系統識別號 | U0002-2002201912305700 |
---|---|
DOI | 10.6846/TKU.2019.00588 |
論文名稱(中文) | 拓撲運算與製造:圖解導向之形態發生學 |
論文名稱(英文) | Topological Computation and Fabrication: Diagrams-Oriented Morphogenesis |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 土木工程學系博士班 |
系所名稱(英文) | Department of Civil Engineering |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 107 |
學期 | 1 |
出版年 | 108 |
研究生(中文) | 李京翰 |
研究生(英文) | Ching-Han Lee |
學號 | 898380034 |
學位類別 | 博士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2019-01-15 |
論文頁數 | 226頁 |
口試委員 |
指導教授
-
陳珍誠
委員 - 倪順成 委員 - 張恭領 委員 - 賴怡成 委員 - 柯純融 |
關鍵字(中) |
形態發生學 圖解 找形 參數化設計 衍生形態 數位製造 |
關鍵字(英) |
morphogenesis diagram form-finding generative morphology digital fabrication |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
形態找尋的發展在設計運算與數位製造的影響與文化下日趨成熟,衍生百花齊放的演算形態與無縫傳遞資訊的新物質主義。深藏於繁複的形式之下,其中包含了設計思維、形態靈感、生成機器、構築系統與美學風格等與時俱進的辯證、方法和討論。然而自從千禧年後,便鮮有研究特別針對數位化的形態發生學進行有系統性地剖析,因此本研究試圖由數位形態找尋以至於數位製造的流程中,一方面整理數位圖解與形態生成的關係,另一方面探討拓撲找形的不同類型,提出以圖解為導向的數位形態發生學之設計方法討論。 本研究分為文獻論述、理論發展、設計實驗與觀點論證四部分。首先將影響數位形態的文獻分類整理成建築理論、自然形態與形態找尋方法三大類。理論論述的主要討論以數位圖解完善整合訂製流程的必要性,自然靈感的形態論述則架構於以演算法為基礎的設計生成,形態找尋方法的轉變則是以離散的拓撲為主軸。理論發展部分,一方面將數位圖解更明確地定義為衍生圖解,且分析涵蓋與影響數位製造流程的相關圖解特性,另一方面定義以演算法與拓撲為分類的形態找尋架構,並以此為設計實驗的框架。綜合上述的文獻整理與理論發展,本研究首先分析數位建築中的相關演算法,實驗相對應的拓撲自主賦形的方法並加以分類,以找到拓撲形態的類型學。最後,以設計實驗中拓撲找形的演算法為基本模式,結合衍生圖解的演算、行為、性能、建造、與進化特性,驗證本研究由形態生成、模擬、分析至建造的複雜建模與製造流程。 經由研究衍生形態到離散製造的複雜建模流程,與參數模型、線性設計流程的精煉方法,提出以群聚模式整合數位圖解與拓撲生形的交互架構,以作為基於數位形態發生學的設計方法論。本研究希望藉此討論自主形態構築的深層結構,並期盼邁向未來建築學的新興典範。 |
英文摘要 |
Abstract: The development of morphological form-finding is increasingly well-established under the influence and culture of design computation and digital fabrication derived diverse algorithmic morphology and the New Materialism of seamless information flow. Reposed deep in the complex forms, are the dialectical, methodological and discussion-centered design thinking, morphological inspiration, generating machine, tectonic system and aesthetic style. However, since the new millennium, there has been rare researches on the systematic methodology of digital morphogenesis, therefore, this study attempts to deploy digital workflow to elucidate digital form and digital fabrication, the relationship between digital diagrams and morphogenesis, while on the other hand, exploring different types of topological form-finding, and proposes a design approach of diagram-oriented morphogenesis. This study is divided into four parts: the literature review, theoretical development, design experiment and demonstration of theoretical framework. Firstly, the classification of the literature affecting the digital morphology is divided into three categories: architectural theory, natural morphology and form-finding methods. The main impetus of the theoretical discussion is to perfect the integration of the bespoke workflow with the digital diagram, while the form of natural inspiration is based on the algorithm-based design generation, and the transformation of the form-finding method focuses on deployment of discrete topology. As for theoretical development, the digital diagram is more clearly defined as the Generative Diagram, and its features covering and affecting the process of digital fabrication is meticulously analyzed, while on the other hand the approach defines the morphology-finding framework based on algorithm and topology for designing experiments. Holistically imbuing the above-mentioned literature and theoretical development, this study first analyzes the related algorithms in digital architecture, and experiments with the corresponding autonomous topology-finding methods and classifies them to elicit their typology. Finally, the algorithm of topology-finding in the design experiments is taken as the basic model, and combined with the Generative Diagram of algorithmic, behavior, performance, fabrication, and evolutionary characteristics. Empirical verification of the complex modeling of this study emerges from morphogenesis, simulation, and analysis to construction of Complex Modelling and fabrication processes. By studying the Complex Modelling process generated discrete forms, and the parametric modeling, linear design process refinement method, aggregated patterns are elucidated and proposed to integrate the digital diagram and the topology-finding of the reciprocal structure, for use as the digital morphogenesis design methodology. This study aspires to deploy this discussion to elicit the deep structure of autonomous tectonics, and aims to develop future novel paradigms in the architecture field. |
第三語言摘要 | |
論文目次 |
目錄 第一章 緒論 1 1.1研究背景 1 1.1.1形式生產與自主賦形 1 1.1.2百花齊放的演算形態 2 1.1.3數位模擬與真實建造 2 1.1.4設計流程的資訊整合 3 1.2 研究動機 5 1.2.1衍生形態的設計方法與教學 5 1.2.2前衛實驗與建築實例的聚合 5 1.2.3混沌與湧現觀點的空間形態 6 1.2.4編程文化的崛起與建築語彙的轉變 8 1.2.5模擬軟體的精進與製造硬體的更新 8 1.2.6探索數位工具產生的新形式與教程 9 1.3 研究目的 11 1.3.1數位模擬為導向的空間形態生成 11 1.3.2整合數位圖解與數據形態之關聯 12 1.3.3定義訂製化流程的數位設計方法 12 1.3.4形態發生學與製造的參數化模型 13 1.3.5形式找尋與生成形態的深層結構 14 1.4 研究方法 15 1.5 流程圖 16 第二章 文獻回顧 17 2.1 理論論述 17 2.1.1形式找尋Frei Otto: Occupying and Connecting 17 2.1.2歷時動態Greg Lynn: Animate Form 19 2.1.3演算形式Kostas Terzidis: Algorithmic Architecture 23 2.1.4場域乍現Stan Allen: Object as Field 25 2.1.5形式法則Peter Eisenman: Diagram Diaries 27 2.2 形態論述 32 2.2.1形態定義與延伸概念 32 2.2.1.1 自然與生物的形態靈感:從對稱性到非線性的新興對稱 33 2.2.1.2 建築與結構的概念差異:從擬化形態邁向進階優化拓撲 36 2.2.1.3 數位形態發生學:從思維方法的異變到資訊傳遞的異化 38 2.3 方法論述 42 2.3.1形式找尋於形態發生的模型 42 2.3.1.1 實體模型:基礎點、線、面、體的綜合 42 2.3.1.1.a The Hanging Chain 42 2.3.1.1.b Hanging Chain Models 44 2.3.1.1.c Surfaces Based Models 47 2.3.1.2 數值模型:無向與離散資料的拓撲集合 50 2.3.1.2.a Particle Spring Simulation 50 2.3.1.2.b Thrust Network Analysis 51 2.3.1.2.c Formula Formation 52 2.4 小結 55 第三章 基於圖解的建築形態 57 3.1 圖解的轉變與衍生 57 3.2 圖解歷程 58 3.3 圖解的分類 61 3.3.1類推圖解 62 3.3.1.1 概念形式的圖解 62 3.3.1.2 結構形式的圖解 63 3.3.1.3 數據形式的圖解 64 3.3.1.4 組織形式的圖解 65 3.3.1.5 生成形式的圖解 66 3.3.2衍生圖解 67 3.3.2.1 演算圖解 Algorithmic Diagrams 67 3.3.2.2 行為圖解 Behaviour Diagrams 67 3.3.2.3 性能圖解 Performnace Diagrams 68 3.3.2.4 建造圖解 Fabrication Diagrams 69 3.3.2.5 進化圖解 Evolutionary Diagrams 70 3.4 小結:圖解機器與形態生成 71 第四章 拓撲找形與生成 72 4.1 以演算法分類 73 4.1.1演算法與設計程序 73 4.1.2演算法與空間運算 74 4.1.3拓撲找形的演算法 75 4.1.3.1 公式找形Formula-Based Topology-Finding 75 4.1.3.1.a Superformula 75 4.1.3.1.b Periodic Tessellations 76 4.1.3.1.c Aperiodic Tessellation 77 4.1.3.2 驅力找形Force-Based Topology-Finding 79 4.1.3.2.a Vector and Scalar Field 79 4.1.3.2.b Particle Spring System 80 4.1.3.2.c Relative Neighborhood Graph 81 4.1.3.3 遞歸找形Recursion-Based Topology-Finding 82 4.1.3.3.a Fractal 82 4.1.3.3.b Subdivision 83 4.1.3.4 疊代找形Iteration-Based Topology-Finding 84 4.1.3.4.a Cellular Automaton 85 4.1.3.4.b Reaction Diffusion 87 4.1.3.4.c Diffusion Limited Aggregation 88 4.1.3.4.d Flocking 88 4.1.3.4.e Differential Growth 89 4.2 相關插件軟體 90 4.2.1 Kangaroo 90 4.2.2 Karamba 91 4.2.3 Millipede 92 4.2.4 Shortest Walk 93 4.2.5 SpiderWeb 94 4.2.6 Relative Neighborhood Graph 94 4.2.7 Rabbit 95 4.2.8 Cocoon 97 4.2.9 Anemone 98 4.2.10 Octopus 98 4.3 設計實驗 100 4.3.1公式找形Formula-Based Topoloy-Finding 101 4.3.1.1 Superformula 101 4.3.1.1.a Morph Machine 101 4.3.1.1.b Sum Surface 104 4.3.1.2 Periodic Tessellation 107 4.3.1.2.a Generative Pattern 107 4.3.1.2.b Discrete Embodiment 112 4.3.1.3 Aperiodic Tessellation 119 4.3.1.3.a Voronoi Variation 119 4.3.1.3.b Detached Dome 123 4.3.2 驅力找形Force-Based Topology-Finding 126 4.3.2.1 Field 126 4.3.2.1.a Bizarre Hex 126 4.3.2.1.b Vector Volume 129 4.3.2.2 Particle Spring System 131 4.3.2.2.a Equilibrium Blob 131 4.3.2.2.b Bilateral Embryo 134 4.3.2.2.c Fermat Form 136 4.3.3 遞歸找形Recursion-Based Topology-Finding 141 4.3.3.1 Fractal 141 4.3.3.1.a Fractal Layer 141 4.3.3.1.b Fractal Tower 145 4.3.3.2 Subdivision 147 4.3.3.2.a Sub Domain 147 4.3.3.2.b Sub Doric 150 4.3.4 疊代找形Iteration-Based Topology-Finding 154 4.3.4.1 CA MetaForm 154 4.3.4.2 WildMultiWalks 157 4.3.4.3 Vanishing Vicissitudes . 160 4.3.4.4 RD-Dome 163 4.3.4.5 DG-Dome 165 4.4 小結︰拓撲找形的類型學 168 第五章拓撲生成與製造 170 5.1 演算圖解與三維塑材列印:Synthetic Totem 170 5.2 衍生圖解與機械手臂疊磚:Parametric Brick Wall 173 5.3 衍生圖解與製造模擬流程:CA Pavilion 191 第六章結論與後續研究 212 6.1 複雜形態之拓撲生成與離散製造 212 6.2 線性資料流程與參數模型的精煉 213 6.3 數位模擬與製造的整合訂製流程 214 6.4 數位圖解與拓撲生形的交互潛力 214 6.5 後續研究與建議 217 6.5.1 非線性運算資訊模型與形態最適化的發展 217 6.5.2 衍生圖解於拓撲生成與空間組織的應用性 218 6.5.3 基於材料形態與建造邏輯的優化設計流程 218 參考文獻 220 圖目錄 圖 1.3-1:以模擬導向的形態生成研究目的 11 圖1.3-2:以數位圖解整合數據形態的目的 12 圖1.3-3:數位形態的訂製化流程目的 13 圖1.3-4:形態發生至數位製造的參數化模型 14 圖1.3-5:隱藏與形式找尋與生成形態的深層結構 15 圖1.5-1:研究流程圖 16 圖 2.2-1:藏紅花粒杆粘細菌的形態分化過程 32 圖 2.2-2:形態生成三個原則位階 32 圖 2.2-3:Leduc 的人工合成生物實驗 33 圖 2.2-4:Thompson 的細胞分化實驗 33 圖 2.2-5:Ernst Hackel《自然界的藝術形態》的數位形態靈感 34 圖 2.2-6:Thompson 的細胞之形 34 圖 2.2-7:立方體縮減的最小曲面、鯊魚椎骨結構組織、相近形式形變比較 35 圖 2.2-8:藻類細胞對稱與極性實驗 35 圖 2.2-9:兩組實驗體在拇指突變的對稱性差異 35 圖 2.2-10:Turing 手繪斑駁紋理 36 圖 2.2-11:Blondel 以側臉作為柱頂剖面比例研究 37 圖 2.2-12:Forth 橋梁懸臂的結構概念、四足動物的應力圖 38 圖 2.3-1:Simon Stevin 描繪懸掛形態之簡圖 43 圖 2.3-2:Hooke 關於拱的數學、結構機制與彈性物件的字謎 43 圖 2.3-3:Poleni 繪製虎克定律單一荷重簡圖與分析聖彼得教堂拱頂 43 圖 2.3-4:Pierre Varignon 描繪之纜索邊形 44 圖 2.3-5:Gösling 的三維懸鏈模型、Gaudi 的懸掛模型、Otto 重建模型 45 圖 2.3-6:Köln Federal Garden Exhibition 入口拱門草圖、慕尼黑曼海姆音樂廳模 型結構 45 圖 2.3-7:曼海姆音樂廳模型立體拍攝後經由電腦處理重繪的平面圖與風向等切 圖 46 圖 2.3-8:Isler 實驗冰與聚酯纖維的懸掛模型47 圖 2.3-9:Ricolais 的皂膜曲面實驗 48 圖 2.3-10:IL 的皂膜儀器與Otto 張拉皂膜實體模型 48 圖 2.3-11:Astico 橋梁的懸鏈張拉模型、Basento 橋梁的橡膠薄膜張拉模型 48 圖 2.3-12:Otto 的充氣薄膜實驗 48 圖 2.3-13:Otto 的自我找形實體模型分類 49 圖 2.3-14:Sketchpad 操作示範與參數拓撲的概念 50 圖 2.3-15:Killan 以粒子彈簧法模擬二維懸掛鏈 50 圖 2.3-16:Lynn 以粒子彈簧系統輔助設計人行橋 51 圖 2.3-17:Bow 的結構桁架與力圖解 52 圖 2.3-18:TNA 的形力互承圖解與找形方法 52 圖 2.3-19:Eladio Dieste 以高斯曲率為原型的雙曲拱頂 53 圖 2.3-20:Eladio Dieste 以直紋曲面生形的教堂牆面 53 圖 2.3-21:Marcel Breuer 設計非對稱教堂形式 53 圖 2.3-22:以黎曼曲面為靈感的展覽館,與延伸成流動曲面的想像 54 圖 2.4-1:理論、形態、方法文獻的論述回顧56 圖 3.2-1:Rudolf Wittkower 分析Palladio 十一種別墅的平面類型 58 圖 3.2-2:Colin Rowe 分析Villa Stein 與Villa Malcontenta 的平面分割 58 圖 3.2-3:John Hejduk 的Texas House 系列 58 圖 3.2-4:Benard Tschumi 於Parc de la Villette 競圖的解構概念圖解 59 圖 3.2-5:Rem Koolhaas 於Parc de la Villette 競圖的集中、分散圖解 59 圖 3.2-6:Stan Allen 以蒙德里安畫作與電荷圖說明場域思維的轉變 60 圖 3.2-7:Peter Eisenman 的程序形式圖解 60 圖 3.2-8:MVRDV 的數據城市 60 圖 3.2-9:Reiser+Umemoto 密度、廣度與深度的圖解 60 圖 3.2-10:Patrik Schumacher 參數化風格下的都市形態 60 圖 3.3-1:當代與數位圖解的差異與轉變 61 圖 3.3-2:Dom-Ino House 圖解 62 圖 3.3-3:Manhattan Transcripts 圖解 61 圖 3.3-4:場域條件圖解 61 圖 3.3-5:Gatti Wool Factory 肋板結構 63 圖 3.3-6:馬德里競技場看台薄殼與應力走向63 圖 3.3-7:Heinz Isler 的翻轉找形模型 63 圖 3.3-8:高斯雙曲殼體的模板 63 圖 3.3-9:Frei Otto 皂膜曲面與羊毛路徑實驗 64 圖 3.3-10:Cecil Balmond 以隨機湧現結構之美 64 圖 3.3-11:MVDV 的現代Borobudur 寓象 65 圖 3.3-12:Mobius House 概念圖 65 圖 3.3-13:Mountain Dwelling 發展過程 65 圖 3.3-14:西雅圖圖書館剖面計畫概念圖 65 圖 3.3-15:金澤21 美術館 65 圖 3.3-16:House XI 歷時性操作物件的圖解 66 圖 3.3-17:Port Autority Triple Bridge Gateway 模擬交通粒子與形體 66 圖 3.3-18:Karl Chu 的星球自動機 67 圖 3.3-19:Subdivided Columns 67 圖 3.3-20:Snooks 以多元代理測試編織組構 68 圖 3.3-21:Oxman 以多元代理模擬細胞差異生長 68 圖 3.3-22:Rhino Vault 模擬形、力圖解 69 圖 3.3-23:Kangaroo 模擬物理性能圖解 69 圖 3.3-24:2011 年ICD/ITKE Research Pavilion 的建造過程圖解 69 圖 4.1-1:演算法的廣義定義 73 圖 4.1-2:演算法的邏輯階層與控制組件 73 圖 4.1-3:藉由超級方程式所衍生的普世之形 76 圖 4.1-4:規則紋理的週期性鑲嵌密鋪{p, q} 76 圖 4.1-5:半規則紋理鑲嵌的八種類型與相對應的對偶鑲嵌 77 圖 4.1-6:Culik II 推演的13 種王氏磚類形單元 78 圖 4.1-7:Truchet 於1704 年的雙色鑲嵌組合與Garden 於1977 年的紋理邊界實 驗 78 圖 4.1-8:為笛卡兒繪製簡圖說明星體流動的概念 79 圖 4.1-9:上為透過Delaunary 建構Voronoi 的方法,下為20 個離散點群的Voronoi 圖形 79 圖 4.1-10:Maxwell 所繪之力流的指數曲面 80 圖 4.1-11:以色階之差表示壓力的純量場域 80 圖 4.1-12:正弦函數中的向量場域 80 圖 4.1-13:Killan 開發的找形軟體CADenary、與版本介面差異 81 圖 4.1-14:左為三、四個點群的費馬點差異,右為隨機點群的相關鄰近圖 82 圖 4.1-15:奇異吸子拓撲集合 83 圖 4.1-16:Koch Curve 的碎形子集法則 83 圖 4.1-17:左為Catmull-Clark 細分,中為Loop 細分,右為√3細分 84 圖4.1-18:初等細胞自動機中NB 為2 的8 種組合 85 圖 4.1-19:Wolfram 列舉256 種初等細胞機的局部規則與衍生圖形 86 圖 4.1-20:左為Game of Life 的規則,右為過程所浮現的類型 86 圖 4.1-21:Reaction Diffusion 方程式與Karl Sims 模擬運算的圖例 87 圖 4.1-22:3600 個粒子於矩形晶格的凝聚形態. 88 圖 4.1-23:Reynolds 使用具有三維座標指向性的個體模型. 89 圖 4.1-24:群聚演算三大基本原則之凝聚、對齊、分離 89 圖 4.1-25:為曲線中的頂點插值取樣圖 89 圖 4.2-1:Karamba 插件的模型框架與資料流程 92 圖 4.2-2:Millipede 插件的模型框架與資料流程 93 圖 4.2-3:以絨泡黏菌運輸模式模不同點數的Steiner Tree 紋理 95 圖 4.2-4:Rabbit 插件元件列表 96 圖 4.2-5:Rabbit 插件中自動細胞機的流程 96 圖 4.2-6:Rabbit 插件中L-System 的建構流程 97 圖 4.2-7:Cocoon 插件的架構 98 圖 4.2-8:Octopus 的可調控圖形介面 99 圖 4.3-1:正弦函數數值與曲面視覺化 101 圖 4.3-2:以二元一次方程式與三角函數的簡單參數衍生的複雜紋理 102 圖 4.3-3:面域等值比例的隨機紋理 102 圖 4.3-4:以方程式找形改變曲面長寬比與U、V 比例衍生之有序複雜形態 103 圖 4.3-5:傅立葉級數的疊加頻譜概念 104 圖 4.3-6:疊加頻譜概念的總和函數衍生紋理實驗。 105 圖 4.3-7:總和函數衍生形態於開口多邊形穹頂與封閉圓形穹頂 106 圖 4.3-8:EmergentTexTiles 之全域鑲嵌、局部元件、棋盤分割、鏡像變量 107 圖 4.3-9:EmergentTexTiles 單元建構順序 108 圖 4.3-10:EmergentTexTiles 單元參數變量組合 108 圖 4.3-11:EmergentTexTiles 鑲嵌實驗 109 圖 4.3-12:上排為全域鑲嵌與細分網格的組成,下排為移動模式與離散向量的差 異 110 圖 4.3-13:Emergent VolaTiles 鑲嵌實驗 111 圖 4.3-14:Discrtet Embodiment 邊界範圍、懸鏈線與頂部開口、初始曲面 112 圖 4.3-15:五種單元編碼與特徵,取樣來源與媒合,衍生Truchet 紋理 113 圖 4.3-16:同一模矩下的五種單元模組外層導角與內層結構分支紋理的差異114 圖 4.3-17:Discrete Embodiment 離散殼體實驗 114 圖 4.3-18:隨機排列、控制組合的模組對應與表層及內層的紋理差異 116 圖 4.3-19:單一、多個吸子、曲率控制組合的紋理實驗與改變密鋪邊形排列的外 部紋理差異 117 圖 4.3-20:單一、多個吸子、曲率控制組合的紋理實驗與改變密鋪邊形排列的內 部紋理差異 118 圖 4.3-21:Voronoi Variation 生成步驟與非週期性紋理鑲嵌 120 圖 4.3-22:相同點群不同排序織非週期性紋理鑲嵌 121 圖 4.3-23:減少座標與增加鑲嵌面域數目的Voronoi Variation 紋理 122 圖 4.3-24:Detached Dome 生成步驟 123 圖 4.3-25:Detached Dome 的兩層殼狀鑲板紋理 124 圖 4.3-26:Detached Dome 形態發生過程圖 125 圖 4.3-27:Bizzare Hex 紋理間變化過程,分別為Maze、Rock 與Tile 三種 127 圖 4.3-28:Bizzare Hex 不同初始點間的紋理形態 128 圖 4.3-29:建構向量場域之網格的四個步驟 129 圖 4.3-30:向量網格平均曲率與向量實體化 129 圖 4.3-31:以向量場域的相對值作為拓撲形態形變的比例變量 130 圖 4.3-32:點群的相對位置、拓撲關係與生成的二維團塊 131 圖 4.3-33:Equilibrium Blob 不同驅力形成的拓撲形態差異 132 圖 4.3-34:雙邊胚胎形態生成的相關參數與階層之拓撲系譜 134 圖 4.3-35:以非均質、孔洞、多體的參數變量所衍生的拓撲世代 135 圖 4.3-36:相關鄰近圖的運算程序與所需參數變量 136 圖 4.3-37 二維矩陣、六角形與混合陣列的相關鄰近圖之紋理實驗 137 圖 4.3-38:以立方體與隨機取樣點進行三維相關鄰近拓撲之生成 138 圖 4.3-39:立方體、隨機點群的拓墣形態生成之連續過程 139 圖 4.3-40:以穹頂為原型的Fermat Form 衍生實驗 140 圖 4.3-41:Fractal Layer 演算程序與規則變量 141 圖 4.3-42:Fractal Layer 單元衍生紋理 142 圖 4.3-43:Fractal Layer 二維鑲嵌紋理 143 圖 4.3-44:Fractal Layer 三維穹頂形態 144 圖 4.3-45:碎形之塔的橫向與縱向剖面 145 圖 4.3-46:以三邊形作為初始幾何的碎形之塔 145 圖 4.3-47:五邊形碎形之塔的橫向與縱向剖面 146 圖 4.3-48:以五邊形作為初始幾何的碎形之塔 146 圖 4.3-49:次區間的程序步驟包含空間邊界與色彩的區分 147 圖 4.3-50:Sub Domain 黑白紋理 148 圖 4.3-51:Sub Domain 彩色紋理 149 圖 4.3-52:Sub Doric 的基本細分原理與步驟 150 圖 4.3-53:Sub Diric 形態群體 150 圖 4.3-54:Sub Doric 柱式與細分細節之一 151 圖 4.3-55:Sub Doric 柱式與細分細節之二 152 圖 4.3-56:Sub Doric 柱式與細分細節之三 153 圖 4.3-57:二維細胞自動機的疊代形態實驗 154 圖 4.3-58:細胞自動機生成格狀系統與後設球的範圍 155 圖 4.3-59:進行等值曲面生成前的後設球相關參數 155 圖 4.3-60:以細胞自動機、後設球、等值曲面實驗非線性的疊代形態生成 156 圖 4.3-61:尋找最短路徑的步驟 157 圖 4.3-62:最短路徑曲率變化與起點、終點變化 157 圖 4.3-63:以最短路徑演算的拓撲找形實驗 158 圖 4.3-64:以多個起點與終點的最短路徑形態 159 圖 4.3-65:粒子運行軌跡與網格的關聯性 160 圖 4.3-66:Vanishing Vicissitudes 穹頂與編織結構形態 160 圖 4.3-67:Vanishing Vicissitudes 穹頂生成過程 161 圖 4.3-68:Vanishing Vicissitudes 編織結構生成過程 162 圖 4.3-69:RD-Dome 的紋理形態生成過程 163 圖 4.3-70:RD-Dome 的結構紋理形態 164 圖 4.3-71:DG-Dome 的形態生成過程 . 165 圖 4.3-72:以差異生長作為各層平面的形態生成過程 166 圖 4.3-73:DG-Dome 上視圖與穹頂內仰視 167 圖 4.3-74:DG-Dome 兩側立面圖 167 圖 5.1-1:Synthetic Totem 設計流程圖 170 圖 5.1-2:Synthetic Totem 的演算圖解與建造圖解 171 圖 5.1-3:Synthetic Totem 拓撲形態與三維列印物件 172 圖 5.2-1:曲面生成、結構分析、磚牆生成、手臂疊磚的無縫資訊流程 173 圖 5.2-2:左為Programmed Wall 定點疊磚,右為Structure Oscillations 移地疊磚 174 圖 5.2-3:左為GSD 輕質木磚案例,右為方程式與圖像演算疊磚 174 圖 5.2-4:左上為SilkWall 三種角度手工疊磚,左下為上色木磚,右為導板疊磚 175 圖 5.2-5:以圖像、方程式、奇異吸子生成曲面與磚牆角度的演算方法 176 圖 5.2-6:向量場域、碎形幾何、細胞自動機、黏菌粒子、反應擴散、鞍形曲面 177 圖 5.2-7:參數磚牆設計流程圖 178 圖 5.2-8:Parametric Wall 曲面生成的變量層級關係 179 圖 5.2-9:Range 與Period 變量下不同UV 參數的衍生形態 180 圖 5.2-10:U=14, V=10 的其他參數變化 181 圖 5.2-11:U=14, V=10, Range=676 的Period 參數變化 182 圖 5.2-12:左為交疊面積計算圖,黃色為重疊區域,右為磚塊碰撞測試 183 圖 5.2-13:結構位移模擬與使用率模擬 183 圖 5.2-14:機械手臂疊磚的實體模型 183 圖 5.2-15:第一組Fractal Evolution 參數磚牆 184 圖 5.2-16:第二組Emergent Grid 參數磚牆 185 圖 5.2-17:第三組Reaction Diffusion 參數磚牆 186 圖 5.2-18:第四組Saddle Creation 參數磚牆 187 圖 5.2-19:第五組Rhythm Field 參數磚牆 188 圖5.2-20:第六組Cellular Automata 參數磚牆 189 圖 5.3-1:綠葉海天牛與腸道消化構造 191 圖 5.3-2:軟體動物的殼體 191 圖 5.3-3:CA Pavilion 設計流程圖 192 圖 5.3-4:殼體拓撲的鑲嵌紋理實驗 193 圖 5.3-5:以不同驅力參數合理化殼狀鑲板 194 圖 5.3-6;三組基本曲面與合理化鑲板的方案 196 圖 5.3-7:三組基本曲面的結構位移、應用率與主應力線 197 圖 5.3-8:殼狀鑲板合理化後的尺寸與相對形變率 198 圖 5.3-9:細胞自動機的兩種規則實驗 199 圖 5.3-10:三種不同結合紋理於殼體的方法 200 圖 5.3-11:以Domain Mapping 結合兩種規則紋理於全域殼體的效果 200 圖 5.3-12:以Projection 結合兩種規則紋理於全域殼體的效果 201 圖 5.3-13:以Surface Based 結合兩種規則紋理於全域殼體的效果 202 圖 5.3-14:兩種潛力點的密度差異 203 圖 5.3-15:第一種以點、邊形交接處交錯點為主的分支形態動態生成過程 204 圖 5.3-16:第二種增加中心點與六邊形內的隨機點的分支形態動態生成過程 205 圖 5.3-17:接地處兩端、殼狀頂點、出挑邊緣作為起始點的動態生成模擬 207 圖 5.3-18:Octopus 尋找結構位移(1 軸)、桿件總長(2 軸)、桿件數目(3 軸) 的優化方案 207 圖 5.3-19:結構位移11.54mm 下較可行的分支結構方案 208 圖 5.3-20:爆炸圖與細部材料說明 209 圖 5.3-21:列印接頭細部說明 210 圖 5.3-22:標籤編碼說明圖 210 圖 5.3-23:組裝流程示意圖 210 圖 6.2-1:非線性資訊建模管線示意圖 213 圖 6.4-1:演算法與圖解生成拓撲的疊加模式流程 216 圖 6.5-1:Lalvani 的形態維度研究 217 圖 6.5-2:GRASP 運算尋找空間組織排序 218 圖 6.5-3 以SOM 排序的平面組織與簇群 218 表目錄 表 5.3-1 206 |
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