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Computational Design Framework 3D Graphic Statics Computational Design Framework for 3D Graphic Statics 3D Graphic for Computational Design Framework Computational Design Framework for 3D Graphic Statics Juney Lee Juney Lee Juney ETH Zurich • PhD Dissertation No. 25526 Diss. ETH No. 25526 DOI: 10.3929/ethz-b-000331210 Computational Design Framework for 3D Graphic Statics A thesis submitted to attain the degree of Doctor of Sciences of ETH Zurich (Dr. sc. ETH Zurich) presented by Juney Lee 2015 ITA Architecture & Technology Fellow Supervisor Prof. Dr. Philippe Block Technical supervisor Dr. Tom Van Mele Co-advisors Hon. D.Sc. William F. Baker Prof. Allan McRobie PhD defended on October 10th, 2018 Degree confirmed at the Department Conference on December 5th, 2018 Printed in June, 2019 For my parents who made me, for Dahmi who raised me, and for Seung-Jin who completed me. Acknowledgements I am forever indebted to the Block Research Group, which is truly greater than the sum of its diverse and talented individuals. The camaraderie, respect and support that every member of the group has for one another were paramount to the completion of this dissertation. I sincerely thank the current and former members of the group who accompanied me through this journey from close and afar. I will cherish the friendships I have made within the group for the rest of my life. I am tremendously thankful to the two leaders of the Block Research Group, Prof. Dr. Philippe Block and Dr. Tom Van Mele. This dissertation would not have been possible without my advisor Prof. Block and his relentless enthusiasm, creative vision and inspiring mentorship. I thank Dr. Van Mele for giving all of us the gift of COMPAS, his constant technical support and thorough reviews of my writing and presentations. They both have taught me so much on how to become an independent researcher and pursue a career in academia. I am thankful to the three then-postdoctoral researchers of the Block Research Group, Dr. Matthias Rippmann, Dr. Tomás Méndez Echenagucia and Dr. Andrew Liew. I am deeply grateful for their constant support, enthusiasm, wisdom, humour, advice and patience with my countless questions about anything and everything, to which one of them always seemed to have an answer for. I would also like to thank the PhD researchers of the Block Research Group, especially those who have been with me from the very beginning: David López López, Mariana Popescu, Cristián Calvo Barentin, Shajay Bhooshan and Robin Oval. My special gratitude goes to Dr. Noelle Paulson for helping me with everything related to administration, German translations and processing endless receipts. Furthermore, I would like to thank my co-advisors, Mr. William (Bill) F. Baker and Prof. Allan McRobie. Their expert knowledge and experience were profoundly resourceful during the development of the research, and their insightful feedback were greatly helpful during the final stages of the dissertation. Finally, I thank my family, especially my dear wife Seung-Jin, for their unconditional love and support. i Contents Abstract................................................................... 1 Zusammenfassung...................................................... 3 I Introduction 5 1 Research Statement 7 1.1 Introduction........................................................ 7 1.2 Thesis statement .................................................. 8 1.2.1 Open design problems in 3D graphic statics .............. 8 1.2.2 Lack of computational framework for 3D graphic statics . 9 1.3 Originality ......................................................... 10 1.4 Relevance........................................................... 11 1.4.1 Advent of research in graphic statics ................... 11 1.4.2 Towards a new design paradigm ..................... 13 1.4.3 Discovery of new structural forms .................... 13 1.4.4 Practical relevance to digital fabrication . 14 1.5 Thesis structure and outline..................................... 14 2 Literature Review 19 2.1 Graphic statics..................................................... 19 2.2 Computational graphic statics.................................. 23 2.2.1 Interactive Graphic Statics Tools ...................... 23 2.2.2 Algebraic Graph Statics ........................... 25 2.3 3D graphic statics ................................................. 26 2.3.1 From 2D to 3D ................................. 26 2.3.2 Vectorial 3D graphic statics ......................... 26 2.3.3 Polyhedral 3D graphic statics ........................ 27 iii 2.4 Graphic statics and engineering applications ................ 30 2.4.1 Graphic statics and structural optimisation . 30 2.4.2 Force-driven design .............................. 31 2.5 Computational tools for polyhedral geometries ............. 33 2.5.1 Polyhedral mesh ................................ 34 2.5.2 Volumetric mesh ................................ 36 2.6 Materialisation .................................................... 37 2.7 Summary........................................................... 39 3 Scope of Work 41 3.1 Problem statements............................................... 41 3.2 Research objectives ............................................... 44 3.3 Summary........................................................... 45 II Computational Framework 47 4 Theoretical background 49 4.1 Introduction........................................................ 49 4.1.1 Overview and key terminology ...................... 49 4.1.2 Notation ..................................... 51 4.1.3 Chapter outline ................................. 53 4.2 Polyhedral cell..................................................... 54 4.2.1 Definition ..................................... 54 4.2.2 Datastructure .................................. 55 4.2.3 Duality ...................................... 57 4.2.4 Extended Gaussian Image .......................... 58 4.2.5 Types ....................................... 60 4.2.6 Faces ........................................ 65 4.2.7 Interpretation .................................. 70 4.2.8 Operations .................................... 74 4.2.9 Construction ................................... 77 4.2.10 Summary ..................................... 83 4.3 Multi-cell polyhedron............................................ 84 4.3.1 Definition ..................................... 84 4.3.2 Datastructure .................................. 84 4.3.3 Interpretation .................................. 86 4.3.4 Hierarchy ..................................... 88 iv 4.3.5 Unified diagram ................................ 89 4.3.6 Operations .................................... 92 4.3.7 Summary ..................................... 94 4.4 Cell network....................................................... 95 4.4.1 Definition ..................................... 95 4.4.2 Datastructure .................................. 95 4.4.3 Hierarchy ..................................... 98 4.4.4 Unified diagram ................................ 98 4.4.5 Summary ..................................... 98 4.5 Summary........................................................... 100 5 compas_3gs 101 5.1 Introduction........................................................ 101 5.1.1 About ....................................... 101 5.1.2 General approach ............................... 101 5.1.3 Library structure ................................ 103 5.1.4 Online documentation ............................ 103 5.1.5 Public release .................................. 103 5.2 Datastructures..................................................... 104 5.2.1 Types ....................................... 104 5.2.2 3D form and force diagrams . 106 5.2.3 Computational interpretation of diagrams . 106 5.3 Key algorithms .................................................... 109 5.3.1 Planarisation .................................. 109 5.3.2 Arearisation ................................... 110 5.3.3 Reciprocation .................................. 119 5.4 CAD integration................................................... 121 5.4.1 Setup ....................................... 122 5.4.2 Wrappers ..................................... 122 5.4.3 Control ...................................... 123 5.4.4 Display ...................................... 123 5.5 Summary........................................................... 127 III Applications 129 6 Addressing boundary conditions 131 6.1 Goals................................................................ 131 v 6.2 Setup................................................................ 132 6.2.1 Basic approach ................................. 132 6.2.2 Concurrent cases ................................ 133 6.2.3 Partially concurrent cases . 134 6.2.4 Non-concurrent cases ............................. 135 6.3 Results.............................................................. 136 6.3.1 Simple examples ................................ 136 6.3.2 Design scenario ................................. 137 6.4 Outlook............................................................. 139 7 Generating new topologies 141 7.1 Goals................................................................ 141 7.2 Setup................................................................ 142 7.3 Results.............................................................. 142 7.4 Outlook............................................................. 143 8 Exploring non-polyhedral structures 151 8.1 Goals................................................................ 151 8.2 Setup...............................................................
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