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We also thank our user study participants and anonymous reviewers.\r\nThis material is based upon work supported by the National Science Foundation\r\n(NSF) Graduate Research Fellowship under Grant No. 2141064; the MIT Morningside\r\nAcademy for Design Fellowship; the Defense Advanced Research Projects Agency\r\n(DARPA) Grant No. FA8750-20-C-0075; the ERC Consolidator Grant No. 101045083,\r\n“CoDiNA: Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena”; and the NewSat project, which is co-funded by the Operational Program for Competitiveness and Internationalisation (COMPETE2020), Portugal 2020, the European Regional Development Fund (ERDF), and the Portuguese Foundation for Science and Technology (FTC) under the MIT Portugal program.","volume":42,"article_type":"original","month":"10","publication_identifier":{"issn":["0730-0301","1557-7368"]},"quality_controlled":"1","type":"journal_article","doi":"10.1145/3605389","language":[{"iso":"eng"}],"year":"2023","publisher":"Association for Computing Machinery","date_published":"2023-10-01T00:00:00Z","author":[{"last_name":"Makatura","full_name":"Makatura, Liane","first_name":"Liane"},{"last_name":"Wang","first_name":"Bohan","full_name":"Wang, Bohan"},{"id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","last_name":"Chen","full_name":"Chen, Yi-Lu","first_name":"Yi-Lu"},{"full_name":"Deng, Bolei","first_name":"Bolei","last_name":"Deng"},{"orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan","first_name":"Christopher J","full_name":"Wojtan, Christopher J"},{"orcid":"0000-0001-6511-9385","last_name":"Bickel","id":"49876194-F248-11E8-B48F-1D18A9856A87","first_name":"Bernd","full_name":"Bickel, Bernd"},{"full_name":"Matusik, Wojciech","first_name":"Wojciech","last_name":"Matusik"}],"_id":"14628","oa":1,"issue":"5","has_accepted_license":"1","citation":{"ama":"Makatura L, Wang B, Chen Y-L, et al. Procedural metamaterials: A unified procedural graph for metamaterial design. <i>ACM Transactions on Graphics</i>. 2023;42(5). doi:<a href=\"https://doi.org/10.1145/3605389\">10.1145/3605389</a>","apa":"Makatura, L., Wang, B., Chen, Y.-L., Deng, B., Wojtan, C., Bickel, B., &#38; Matusik, W. (2023). Procedural metamaterials: A unified procedural graph for metamaterial design. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3605389\">https://doi.org/10.1145/3605389</a>","ista":"Makatura L, Wang B, Chen Y-L, Deng B, Wojtan C, Bickel B, Matusik W. 2023. Procedural metamaterials: A unified procedural graph for metamaterial design. ACM Transactions on Graphics. 42(5), 168.","mla":"Makatura, Liane, et al. “Procedural Metamaterials: A Unified Procedural Graph for Metamaterial Design.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5, 168, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3605389\">10.1145/3605389</a>.","short":"L. Makatura, B. Wang, Y.-L. Chen, B. Deng, C. Wojtan, B. Bickel, W. Matusik, ACM Transactions on Graphics 42 (2023).","ieee":"L. Makatura <i>et al.</i>, “Procedural metamaterials: A unified procedural graph for metamaterial design,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5. Association for Computing Machinery, 2023.","chicago":"Makatura, Liane, Bohan Wang, Yi-Lu Chen, Bolei Deng, Chris Wojtan, Bernd Bickel, and Wojciech Matusik. “Procedural Metamaterials: A Unified Procedural Graph for Metamaterial Design.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3605389\">https://doi.org/10.1145/3605389</a>."},"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083"}],"publication":"ACM Transactions on Graphics","title":"Procedural metamaterials: A unified procedural graph for metamaterial design","file":[{"date_updated":"2023-11-29T15:16:01Z","success":1,"file_id":"14630","checksum":"0192f597d7a2ceaf89baddfd6190d4c8","date_created":"2023-11-29T15:16:01Z","file_size":95467870,"file_name":"tog-22-0089-File004.zip","relation":"main_file","content_type":"application/zip","access_level":"open_access","creator":"yichen"},{"relation":"main_file","content_type":"application/zip","access_level":"open_access","creator":"yichen","date_updated":"2023-11-29T15:16:01Z","success":1,"file_id":"14631","date_created":"2023-11-29T15:16:01Z","checksum":"7fb024963be81933494f38de191e4710","file_size":103731880,"file_name":"tog-22-0089-File005.zip"},{"file_size":57067476,"file_name":"2023_ACMToG_Makatura.pdf","success":1,"date_updated":"2023-12-04T08:04:14Z","date_created":"2023-12-04T08:04:14Z","file_id":"14638","checksum":"b7d6829ce396e21cac9fae0ec7130a6b","creator":"dernst","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"status":"public","date_updated":"2023-12-04T08:09:05Z","day":"01","oa_version":"Published Version","publication_status":"published","abstract":[{"text":"We introduce a compact, intuitive procedural graph representation for cellular metamaterials, which are small-scale, tileable structures that can be architected to exhibit many useful material properties. Because the structures’ “architectures” vary widely—with elements such as beams, thin shells, and solid bulks—it is difficult to explore them using existing representations. Generic approaches like voxel grids are versatile, but it is cumbersome to represent and edit individual structures; architecture-specific approaches address these issues, but are incompatible with one another. By contrast, our procedural graph succinctly represents the construction process for any structure using a simple skeleton annotated with spatially varying thickness. To express the highly constrained triply periodic minimal surfaces (TPMS) in this manner, we present the first fully automated version of the conjugate surface construction method, which allows novices to create complex TPMS from intuitive input. We demonstrate our representation’s expressiveness, accuracy, and compactness by constructing a wide range of established structures and hundreds of novel structures with diverse architectures and material properties. We also conduct a user study to verify our representation’s ease-of-use and ability to expand engineers’ capacity for exploration.","lang":"eng"}]},{"oa":1,"_id":"11993","author":[{"first_name":"Thomas","full_name":"Alderighi, Thomas","last_name":"Alderighi"},{"full_name":"Malomo, Luigi","first_name":"Luigi","last_name":"Malomo"},{"full_name":"Auzinger, Thomas","first_name":"Thomas","id":"4718F954-F248-11E8-B48F-1D18A9856A87","last_name":"Auzinger","orcid":"0000-0002-1546-3265"},{"id":"49876194-F248-11E8-B48F-1D18A9856A87","last_name":"Bickel","orcid":"0000-0001-6511-9385","first_name":"Bernd","full_name":"Bickel, Bernd"},{"first_name":"Paulo","full_name":"Cignoni, Paulo","last_name":"Cignoni"},{"last_name":"Pietroni","full_name":"Pietroni, Nico","first_name":"Nico"}],"date_published":"2022-09-01T00:00:00Z","publisher":"Wiley","year":"2022","language":[{"iso":"eng"}],"doi":"10.1111/cgf.14581","type":"journal_article","quality_controlled":"1","publication_identifier":{"eissn":["1467-8659"],"issn":["0167-7055"]},"month":"09","volume":41,"article_type":"original","isi":1,"department":[{"_id":"BeBi"}],"date_created":"2022-08-28T18:17:01Z","keyword":["Computer Graphics and Computer-Aided Design"],"intvolume":"        41","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","ddc":["000"],"file_date_updated":"2022-08-28T18:18:08Z","abstract":[{"lang":"eng","text":"Moulding refers to a set of manufacturing techniques in which a mould, usually a cavity or a solid frame, is used to shape a liquid or pliable material into an object of the desired shape. The popularity of moulding comes from its effectiveness, scalability and versatility in terms of employed materials. Its relevance as a fabrication process is demonstrated by the extensive literature covering different aspects related to mould design, from material flow simulation to the automation of mould geometry design. In this state-of-the-art report, we provide an extensive review of the automatic methods for the design of moulds, focusing on contributions from a geometric perspective. We classify existing mould design methods based on their computational approach and the nature of their target moulding process. We summarize the relationships between computational approaches and moulding techniques, highlighting their strengths and limitations. Finally, we discuss potential future research directions."}],"oa_version":"Submitted Version","publication_status":"published","page":"435-452","day":"01","date_updated":"2023-08-03T13:21:55Z","status":"public","external_id":{"isi":["000842638900001"]},"title":"State of the art in computational mould design","file":[{"date_updated":"2022-08-28T18:18:08Z","checksum":"c40cc8ceb7b7f0512172b883d712198e","file_id":"11994","date_created":"2022-08-28T18:18:08Z","file_size":32480850,"file_name":"star_molding_preprint.pdf","content_type":"application/pdf","relation":"main_file","description":"This is the pre-peer reviewed version of the following article: Alderighi, T., Malomo, L., Auzinger, T., Bickel, B., Cignoni, P. and Pietroni, N. (2022), State of the Art in Computational Mould Design. Computer Graphics Forum, which has been published in final form at https://doi.org/10.1111/cgf.14581. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.","access_level":"open_access","title":"pre-peer reviewed version","creator":"bbickel"}],"publication":"Computer Graphics Forum","citation":{"ista":"Alderighi T, Malomo L, Auzinger T, Bickel B, Cignoni P, Pietroni N. 2022. State of the art in computational mould design. Computer Graphics Forum. 41(6), 435–452.","apa":"Alderighi, T., Malomo, L., Auzinger, T., Bickel, B., Cignoni, P., &#38; Pietroni, N. (2022). State of the art in computational mould design. <i>Computer Graphics Forum</i>. Wiley. <a href=\"https://doi.org/10.1111/cgf.14581\">https://doi.org/10.1111/cgf.14581</a>","mla":"Alderighi, Thomas, et al. “State of the Art in Computational Mould Design.” <i>Computer Graphics Forum</i>, vol. 41, no. 6, Wiley, 2022, pp. 435–52, doi:<a href=\"https://doi.org/10.1111/cgf.14581\">10.1111/cgf.14581</a>.","short":"T. Alderighi, L. Malomo, T. Auzinger, B. Bickel, P. Cignoni, N. Pietroni, Computer Graphics Forum 41 (2022) 435–452.","ama":"Alderighi T, Malomo L, Auzinger T, Bickel B, Cignoni P, Pietroni N. State of the art in computational mould design. <i>Computer Graphics Forum</i>. 2022;41(6):435-452. doi:<a href=\"https://doi.org/10.1111/cgf.14581\">10.1111/cgf.14581</a>","chicago":"Alderighi, Thomas, Luigi Malomo, Thomas Auzinger, Bernd Bickel, Paulo Cignoni, and Nico Pietroni. “State of the Art in Computational Mould Design.” <i>Computer Graphics Forum</i>. Wiley, 2022. <a href=\"https://doi.org/10.1111/cgf.14581\">https://doi.org/10.1111/cgf.14581</a>.","ieee":"T. Alderighi, L. Malomo, T. Auzinger, B. Bickel, P. Cignoni, and N. Pietroni, “State of the art in computational mould design,” <i>Computer Graphics Forum</i>, vol. 41, no. 6. Wiley, pp. 435–452, 2022."},"has_accepted_license":"1","issue":"6","scopus_import":"1"}]