the three-dimension printer, digital manufacturing was not conducive and unfold the model was necessary. Several different surfaces were divided in the hyperboloid, which were in different scale according to different parameters of the curvature. In the second step, the model was optimized. The membrane-like surface was created from by hyperboloid from algorithm, which was thickness and without structural function. The feedback loop was created immediately by the parametric model imported into GSA structural analysis software from the suggestion of the solver. With this feedback loop, the structure of model by transmitting parametric data could be improved. In the third step, the model for creating shading and lighting was evaluated in the imaginary site in Tainan by importing model into solar analysis software, Ecotect. In order to create different opening and pattern, the parametric data according to solar radiation analysis was transmitted instantly from Ecotect In the fourth step, the feasibility of the physical model by folding 1:10 model was being tested, but the physical model was unstable owing to sliding without basement. The settee in the pavilion was added to improve the stability of the structure. The beneficial result in this method was not only fixed the instability, but also provided furniture to seat. The depth of the bench was related to structural analysis result. For this reason, the depth of the bench was the widest in corner. The folding and section manufacturing methods mentioned in the previous chapter was applied, were indicated in the book," Digital Fabrication", written by Lisa Lwamoto. The surface of ecological patter was fabricated by the method of folding, and the settee for strengthening the structure was fabricated by the method of sectioning.
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figure 5.2 Minimal surface curvature planes (http://commons.wikimedia.org/wiki/Main_Page)
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5.3 Psychedelic Rhapsody---Ecological pattern in architecture In the Qing Dynasty, Ximen, outside the city wall, was completely apart from the field of control. From the Japanese colonial period, Ximending, where Japanese sought pleasure, was defined as the field of entertainment. In different periods, different meanings were given, but all of them were regarded it as a ground of unrestrained. Nowadays, Ximending has become a field for teenager seeking spiritual sustenance, and they want to get away from the turbulence temporarily in real life, just like the protagonist in the move, "Paranoid Park".Teenagers were confused and wandering, and they tried to seek for the relief of spiritual and the peers through communication. A field for teenager was created, interchange, communicate, loiter and release their melancholy could be done in this field. The communication space was the base of the building, which commercial space and recreation space were contained. The temporary living spaces were upstairs, accommodation was provided for international youngsters and non-local youth youngsters. Due to the spatial of properties were different, the size of the spaces were also different. The algorithm, three-dimension Voronoi, was applied to generate psychedelic field. In the process of computing, the component, geno form, was selected to ensure each of the unit able to accommodate basic volume of space. Six optimal results were generated by the computer and all of them were imported into Ecotect. Maximum solar radiation was received in the best form, and the energy of solar panels and photosynthesis inside roof plant were generated by the solar radiation. The function of structure was not generated from the algorithm. As a result, the feedback of structural analysis software was optimized, and the connected cells in three-dimension structure of voronoi were found in the ventilating core. Vertical traffic system such as stairs in the ventilating core could be arranged. Finally, the environmental analysis software was being used to analyze the surface, and different scales of the opening were created according to different parametric data. The landscape of the field was generated from the algorithm, Flowl. The building massing and square was assigned to the greatest intensity and these fields became major parametric points. Algorithm was applied to generate flow pattern, which contained lines for moving guide and squares for staying.
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figure 5.3 real psychological depth in teenager (http://www.filmin.es/pelicula/paranoid-park)
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Design Issue
1Stitching Urban Structure Creating new urban structure Reshape urban structure Developing new industrial model Strengthening of public space
2 Creating New Urban Image Urban regeneration Rebuilding the image of new landmarks
3 Revitalizing Historic Assets Enhance public space and historic area Reuse the preservation aera
4 Prompting Transit-Oriented Development Reinforce city center link Consolidation station stransport functio Enhance public transport-sccessibility
5 Eco-city Development Mechanism Strengthen ecological land use Low-Carbon transport
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(The issue reference from Tainan Urban Development Department)
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5.5 Conclusion According to the above experimental design, the conclusions were acquired as follows:
1 The necessity of optimization Many algorithms were derived from the mathematical or physical principles, if the form was generated from applying these algorithm, the requirement of architectural logic might not be able to meet. Optimize the model was required to modify it closer to the architectural form. The process of optimization was a part of the design, meta-design would be called by some of designers. To certain extents, the process of optimization in algorithm was more important than the final outcome. Each optimizing program was the final outcome generated from the designers deliberating at last.
2 Knowledge-intensive era and integrated design The industry of construction has already transformed from labor-intensive to knowledge-intensive was proposed by Professor Chen Zhen-Cheng. The parametric data was transmitted among different software. More information could be integrated by the designers to improve the diversity and possibility of design in early stage. Digital design was more reasonable during concepts conceived.
3 Considerations of structure and material The structural considerations were slightly different in between designers and engineers. The model from the feedback of the structural analysis software would be able to modify by designers. More factors such as material, earthquake, static Load, living load have to be considered by the structural engineers. When those factors were taken into consideration, decision on if the material should be buckled was difficult to designer. Creating reasonable architectural design in early stage could be assisted by the structural software for designers, the intervention of the Structural Engineers for better safety and feasibility in real architecture was also required.
4 The limitation of the software In the whole process of non-linear parametric design, the limitation of the software was the enormous setback. Compromise in between of what designers want to do and what the software can do was required. Thus, the result was not always the best solution for designers. Two of the most apparent limitations among the current software were unfriendly interface and inadequate function. Numerous time was required for designers to learn the unique interface in different software. As a result, spent more time in learning software rather than cultivating architectural profession was required. Another limitation in function, although Grasshopper program language was easier to learn, not all of ideas could be presented in the software. Other program language such as C++ and VB.net were required. Those program languages could not being used as part of the design unless learnt by designers. The problem could be solved with the progress of technology in the near future.
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5 The gap in between different software The logic of generating model behind the programs was not the same which the gap was existed in different software. Polygon was used by some of them, and NURBS was used for the rest of the software. Divergence was resulted in transmitting file format in between different software. Problem about the file could not be successfully calculated in integrated design process during divergence. In this study, massive amount of time was spent in dealing with the error resulted in the gap between different software.
6 The gap in between virtual world and real world Non-linear parametric design was too complicated to construct from virtual world to real world. In the experimental design, although parametric software was applied to unfold the virtual model for facilitating digital fabrication, inevitable minor errors were existed mainly in the process of complex non-linear form. While these errors were insignificant individually, accumulation of those would result a significant error at the end. The inaccuracy in unfolding the virtual model, the inexactitude of gluing joints, and the thickness of the material were the errors contained. Therefore, the error absorption range was set in order to avoiding the gap. 7 Individualistic to ignore the local characteristics The structural considerations were slightly different in between designers and engineers. The model from the feedback of the structural ana During the process of non-linear parametric design, the factors were considered quantifiable. However, not every factor was quantified, in particular the factor closely related with the local, culture, history and users. Dealing with these local characters in order to avoiding excessive individualism during design process was required to solve in the future. In this study, algorithm generating non-linear parametric form was used and the form by using professional architectural knowledge was modified in order to fit in the program. In future studies, combining these emotional factors into non-linear parametric design for improvement which regarded as aliens implanted in the local place should be required. As indicated above, CAAD changed the thinking mode and design method extensively according to scientific and technological progress was undeniable. More advanced software for non-linear parametric design would emerge in the future with more possibilities and less limitations during the design process. Cultivating professional should be vital in order to take the balance in between digital design and traditional design. Vasari was developed by Autodesk, the most important software company with features of easy-to-use and expressive design tool for creating building concepts. The program was integrated with BIM and analysis program, and Relationship Viewer, the second platform was also similar to Grasshopper. The difference in between of the two was the idea behind the software. Vasari Relationship Viewer was more about parameterization of the object. On the other hand, Grasshopper was emphasized about parameterization of the idea behind the design. Although minor difference was observed in between them, non-linear parametric design was still under development and the software could be enhanced by improving the function to enable the possibility of non-linear parametric design.
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