Computer-Aided Tiled Roof Structures

COMPUTER-AIDED TILED R O O F S T R U C T U R E S A u t h o r : FA N T i a n p e n g Supervisor: Prof. Kristof CROLLA

COMPUTER-AIDED TILED ROOF STRUCTURES BY FAN, TIANPENG (1155099638)

THESIS Submitted in partial fulfillment of the requirement for the degree of Master of Architecture in the School of Architecture The Chinese University of Hong Kong

New Territories, Hong Kong

Supervisor: Prof. CROLLA, Kristof

ACKNOWLEDGMENT

I would first like to thank my thesis advisor Prof. Kristof CROLLA of the School of Architecture at The Chinese University of Hong Kong. The door to Prof. CROLLA’s office was always open whenever I ran into a trouble spot or had a question about my research or design. He consistently allowed this thesis to be my own work, but steered me in the right direction whenever he thought I needed it.

I would also like to thank the classmates who were working together with me throughout the whole thesis year: Olivia SI and Nichol WONG. The discussion about the research and design made my mind clear and gave me some new ideas to push forward the design.

I would also like to acknowledge all of the reviewers of the School of Architecture who gave me sharp comments critically which made me rethink and evaluate the thesis profoundly.

Finally, I must express my very profound gratitude to my parents and girlfriend for providing me with unfailing support and continuous encouragement throughout my years of study and through the process of researching and writing this thesis. This accomplishment would not have been possible without them.

Thank you.

FAN Tianpeng May, 2019

ABSTRACT This thesis expands the design solution space for traditional tiled roof structures without necessarily increasing constructing complexity.

Planar and cylindrical roof surfaces are the most common roof geometries in traditional historic Chinese and Japanese architecture and are found in e.g. temple roof structures or vernacular architecture. In these architectures, wooden structures are clad with identical tiles which are configured parallel to one another, thus reducing construction complexity while increasing the flexibility of roof structure design. Digital technologies nowadays allow for the easy design of geometrically complex surfaces, which are challenging to construct. This thesis aims to expand the construction solution space for tiled roofs to include geometrically complex and doubly curved roof surfaces.

Following analysis of existing roof structures, this thesis focuses on two roof aspects: 1) the roof tiling and 2) the wooden substructure.

For the roof tiling, the thesis starts by looking into “Reaction-Diffusion” simulation algorithms to allow the population of non-developable, doubly curved roof surfaces with identical, equidistantly placed tiles. “Reaction-Diffusion” simulations are used to explain how a system of chemicals can react and diffuse. In nature, this principle e.g. results in the natural striping that resemble a zebra stripes. Here, Reaction-Diffusion algorithms are employed as they allow for the controlled generation of equidistant patterns on any geometrical surfaces. These are then further developed into a construction system that allows for the equidistant placement of standardized tiles.

In translating non-developable geometry into equidistant patterns, certain “singularities” appear at bifurcation points within the pattern. In a chemical reaction-diffusion setup, “pattern singularity” appears where the chemical concentration becomes large enough to result in a new strip. Similarly, this thesis develops “singularity tiles” on the positions of singularities. These tiles are specifically designed according to the size of common tiles to prevent drainage failure.

For the wooden substructure, this thesis develops digital methods, including parametric structural engineering setups combined with genetic algorithms, to optimize the supporting structure for any roof surface. Within 3D modeling software Rhinoceros and its procedural modeler Grasshopper, Galapagos is used for evolutionary optimization and Karamba 3D for parametric structural analysis. In search of most “efficient” structures, the system will automatically adjust geometries in order to minimize bending moments of each column, optimize the thickness of each beam according to the applied forces and minimize the displacement of the roof shell.

This thesis enriches the currently practically available tiled roof structure design solution

space by expanding the available geometries without substantially increasing construction complexity. Thus, a wider design pallet is made available that offers architects a more flexible spatial design response which is still rooted in local craft, tradition, culture and symbolism. As a demonstrator for this gained opportunity space, the design of a modern interpretation of a traditional temple structure is proposed on an ancient kiln ruin of Xi’an.

Keywords: Constructing Complexity, Computational Design, Tiled Roof Structures, Reaction-Diffusion, Structural optimization

Computer-Aided Tiled Roof Structures

TABLE OF CONTENTS CHAPTER 1: INTRODUCTION ������������������������������������������������������������������� 1 1. 1 1. 2 1. 3 1. 4 1. 5 1. 6 1. 7

Constructing Complexity In Digital Era ��������������������������������������������������������������������2 The Traditional Wooden Tiled Roof Structures ���������������������������������������������������������2 Development of Tiled Roof Structures ����������������������������������������������������������������������3 Limitations of The Tiled Roof Structures �����������������������������������������������������������������8 Research Questions ����������������������������������������������������������������������������������������������������9 Hypothesis �����������������������������������������������������������������������������������������������������������������9 Impact ������������������������������������������������������������������������������������������������������������������������9

CHAPTER 2: LITERATURE REVIEW ������������������������������������������������������ 14 2. 1 2. 2 2. 3 2. 4 2. 5

Constructing Complexity ���������������������������������������������������������������������������������������15 Architecture History in China ��������������������������������������������������������������������������������15 The Detail Design of Chinese Traditional Architectures ���������������������������������������15 Fabricating The Future �������������������������������������������������������������������������������������������15 The Wings of The Soul ������������������������������������������������������������������������������������������15

CHAPTER 3: METHODOLOGY ����������������������������������������������������������������� 16 3. 1 The Evolution of Tiles Pattern ������������������������������������������������������������������������������17 3. 2 Optimization Method For The Supporting Structures ������������������������������������������46

CHAPTER 4: RESULTS ������������������������������������������������������������������������������� 54 4. 1 Key Findings ����������������������������������������������������������������������������������������������������������55 4. 2 Other Findings �������������������������������������������������������������������������������������������������������55

CHAPTER 5: DISCUSSION ������������������������������������������������������������������������ 56 5. 1 5. 2 5. 3 5. 4

The Necessity Of Reaction-Diffusion Algorithm ��������������������������������������������������57 The Differences Of Tiles In The East And West ����������������������������������������������������57 How To Proof Water ����������������������������������������������������������������������������������������������57 The Necessity of Structural Optimization For Tiled Roofs �����������������������������������57

CHAPTER 6: DESIGN OPPORTUNITIES ������������������������������������������������ 58 CHAPTER 7: A DESIGN DEMONSTRATOR ������������������������������������������� 64 REFERENCE ������������������������������������������������������������������������������������������������� 92

CHAPTER 1 INTRODUCTION

Computer-Aided Tiled Roof Structures

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1. 1 Constructing Complexity In Digital Era Since the 1970s, computer aided design systems have gradually evolved the design methods all over the world. The majority of design companies in the world exploit multiple design softwares to express ideas and output materialized digital information. Digital era brings an increasingly richness of design content which encodes more and more stylistic conventions. Thus, architects have more flexibilities to input more personalities in the design system because the conventional elements are not necessary to worry about longer. For example, a software encodes an operation to draw a line in the system and three parameters for users to define that line. In this system, how to draw a line is encoded and the start points, end points and length are defined by users. The rule of using a ruler to draw a line is encoded in the design content.

So the richness of encoded design content not only brings designers an efficient computer aided design system, but also broadens the boundary of design solutions.

With digital tools emerging, construction contents are enriched by an increasing number of fabrication methods. Advanced technology provides more flexibilities for designers to input added design contents into the constructing process. Thus, constructing complexity not only includes the encoded construction content and the added construction content, but also result in the emergence of design content in the constructing fields. Before the conventional constructing content was encoded as an easily accessible system, designers were not able to add too many “values” to the construction part. However, for example, when the laser cutter has been encoded, designers input the parameters relative to the design and define the fabrication methods instead of inventing codes. In this process, added construction content is relatively less that the design content, which makes the whole design and fabrication more flexible to designers. Complexity was defined as the ratio of added design content to added construction content.1 High complexity achieves highly fabricated products.

Now many architects and designers are exploring in this field to enrich the encoded construction contents.

A reduced design and construction complexity allows for a more flexible spatial design response by architects that is still rooted in local craftsmanship, traditions, culture and symbolism.

This thesis focuses on researching the traditional wooden tiled roof structures which have been popular among Eastern countries for centuries and then proposes 1) a set of computer-aided solutions for tiling on geometrically complex roof surfaces, 2) the optimization method for supporting structures, which explores the potentials for the combination of computation and cultural inheritance and 3) the criteria for the spatial with the interaction of computation and tradition.

1. 2 The Traditional Wooden Tiled Roof Structures In Eastern countries, like China, Japan, Korea and Vietnam, the tiled roof structure has been existing for thousands of years since the human civilization begun. Tiled roof structures have become a complex structural system which inherits and reserves the culture and traditions of a nation.

Generally speaking, traditional wooden tiled roof structures can be divided into two main parts: tiles and the supporting structures. The former relates to geometrical and symbolic issues, like the geometry of roof surfaces, the form of a typical tiles and how tiles are configured. In many rural places of Asia, local people consider the traditional tiles as the first choice when constructing roofs for several reasons: 1) economical access in local markets, 2) easy fabrication for any sizes of tiles and 3) low construction complexity with standardized tiles. Nowadays, among a large range of architectures, temples, vernacular dwellings and palaces of old styles are still using traditional tiles which are regarded as the symbol of traditions. Compared to the tile, the supporting structure is more related to craftsmanship and spatial response. In China, structures with tiled roofs had strict limitations. For example, ancient craftsmen defined the space limited by four columns as a “room”. Only the royal and some authorized religious architectures were allowed to have nine rooms or above. Common dwellings could only have three rooms at maximum in which to show the respects to dominator. Similarly, others structural components like beams, rafters, Tou-Kung as well as paintings and sculptures were strictly used by different social classes.

1

2

Mitchell, William J. “Constructing Complexity.”

Introduction

1. 3 Development of Tiled Roof Structures Tiled roof structures have experienced a long history since human beings learned to build shelters to protect them from rain and sunshine. This thesis mainly researched the development of tiled roof structures in the Eastern world because there exist richer meanings in culture, traditions, engineering, symbolism, spatial response as well as craftsmanship than those in the ancient West.

In China, the development of tiled roof structures can be divided into 1) the advance of building technology and 2) the enriched spatial language.

Figure 1 Wooden Frames of The Taihe Temple, Forbidden City

Figure 2 11 “rooms” of The Taihe Temple, Forbidden City In early centuries, people did not prevent ceramic tiles as a building component until the Zhou dynasty. In this period, casting and building technology were advanced because of the frequent wars. With ceramic tiles, dwellings would not catch fire easily. Since the Han dynasty, people had been able to use complex structures to build in order to expand the interior space. One typical example was the popularity of “TouKung”, which is a wooden structural component used for the transfer of vertical loads. In this period, the main structure of tiled roof had been rooted. After the “three kingdoms” being unified by the Jin dynasty, Buddhist architectures became popular. Emperors employed craftsmen and monks to build grand temples Computer-Aided Tiled Roof Structures

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Figure 3 Kwan-yin Pavilion section

Figure 4 Kwan-yin Pavilion

to provide common people with holy spaces to visit and pray. The roof structure became large in order to accommodate the figure of Buddha. In some places, craftsmen build temples in stone caves which referenced to Indian Buddhist architectures. At this time, it was common that Japan and Korea dispatched learners to China to learn building technologies and then developed their own building types with national characteristics. After the Tang dynasty, tiled roof structures became grand and structurally efficient. Some architectures exist well nowadays even after a thousand years, like Foguang Temple in Shanxi, China.

Kwan-yin Pavilion, Dule Temple, Hebei Province, accommodated the largest Kwan-yin statue in history1 . Three floors high void space was designed to accommodate the statue of 16 meters. Meanwhile, visitors could walk around the statue on every floor which increased the holy atmosphere inside(Figure 3 &4). In the Ming dynasty, Forbidden City was built for emperors and the royal families. At this time, the building technology was advanced enough to build complex roof structures. Some craftsmen were able to design and construct palaces or temples of curved roof surfaces, like the hall of Prayer for Good Harvest, the Temple of Heaven, which was built with triple round roofs. In the late feudal society, architectures were strictly graded by ruler. For example, colors could be simply divided to three types: yellow, blue and dark.

Only royal members were able to use tiles of yellow or similar colors. Most of temples and ministers were allowed to use blue or green tiles. Few non-royal architectures could tile the roof in yellow which was regarded as the greatest honor. In Ching dynasty, the architecture was designed as a library of traditional building technologies and cultural symbolism. Roof tiles and the wooden supporting structures were decorated by ceramic items, precious jewels and some frescoes to make the whole building traditional and beautiful.

New technological revolution and economical globalization in the 20th century allowed for more possibilities in construction and architectural design. Some architects would like to use traditional languages to design an architecture with a complex form. Szigetvar Community Center was such a case that designed

by Imre Makovecz who was regarded as the Hungary’s most highly acclaimed architect. Roof surfaces of this building are all doubly-curved which results in unparalleled tile patterns from one to another. (Figure 5) Since the roof tiles did not follow the substructure which was the wooden board, Makovecz did not have to design the tile pattern which was randomly defined by craftsmen.

Digital design methods evolute the way architects defines an architectural roof. Nowadays, architects can design a geometrically complex roof surfaces easily with the aid of computer. However, it needs more design contents to reduce the construction complexity which makes the building physically possible. In 1

4

Liu, D. (2009). Zhongguo gu dai jian zhu shi. Beijing: Zhongguo jian zhu gong ye chu ban she. p.p. 204-206 Introduction

Figure 5 Szigetvar Community Center by Imre Makovecz Daniel Libeskind’s project, Vanke Pavilion-Milan Expo 2015, the architect designed a roof surface( or facade) of high geometrical complexity and then tiled it with over 4,000 metalized tiles to express his concept: dragon-like skin. Libeskind and his team used computational methods to generate the form and encoded the tile pattern on surface. With a few types of metal tiles(or panels) as well as the flexible supporting structures (Figure 6), craftsmen could be able to implement the construction easily.

In Asia, some architects are exploring the tiled roof structures for broader uses. In the 10th Venice Biennial of Architecture, Wang Shu and his team built and exhibited a pavilion called

Computer-Aided Tiled Roof Structures

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Figure 6 Vanke pavilion-Milan Expo 2015 by Studio Libeskind the Tiled Garden( Figure 7) which reused the tiles recovered from razed buildings in China. This typical traditional tiled roof structure was the architect’s complaint to the large-scale development in some places of China. Tiled roof structure here focuses on the expression of the cultural meaning in this age. Compared to Wang Shu’s exhibition, another case called In Bamboo by Archi-Union Architects announces the technological break-through in the field of tiled roof structures. In this project, Philip Yuan and his team tiled the curved surface with standardized tiles which were fabricated by a traditional tile producing factory. The supporting structures were partly re-fabricated by robot (Figure 8)which made the on-site construction more efficient. This project explored a new possibility that architects can advance the interaction of digital design, tradition and localization. After the

6

Introduction

Figure 7 The Tiles Garden-The 10th Venice Biennial by Wang Shu

Computer-Aided Tiled Roof Structures

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Figure 8 In Bamboo by Philip F. Yuan pavilion was built with a big success, the local government has employed Philip and his team to handle the upgrading and transformation of the entire village.

With the development of computation and the computer-aided design methods, architects are now able to explore a broader filed where traditional architectural elements are recovered from the forest of steel and concrete with expanded design solutions.

1. 4 Limitations of The Tiled Roof Structures There are three aspects of limitations in the tiled roof structures: 1)limited popularity of standardized tiles on geometrically complex roof surfaces, 2) the lack of structural optimization and 3) difficulty in getting a flexible spatial response which is rooted in craftsmanship, culture and symbolism.

Standardized roof tiles are still difficult to be use on geometrically complex roof surfaces. In the Ching dynasty, the Hall of Prayer for Good Harvest in the Temple of Heaven was built with triple round roof which was conic. Craftsmen used different sizes of glazed tiles on the roof which generated radiate tiles pattern. Nowadays, buildings and the geometry of facade and roof have become more and more complex.

In Daniel Libeskind’s project, Vanke Pavilion-Milan Expo 2015, some tiles were folded to fit the irregular envelope which made the repeatability of tiles low. In Philip’s project in Sichuan, the tiled roof structure 8

Introduction

is actually far away from a traditional wooden tiled roof structure. Roof tiles were nailed on a layer of plywood instead of the substructures. This operation solved the problem of tiles’ configuration in a geometrical way that it was not necessary for roof tiles to follow the pattern of substructures. To conclude, Libeskind and Philip Yuan have encoded a certain method to tile a certain geometrically complex roof surface respectively which made great contributions to this field even though they did not advance a solution for tiling on any geometrically complex roof surfaces with standardized tiles.

Most of tiled roof structures do not have an efficient structural system because of the abuse of concrete and timber. In Philip’s project, the added plywood underneath ceramic tiles were not necessary if he could have designed a proper substructure for roof tiles.

Tiled roof structures are now limited in a narrow range of projects like Taoist temples, Buddhist temples, traditional palaces, vernacular dwellings and pavilions. The criteria for the spatial design in these projects are still rooted in the culture, tradition and localization.

1. 5 Research Questions 1. 5. 1 How can we design geometrically complex roof structures in such a way that they can use standardized roof tiles?

A. How can we control the roof tile pattern? a) Relatively constant tile width b) Proper drainage solutions B. How can we maximize the repetition of tiles and minimize the unique tile configurations?

1. 5. 2 How can we support such roof geometries efficiently and practically?

A. Can genetic algorithmic optimization help in deriving optimal structural support solutions?

B. Can planar geometry be used efficiently to support complex roof surfaces?

1. 5. 3 What are the criteria for the spatial with the interaction of computation and tradition?

A. How can we get flexible spatial design response in a project with the developed tiled roof structure?

B. How to make the space created by tiled roof structures acceptable and significant to current users?

1. 6 Hypothesis • There exists a mathematical pattern logic that we can employ to generate a new tiles pattern.

• Some structural optimization softwares can be employed in this thesis.

1. 7 Impact • With the advanced roof tiles pattern, architects can use standardized tiles which can be fabricated easily in local factories to tile any geometrically complex roof surfaces or facade. This new tiling method will evolve the current tiled roof structures in a geometrical way.

• Computer-aided tiled roof structures allow for more convenient ways in which the tiled roofs are built.

This system will dramatically decrease the construction complexity for tiled roof structures with geometrically complex roof surfaces.

• A structural optimization method will reduce the abuse of material and achieve a more efficient material use structurally. This results in an economical and environmental-friendly construction system.

• Wooden structures will revive from the forest of concrete which bring back the traditional habitat of culture, tradition and localization.

Computer-Aided Tiled Roof Structures

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Ceramic Tiles

Religions (Taoism, Buddhism, Confucianism)

Material Changes (Wood+Stone)

Structural Advance S

Hōryū-ji, The Asuka Period, Japan

Foguang Temple, The Tang Dynasty

Doubly-curved Roof Surfaces

Prehistoric Dwelling about B.C. 2000

Singly-curved Roof Surfaces

about A.D. 607

A.D. 857

A

Cylindrical Roof Surfaces

Prehistoric Dwelling about B.C. 2000

Capital Plan, The Zhou Dynasty about B.C. 770

Li-Temple, The Han Dynasty about A.D. 8

Seven Buddha Stone Cave, The Jin Dynasty about A.D. 500

Yongning Pagoda, The Jin Dynasty about A.D. 516

Planar Roof Surfaces

<B.C. 2000

A.D. 1

A.D. 500

A.D. 1000

Figure 9 Development of Tiled Roof Structures

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Introduction

S g D

Spatial Response

Kakasd Community Centre By Imre Makovecz A.D. 1985-96

Temple of Heaven, The Ming Dynasty

A.D. 1420

Sakyamuni Pagoda, The Liao Dynasty

A.D. 1056

Keywords

Computation

Symbolism

Pavilion In Zhuozheng Garden, The Ming Dynasty

Vanke Pavilion Expo 2015 By Studio Daniel Libeskind A.D. 2015

In Bamboo By Archi-Union A.D. 2017

about A.D. 1500

Taihe Temple, The Ming Dynasty A.D. 1420

A.D. 1500

Computer-Aided Tiled Roof Structures

A.D. 2000

Now

Year

11

Reference 1.

Cover Image: “Taiwan.” Travel Photography and Stock Images by Manchester Photographer Darby Sawchuk - Dsphotographic.com.

May 14, 2012. Accessed March 01, 2019. http://dsphotographic.com/photos/taiwan/.

2.

Gooood.cn. (2018). In Bamboo, China by Archi-Union Architects. [online] Available at: https://www.gooood.cn/in-bamboo-chinaby-archi-union-architects.htm [Accessed 10 Sep. 2018].

3.

Heathcote, E., & Makovecz, I. (1997). Imre Makovecz : The wings of the soul (Architectural monographs (London, England) ; 47).

West Sussex : Lanham, Maryland: Academy Editions ; distributed by National Book Network.

4.

“Vanke Pavilion - Milan Expo 2015 / Daniel Libeskind.” ArchDaily. May 07, 2015. Accessed September 10, 2018. https://www. archdaily.com/627994/vanke-pavilion-milan-expo-2015-daniel-libeskind.

5. “王澍/瓦园--威尼斯第十届国际建筑展双年展中国馆 0184|Ikuku.cn|在库言库.” Ikuku.cn, www.ikuku.cn/project/ weinisidishijie-guojijianzhu-shuangnianzhan-wangshu.

6.

Liu, D. (2009). Zhongguo gu dai jian zhu shi. Beijing: Zhongguo jian zhu gong ye chu ban she.

7.

梁思成. 中囯建筑史. 第1版 ed. 天津市: 百花文艺出版社, 1998.

8.

“Domus.” Naoto Jasper = Super Normal. Accessed December 18, 2018. https://www.domusweb.it/en/news/2015/03/06/ expo_2015_vanke.html.

9. 白菜君集贫穷与平胸于一身的画图狗。. “”双最”之寺，空间之美--天津蓟县独乐寺（下）.” 知乎专栏. Accessed December 18, 2018. https://zhuanlan.zhihu.com/p/33153574.

10.

Mitchell, William J. “Constructing Complexity.” Computer Aided Architectural Design Futures 2005: 41-50. doi:10.1007/1-40203698-1_3.

11.

谢玉明., 李东禧., 谢玉明, and 李东禧. 中国传统建筑细部设计. 第1版 ed. 北京: 中國建筑工业出版社, 2001.

12.

Field, Robert. Geometric Patterns from Tiles & Brickwork. Diss: Tarquin, 1996.

Figures Source Figure 1 ://cnki55.sris.com.tw/refbook/ShowDetail.aspx?Table=CRFDOTHERINFO&ShowField=Content&TitleField=Title-ShowTitle&Field=OTHERID&Value=R20060606500A000004 Figure 2 Liu, D. (2009). Zhongguo gu dai jian zhu shi. Beijing: Zhongguo jian zhu gong ye chu ban she. p.p 10 Figure 3 梁思成. 中囯建筑史. 第1版 ed. 天津市: 百花文艺出版社, 1998.p.p 173 Figure 4 白菜君集贫穷与平胸于一身的画图狗。. “”双最”之寺，空间之美--天津蓟县独乐寺（下）.” 知乎专栏. Accessed December 18, 2018. https://zhuanlan.zhihu.com/p/33153574.

Figure 5 Heathcote, E., & Makovecz, I. (1997). Imre Makovecz : The wings of the soul (Architectural monographs (London, England) ; 47). West Sussex : Lanham, Maryland: Academy Editions ; distributed by National Book Network. p68-69 Figure 6 “Vanke Pavilion - Milan Expo 2015 / Daniel Libeskind.” ArchDaily. May 07, 2015. Accessed September 10, 2018. https://www. archdaily.com/627994/vanke-pavilion-milan-expo-2015-daniel-libeskind.

Figure 7 “王澍/瓦园--威尼斯第十届国际建筑展双年展中国馆 0184|Ikuku.cn|在库言库.” Ikuku.cn, www.ikuku.cn/project/weinisidishijie-guojijianzhu-shuangnianzhan-wangshu.

Figure 8 Gooood.cn. (2018). In Bamboo, China by Archi-Union Architects. [online] Available at: https://www.gooood.cn/in-bamboo-china-by-archi-union-architects.htm [Accessed 10 Sep. 2018].

Figure 9 By Author Self

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Introduction

Computer-Aided Tiled Roof Structures

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CHAPTER 2 LITERATURE REVIEW

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Literature Review

2. 1 Constructing Complexity This paper was published by Mitchell William J. who was the former dean of School of Architecture and Planning, MIT, USA. In this paper, Prof. Mitchell defines construction complexity as “the ratio of added design content to added construction content”1. This definition suggests that larger added construction content which means more supporting constructing technologies or larger encoded design content which means more computer-aided design methods results in a lower constructing complexity. It narrows the studying field and one of the research goal for this thesis.

2. 2 Architecture History in China This book was published by Liang Sicheng, who was known as “the father of modern Chinese architecture”.2 He visited through out China with his students to investigate and record existing architectures which were preserved from history. In his publication, Prof. Liang records the information of a lot of great architectures on the aspects of structure, material, craftsmanship, uses, culture and symbolism. He is the architectural ideologist at that age who insisted on conservation of historic buildings.

2. 3 The Detail Design of Chinese Traditional Architectures This book introduces the detail design of traditional architectures in China with beautiful drawings and images which gives a lot of references to designers.

2. 4 Fabricating The Future This book records the achievements of the workshop, “Digital Future”, in Tongji University. It was published by Neil Leach and Philip F. Yuan. It introduces a series of digital fabrication methods as well as the advanced computational design theory which supports the realization of the fabrication.

2. 5 The Wings of The Soul This book records the entire architectural works of Imre Makovecz, who was regarded as the Hungary’s most highly acclaimed architect. Makovecz was a pioneer who built buildings with irregular forms in 1980s and 1990s. All of his projects were tiled with standardized shingles without computational design methods. He believe the space he built was for both body and soul, which connects the earth and the sky.

Makovecz opened up the door how to achieve the interaction of modern architecture and local culture.

1

B. Martens and A. Brown (eds.), Computer Aided Architectural Design Futures 2005, 41-50. © 2005 Springer. Printed in the Netherlands.

2 “Liang Sicheng.” Wikipedia, Wikimedia Foundation, 5 Dec. 2018, en.wikipedia.org/wiki/Liang_Sicheng#Publications.

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CHAPTER 3 METHODOLOGY

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Methodology

This thesis develops a set of computer-aided design solutions for standardized tiles’ configuration on any geometrically complex roof surfaces, including planar surfaces, singly-curved surfaces and doubly-curved surfaces, and the optimization solutions for the supporting structures. This chapter displays and explains how those solutions are developed and how they response to the research questions mentioned in the previous chapter.

3. 1 The Evolution of Tiles Pattern This thesis explores how to tile the geometrically complex roof surfaces with standardized ceramic tiles.

It explains how traditional tiling method works at beginning and then employs the “Reaction-Diffusion” Algorithm to develop a new organic tiles pattern with equidistant lines of tiles from one to another. “RainFlow Path” is defined as the direction of the developed pattern. At last, “Singularity” is proposed to translate the bifurcate patterns into continuous pattern.

3. 1. 1 Tiles Pattern on Planar Roof Surfaces The pattern of tiles on a traditional tiled roof is equidistant because any developable geometries can be subdivided with equidistant lines. These lines can be developed to the configuration of tiles’ substructures.

With the equidistant substructures, standardized tiles can be installed on them.(Figure 1) In the past, most of Chinese traditional tiled roof surfaces were cylindrical or planar which could be tiled with equidistant tiles pattern. The round roof is a very special kind of situation because the geometry is conical. Buildings with this kind of roofs like the Hall of Prayers for Good Harvest in the Temple of Heaven could be subdivided with radiate lines which could not be tiled with constant tiles. Instead, various sizes of tiles were used to cover the roof. ( Figure 2) Now architects have already known those equidistant lines or radiate lines on roof surfaces are called isocurve, which can be defined with simple computational and geometrical knowledge. With this knowledge, we can now look into some basic geometries with slopes which can be potentially developed into

Figure 1 Traditional Tiles’ Configuration

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Tiled Roof Structure On A Planar Roof Surface: Tiling Lines

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Tiled Roof Structure On A Planar Roof Surface: Tiling Substructures

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Figure 2 Prof. Liang Sicheng And The Conservation Project of The Temple of Heaven roof surfaces.(Figure 3& 4) Isocurves can be only found among planar and singly-curved geometries, excluding doubly-curved surfaces. Even though singly-curved surfaces have isocurves, the space between one line and another changes according to the curvature on the position of a surface which explains why we cannot tile a round roof with constant tiles. Some architects are trying to tile a curved surface with constant tiles following the isocurves of the roof surface. That sometimes causes an invalid roof drainage because when the space between two lines of tiles become larger than the width of a tile, it is difficult to cover the space by shifting tiles.(Figure 5) 3. 1. 2 Tiles Pattern on Geometrically Complex Roof Surfaces The traditional tiled roof employs “isocurves” as the reference of tiles pattern which achieves valid tiling on planar and singly-curved roof surfaces. Even though sometimes architects uses different sizes of tiles 20

Methodology

Figure 3 Chinese Traditional Roof Types

Figure 4 “Isocurves” on Basic Geometries

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on curved surfaces, the patterns of tiles still follow the isocurves. In those cases, like the Hall of Prayers for Good Harvest and Vanke Pavilion, roof tiles are not standardized which are negative for tiling construction. In other projects, like Makovecz’s great organic architectures and In Bamboo by Philip, architects designed architectures with standardized tiling. However, the tiles were architects’ added design

Figure 5 Tiling Along The Isocurves of A Singly-curved Roof Surface content which did few contributions to the structural system.1 So as what have been analyzed above, a research question has become clear: How can we tile a geometrically complex roof surfaces with constant tiles?

To realize standardized tiling on geometrically complex roof surfaces, a new tiles pattern should be designed for tiling. This tiles’ pattern works like the isocurves on a planar or singly-curved surface symmetrically.

Reaction-Diffusion Pattern There exist some natural patterns on animal epidermis, such as zebra stripes, the structure of gills of a mushroom and the pattern on a puffer fish and son on. These patterns are called Reaction-Diffusion pattern.(Figure 6-8) In 1952, Alan Turing, an English mathematician, supposed that there exists a system of dynamic reaction and diffusion in the development of patterns and shapes in biological organisms.2 This pattern is called Reaction-Diffusion pattern. In 1993, mathematician John. E. Pearson suggested a mathematical model to simulate the Reaction-Diffusion pattern in his paper “Complex Patterns in a Simple System”3. In his system, two key values were pointed out that impact the Reaction-Diffusion Pattern dramatically. These two values are “feeding value” and “killing value”.

For easier understanding, some people are now trying to express the reaction diffusion equation in different ways. The following expression is simplified by Karl Sims who is a digital media artist and visual effects software developer.4(Figure 9)

1 2 3 4

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See the Chapter 2 See Wikipedia: Alan Turing. https://en.wikipedia.org/wiki/Alan_Turing Science, New Series, Vol. 261, No. 5118. (Jul. 9, 1993), pp. 189-192 See website: https://www.karlsims.com/ Methodology

Figure 6 Zebra Stripes

Figure 7 Mushroom Gills

Figure 8 Puffer Fish Pattern

Pearson’s Reaction-Diffusion Equation:

Figure 9 Karl Sims’ Annotation for Reaction-Diffusion Equation Computer-Aided Tiled Roof Structures

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Figure 10 Patterns by Pearson

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Methodology

Figure 11

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Map of Feeding and King values by Pearson

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Figure 12 Housewares by N-E-R-V-O-U-S

Optimization of Reaction-Diffusion Scripts Additionally, some programmers have encoded the Reaction-Diffusion pattern in computational language so that some design products have been produced and sold in the market.(Figure 12) The products demonstrate that Reaction-Diffusion pattern can be developed and used for design. Inspired by this, scripts from the Grasshopper 3D Online Forum1 are referenced for the thesis to advance the research on tiles pattern, which lays the foundation stone for the future study.

The optimization can be divided into two parts: 1) f and k values research and 2) architectural translation.

According to Pearsonâ&#x20AC;&#x2122;s theory, different composition of feeding and killing values can cause different patterns. When f equals to k in the range of 0.04 to 0.07, the pattern becomes stripes instead of dots which is what we what in the thesis research.(Figure 13-14)

1 See Grasshopper 3D website: https://www.grasshopper3d.com/forum/topics/reaction-diffusion-on-triangular-mesh?id=2985220:T opic:1340165&page=2#comments.

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Figure 13 Samples of Simulation Results 1. The Guide Curve 2. Pattern Parallel to The Guide Curve 3. f=0.030, k=0.041, Perpendicular to The Guide Curve 4. f=0.041, k=0.030, Perpendicular to The Guide Curve

Figure 14 Referenced Scripts Posted by Laurent Delrieu on August 8, 2015

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Added contents Referenced contents

Guide lines f,k values

Referenced Surface

Size of Equidistant Space

Customized Reaction-Diffusion Scripts

The Architectural Demonstrator

Referenced R-D simulation scripts

Figure 15 Diagram of Methodology

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Methodology

Input A typical doubly-curved surface

Input

Output

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“Rain-flow” path as the direction lines

3D mesh R-D mesh with space of 12.5mm

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Medial lines

Figure 16 Diagram of Simulating Logic

Reaction-Diffusion Pattern Simulation Generally speaking, the reaction-Diffusion explains how two chemicals react and diffuse in the given concentrations and finally achieve a dynamic equilibrium. The simulation of the algorithm starts by placing enough amount (normally over 100k) of points on the given field e.g. a geometrical surface, which are the cells of two “chemicals A and B”. And then the algorithm calculates which part of the points are grouped in A or B. the grouped points can be visualized to be a pattern which can be called “zebra pattern”.

This stage of research focuses on Reaction-Diffusion Pattern simulation and visualization on three dimensional geometries. The tested geometry is a doubly-curved surface which cannot be subdivided with equidistant lines and the curvature changes from -0.5π to 0.5π. Due to the large curvature changes, this surface can be regarded as a ideal complex geometry to study.(Figure 16-20) The model scale is 1 to 20 and the size is 200mm x 200mm x200mm. The range of equidistant space refer to the width of a common tile(200 to 300mm).

The goal of the simulation is to find out the way in which we can select proper patterns for the extrusion of medial lines.(Figure 21) An ideal medial line can be developed into the substructure of tiles which is similar to the function of isocurves. The criteria of pattern selection include 1) good continuity, 2) small deviations compared to the given equidistant size, and 3) few interactions.

With the medial lines developed into the “substructure” for tiles, we can tile the entire surface with constant tiles. Since the equidistant spacing is set according to the width of the constant tile, the substructure will always hold the tile which is similar to the traditional roof structures.(Figure22) Computer-Aided Tiled Roof Structures

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Figure 17 Perspective View of Pattern Simulation Process

Figure 18 Elevation View of Pattern Simulation Process 30

Methodology

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Figure 19 Perspective View of Pattern Simulation With different Equidistant Spacings

Figure 20 Elevation View of Pattern Simulation With Different Equidistant Spacings Computer-Aided Tiled Roof Structures

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Equidistant Spacing=12.5 mm Guide lines=Rain-Flow path

Figure 21 Selected Reaction-Diffusion Pattern Defined by Equidistant Space and Rain-Flow Path

3. 1. 3â&#x20AC;&#x192; Rain-Flow Path The following discussion will focus on how to generate the flowing path of rain on a roof surface and the criteria for drainage scenarios.

For any tiled roof structures, the most basic function should be prevent the underneath structures and space from rain. For any roof surfaces, rain will always flow from the higher positions to the lower positions. Following this logic, we can simulate the rain-flow path in grasshopper which will be used as the guide lines for Reaction-Diffusion pattern. (Figure 23-25) 32

Methodology

Figure 22 Tiling on Reaction-Diffusion Pattern

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Figure 23 Typology of Rain-Flow Path on Basic Geometrical Surfaces

Figure 24 Typology of Reaction-Diffusion Pattern with the Guidance of Rain-Flow Path

Figure 25 Typology of Invalid Drainage Areas on Geometrical Surfaces

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Invalid

Valid

Invalid

Valid

Figure 26 Samples of Drainage on Tiles

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3. 1. 4â&#x20AC;&#x192; Singularity On any non-developable surfaces, Reaction-Diffusion Pattern will encounter the positions where patterns become bifurcate.

These bifurcation positions will influence the drainage of the surrounding tiles. Taking the tested case above as example, the influenced areas on surface can be easily identified.(Figure 26) However, not all the tiles in bifurcation areas are failures of drainage. In fact, only one of influenced tiles in each bifurcation areas causes invalid drainage. This is because the common tile at a bifurcate point cannot cover the space defined by three lines of pattern.(Figure 26 -28)

Front

Back

Figure 27 Bifurcation Areas

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Figure 28 Tiles At Bifurcate Positions 36

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Configuration without Singularity Tile

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Figure 29 Singularity Tiling Computer-Aided Tiled Roof Structures

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Figure 30 Tiling together with Common Tiles and Singularity Tiles The â&#x20AC;&#x153;Singularity Tileâ&#x20AC;? is defined as the specific tile which will only be used at the bifurcating positions. A singularity tile can replace the tile which causes the drainage problem. The basic logic to design a singularity tile is that the size of the wider side should be double of that of a common tile. This setup allows for water collection from other tiles. The narrow side is just the same as a common tile.(Figure 29) Singularity tiles can be specifically designed according to different situations. The singularity tile in this example is just proposed to demonstrate the feasibility of using this method to solve drainage problems.

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Physical Model for The Study of Standardized Tiling And Panelized Fabrication for Wooden Structure

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Figure 31 Panelized Wooden Structure Diagram

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Figure 32 Panelized Wooden Structure Drawing 44

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Figure 33 Panelized Wooden Structure Drawing Computer-Aided Tiled Roof Structures

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3. 2 Optimization Method For The Supporting Structures Traditional tiled roofs employ timber as the main structural material. Ancient craftsmen designed the great structural system with limited mechanical calculations. Those structures are still widely used in conservation of historic buildings, vernacular dwellings in some remote areas and pavilions. However, at present, digital tools allow for more options in spatial design. A wider range of design solutions for structures will give architects more feasibilities in spatial design. So this thesis also suggests a structural optimization method for tiled roof structures with the aid of computation.

3. 2. 1 Brief Introduction To Galapagos And Karamba 3D Within 3D modeling software Rhinoceros and its procedural modeler Grasshopper, Galapagos is used for evolutionary optimization and Karamba 3D for parametric structural analysis. In search of most “efficient” structures, the system will automatically adjust geometries in order to minimize bending moments of each column, optimize the thickness of each beam according to the applied forces and minimize the displacement of the roof shell.

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Galapagos will search for the highest z values for every point.

Figure 34 A Sample of Galapagos Optimization

Karamba 3D will calculate the thickness of the beam according to the applied forces.

Figure 35 A Sample of Karamba 3Dâ&#x20AC;&#x2122;s Structural Analysis

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Galapagos (10 minutes)

Displacement=13.5 cm

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Figure 36 Samples of Structural Optimization

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Figure 37 Samples of Karamba 3Dâ&#x20AC;&#x2122;s Structural Solutions Red Column: Applied compression Green Column: Applied tension

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Scale=1:20 Columns=15 Structural Optimization Model: Elevation 3. 2. 2â&#x20AC;&#x192; Structural Solutions Generation The first breakthrough by using the digital tools is the instant output of structural solutions. A tiled roof can be regarded as a solid shell which requires beams and columns for load transfer. To study the structural solutions for a complex tiled roof, a singly-curved surface is employed for structural analysis. In this example, Karamba 3D calculates structural solutions by testing every single scenario within the given field.(Figure 36) Each solution can be potentially useful depending on architectsâ&#x20AC;&#x2122; choices. With the encoded scripts in grasshopper, architects just need to input a roof shell to test, the number of beams and columns and the material they want to use. Then they can quickly get feedback from computation.

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Scale=1:20 Columns=15 Model Photos for The Study of Structural Optimization 3. 2. 3â&#x20AC;&#x192; Structural Optimization In some scenarios, the sporting structures for tiled roof require a list of optimized structural solutions.

In this case, we can use Galapagos and Karamba 3D as well as grasshopper to calculate the optimized structural solutions.(Figure 37) The optimization aims to achieve a supporting structure with minimized bending force applied on each column, optimized thickness of each beam and the smallest displacement of the shell. The computation will keep going until the targets are achieved or it is terminated by physical force.

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Reference 1.

Pearson, J. E. “Complex Patterns in a Simple System.” Science 261, no. 5118 (1993): 189-92. doi:10.1126/science.261.5118.189.

2.

System, Inc. Nervous. Nervous System Blog. Accessed December 18, 2018. https://n-e-r-v-o-u-s.com/shop/line.php?code=7.

3.

“Vanke Pavilion - Milan Expo 2015 / Daniel Libeskind.” ArchDaily. May 07, 2015. Accessed September 10, 2018. https://www. archdaily.com/627994/vanke-pavilion-milan-expo-2015-daniel-libeskind.

4.

Liu, D. (2009). Zhongguo gu dai jian zhu shi. Beijing: Zhongguo jian zhu gong ye chu ban she.

5.

梁思成. 中囯建筑史. 第1版 ed. 天津市: 百花文艺出版社, 1998.

6.

Delrieu, Laurent, Alex, Daniel González Abalde, Pieter Segeren, David Stasiuk, Vicente Soler, and Permalink Reply. “Reaction Diffusion on Triangular Mesh.” Grasshopper. Accessed December 18, 2018. https://www.grasshopper3d.com/forum/topics/reaction-diffusion-on-triangular-mesh?id=2985220:Topic:1340165&page=2#comments.

7.

“Reaction-Diffusion Tutorial.” Karl Sims Home Page. Accessed December 18, 2018. http://www.karlsims.com/rd.html.

8.

“Degenerate State.” Degenerate State Atom. Accessed December 18, 2018. http://www.degeneratestate.org/posts/2017/May/05/ turing-patterns/.

9.

Munafo, Robert. “Pearson’s Classification (Extended) of Gray-Scott System Parameter Values .” Movies: Top 232 by U.S. Theatre Attendance (All-Time) at MROB. Accessed December 18, 2018. http://mrob.com/pub/comp/ xmorphia/pearson-classes.html.

10.

“Evolutionary Principles Applied to Problem Solving.” I Eat Bugs For Breakfast. March 19, 2011. Accessed December 18, 2018. https://ieatbugsforbreakfast.wordpress.com/2011/03/04/epatps01/.

Figures Source Figure 1 By Author Self Figure 2 “民國的大家們，最敬佩的是梁思成，一生致力於保護中國古建.” IFuun. July 29, 2017. Accessed December 18, 2018. http://www.ifuun.com/a20177294230123/.

Figure 3 https://oss.adm.ntu.edu.sg/tzhao002/pitched-roof-in-chinese-architecture-and-hierarchies/ Figure 4 By Author Self Figure 5 By Author Self Figure 6 Google Image. https://www.google.com.hk/search.

Figure 7 Google Image. https://www.google.com.hk/search Figure 8 Google Image. https://www.google.com.hk/search Figure 9 “Reaction-Diffusion Tutorial.” Karl Sims Home Page. Accessed December 18, 2018. http://www.karlsims.com/rd.html.

Figure 10 Pearson, J. E. “Complex Patterns in a Simple System.” Science 261, no. 5118 (1993): 189-92. doi:10.1126/science.261.5118.189.

Figure 11 Pearson, J. E. “Complex Patterns in a Simple System.” Science 261, no. 5118 (1993): 189-92. doi:10.1126 /science.261.5118.189.

Figure 12 System, Inc. Nervous. Nervous System Blog. Accessed December 18, 2018. https://n-e-r-v-o-u-s.com/shop/line.php?code=7.

Figure 13 (to 37) By Author Self

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CHAPTER 4 RESULTS

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Results

4. 1 Key Findings 4. 1. 1 Reaction-Diffusion Algorithm And the Simulation The Reaction-Diffusion algorithm can be scripted into grasshopper and python and then be introduced to architectural field. The gained digital tool automatically finds the bifurcation points and adds an additional pattern between two in order to keep the whole pattern continuous with an relatively equidistant spacing.

This method works well without dimension limitation even though it needs a large amount of time to get the result.

Several parameters can be defined by hand easily, which includes the direction of the pattern, spacing, density, and the continuity.

4. 1. 2 Zebra Pattern And The Tiling Pattern The simulation makes it possible to tile a complex roof surface with a similar strategy as zebra patterns do. Within grasshopper and python, all the meshes of the pattern can be translated into curves and points, which is a big milestone for the whole research. Tiles then follow the pattern with a similar configuration to Chinese traditional tiling system.

4. 1. 3 Tiles And Structures It is possible to use existing standardized tiles and few specifically designed tiles to cover any geometrical roof surfaces. The gained tiling method basically follows the rule that standardized tiles cover a whole roof surface and at them same time show the underneath structure. In Chinese traditional tiled roof structures, tiles are standardized and they illustrate how the underneath structure works which is totally different from those in Europe.1 Singularity is a new concept for tiled roof structures and its goal is to make tiling pattern continuous. This setup aims to achieve a continuous drainage system and an environmentally comfortable indoor space.

Additionally, the research also proposed new approaches for supporting structures and the optimization, which largely enriches the current tiled roof structure system and the decision space architects can make.

4. 2 Other Findings 4. 2. 1 The Difference Of Tiles In The East And West The tiles in the Eastern and Western world differ in two aspects:1) use and 2) form. They influence the structural configuration, construction, appearance and symbolism.2 4. 2. 2 Symbolic Meanings Of Tiles Colors, forms, configurations can display the type of architecture. For example, In China, red or yellow tiles are often used on the roof of a palace of royal family. While green and blue are used for some cultural architectures and temples.

1 2

see Chapter 5 Discussion see Chapter 5 Discussion

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CHAPTER 5 DISCUSSION

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Discussion

5. 1 The Necessity Of Reaction-Diffusion Algorithm In this research, Reaction-Diffusion algorithm is employed to calculate the bifurcated pattern on any geometrically complex surfaces and then translate the pattern for architectural use. It automatically compares all the points on a given mesh and the normals of each point on mesh, and then find out the points where the curvature of the surface (mesh) changes dramatically. There are several ways in which bifurcation can be generated e.g. hiring Hoopsnake to generate water-flowing lines on a surface or drawing curves based on UV and then trimming them to keep all the curves roughly equidistant. However, what prevents these scripting working for complex geometries is they can hardly locate the correct bifurcating points and meanwhile keep all the lines equidistant.

This algorithm is the first attempt for the research goal. The current research results illustrate it is physically possible to use standardized tiles as well as few singularity tiles to cover an entire surface following the Reaction-Diffusion principle. For a further research in the future, there must be a more suitable algorithm or a more advanced scripting method to make the pattern work more efficiently.

5. 2 The Differences Of Tiles In The East And West The following explains the reason why the research focuses on tiles in the East instead of those in the West at this stage.

In China and Japan, most of roof tiles follow the below wooden structures even thought the forms or materials can be different. Craftsmen benefit from that setup because they do not have to be trained to install tiles on any roof. This research basically follows this construction logic and advances it for a low constructing complexity. European tiles are often installed by skillful craftsmen because they need to identify where to put an additional tile on a curved surface. Structurally, the symbolic and decorative meanings are more important in the roof system than showing the structures.

There are cultural differences between tiles in these two regions. The tiles in China share the history of making with ceramics. Some tiles would be signed by the handicraftsmen with special icons or even hand-prints in ancient times. Shingles are more popular in the West. Colorful pattern of terracotta roof tiles in Spain or Italy shows local conventions, while it seldom appears in China or Japan.

5. 3 How To Proof Water In southern China, ceramic tiles are all laid on the roof structure and the friction caused by Gravity keeps all the tiles still. All the tiled roofs are water-proofing and well-ventilated. The drawbacks of this type of tiled roof are 1) bad wind-proofing and 2) only gently pitched roof allowed. However, in the north, tiles are always glued to the wooden structure by cement or lime which makes the whole roof sealed and totally isolated from the outside. The tiling based on the thesis can also reference to the above strategies according to the on-site situations. Both of the above tiled roof structures are common and easy to construct in China.

5. 4 The Necessity of Structural Optimization For Tiled Roofs Basically, the structural optimization aims to broaden the structure design and selection space for traditional tiled roof structures. This part is not necessary for the new tiled roof as it can be also supported by a traditional wooden structure of columns and beams. However, it is worthwhile to explore a new spatial response and quality for architects and at the same time reduce the construction complexity of this new structural proposal.

For the structure, the research explores how to make all structural components planar so that they can be prefabricated in common factories instead of by robot or other expensive tools. Additionally, an efficient structural system also save the cost for materials and labor.

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CHAPTER 6 DESIGN OPPORTUNITIES

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Design Opportunities

With digital tools gained, design opportunities for traditional tiled roof structures are enriched, in which way architects have a more flexible response and selection space.

GAINED DESIGN SPACE

DESIGN OPPORTUNITIES

DESIGN POTENTIALS

Roof Tiles Design

Tiled Roof Design for A Greater Range of Geometries

• planar surfaces • developable surfaces • non-developable surfaces

Structural Optimization

Tiles Design for Symbolism and Local History

• tiles’ color • tiles’ geometries • material

Reduced Construction Complexity for Complex Roof/Facade Design

Specific Tiles Design

• ornamental design • ending tiles • ridge design

Optional Structural Solutions • structural materials • optimized sizes of structural members Optimized Supporting Structures

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Opportunity Example 1: A Flexible TYPICAL PLANAR GEOMETRY

OPPORTUNITIES

OPPORTUNITIES

CHALLENGES

• extra design for the roof ridge(peak of the cylinder) • too large curvature changes

• traditional declining roofs • planar pattern language • new tiles pattern for traditional roofs • extra design for the roof ridge • disconnected patterns on different surfaces • too complex tiling patterns for a simple roof surface

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TYPICAL CYLINDRICAL GEOMETRY

• a cylindrical roof surface • a complete pattern applied on the surface

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TYPICAL DEV GEOME

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• a developable roof s • small amount of sin • flexible structural de

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• too large curvature c age • not necessary to use

Design Opportunities

Selecting Space For Roof Geometries

VELOPABLE ETRY

TYPICAL NON-DEVELOPABLE GEOMETRY

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surface ngularity esign

• a non-developable roof • pavilion, temple, gallery

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can cause invalid drain-

• extra design for the roof ridge(at peak)

MORE COMPLEX GEOMETRY

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• a complex surface • an ideal demonstrator

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• the amount of singularity will be large • the structural design will be complex

e the gained pattern

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Opportunity Example 2: Colored Tiles as Sy

Colors Of Tiles In Different Dynasties In Ancient China1 1

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Aiping Gou, Jiangbo Wang: The Development of Roof Color in Ancient China; 2008 Design Opportunities

ymbolic Expression for Culture and Tradition

References For Tiles In Various Colors1

1

Image source: Google Image

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CHAPTER 7 A DESIGN DEMONSTRATOR A design demonstrator is a designed architecture aiming to push forward the thesis research. It includes spatial design, some programs and a proper structure solution for a given site.

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SITE

Sangyuan Kiln, a kiln built for the emperorâ&#x20AC;&#x2122;s tomb Gonglizhen, Fuping, Xiâ&#x20AC;&#x2122;an, China 0

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The Destroyed Kiln (now nothing left)

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This is a design aiming to explore the possibilities of a tiled roof structure based on the gained tools and some extra symbolic meanings.

Massing and Programs Roof Geometry Supporting Structure Color of Tiles

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A Design Demonstrator

Project: The Museum Of Ceramic Tiles And Bricks Programs: Exhibition Zones Presentation Zone Staff Office Front Reception Outdoor Event Space Toilet (including toilet for the disabled) Site Area: 1296 m2 The study starts by looking into programs and the rough space they occupy. Then the form of roof, structural system and the spatial quality continuously give feedback to the programmatic organization and also influence each other.

For a clear view of the original site and the largest protection to the kiln, all the functional spaces are finally moved to the underground, leaving the pure space generated by structures.

Massing and Programs Roof Geometry

Massing Study

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Massing Study With Dimensional Volumes

1st Attempt Of Form-Finding With A Vacuum Former

The Improved Support for Vacuum Forming

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2st Attempt Of Form-Finding With A Vacuum Former Computer-Aided Tiled Roof Structures

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Physical Model Photos

3D Scanning (Autodesk ReCap Photo)

A sharp roof ridge is more efficient for drainage and tiling. And at the same time, a large roof surface will be subdivided into several which makes a more flexible roof design strategy.

3D Model Rebuilding and Modification (Rhinoceros)

Selecting from Multiple Results

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A Design Demonstrator

Supporting Structures

The structural optimization aims to search for the most efficient option of inclined columns, which means the total mass, distribution and intersection will be optimized to be as smaller as possible. All of the structural solutions must make zero bending moment on the column.

Utilization of Stress

Samples Of The Process Of Optimization

Charts Of Data Changes In Glapagos

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Tilesâ&#x20AC;&#x2122; Substructure

Ridge Beams (Planar)

Secondary Beams (Planar)

Main Beams (Planar)

Ring Beams (Metal)

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A Design Demonstrator

1. Ridge Beams & Main Columns

2. Optimized Main structures

3. Ring Beams & Inclined Columns

4. Main Beams

5. Secondary Beams to Support Tiling Structure

6. Tiling Structure and Tiles

Construction Diagram

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Color and Symbolism The color research aims to explore a new possibility that how the meaning and culture of ancient tiles get interpreted through computational design.

In the design, singularity tiles are highlighted in red, the color which would only be used in royal architectures. Then according to the distance between common tiles and the closest singularity tile, the color gradually changes from red to blue.

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17.8m

21.6m 13.4m

N

19.4m

Roof Plan

A

N

A

Ground Floor Plan

A

N

A

Underground Floor Plan

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North Elevation

East Elevation

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