{"publication_identifier":{"issn":["0730-0301","1557-7368"]},"publication":"ACM Transactions on Graphics","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","citation":{"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>","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>.","short":"L. Makatura, B. Wang, Y.-L. Chen, B. Deng, C. Wojtan, B. Bickel, W. Matusik, ACM Transactions on Graphics 42 (2023).","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>","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>.","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."},"publisher":"Association for Computing Machinery","date_created":"2023-11-29T15:02:03Z","file":[{"file_size":95467870,"creator":"yichen","file_id":"14630","date_created":"2023-11-29T15:16:01Z","access_level":"open_access","success":1,"checksum":"0192f597d7a2ceaf89baddfd6190d4c8","content_type":"application/zip","date_updated":"2023-11-29T15:16:01Z","relation":"main_file","file_name":"tog-22-0089-File004.zip"},{"content_type":"application/zip","relation":"main_file","date_updated":"2023-11-29T15:16:01Z","file_name":"tog-22-0089-File005.zip","creator":"yichen","file_size":103731880,"success":1,"access_level":"open_access","file_id":"14631","date_created":"2023-11-29T15:16:01Z","checksum":"7fb024963be81933494f38de191e4710"},{"date_updated":"2023-12-04T08:04:14Z","relation":"main_file","file_name":"2023_ACMToG_Makatura.pdf","content_type":"application/pdf","checksum":"b7d6829ce396e21cac9fae0ec7130a6b","creator":"dernst","file_size":57067476,"success":1,"date_created":"2023-12-04T08:04:14Z","access_level":"open_access","file_id":"14638"}],"oa":1,"file_date_updated":"2023-12-04T08:04:14Z","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"},{"_id":"BeBi"}],"month":"10","article_type":"original","day":"01","issue":"5","language":[{"iso":"eng"}],"author":[{"first_name":"Liane","full_name":"Makatura, Liane","last_name":"Makatura"},{"last_name":"Wang","full_name":"Wang, Bohan","first_name":"Bohan"},{"id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","first_name":"Yi-Lu","last_name":"Chen","full_name":"Chen, Yi-Lu"},{"first_name":"Bolei","full_name":"Deng, Bolei","last_name":"Deng"},{"first_name":"Christopher J","orcid":"0000-0001-6646-5546","last_name":"Wojtan","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bickel, Bernd","last_name":"Bickel","orcid":"0000-0001-6511-9385","first_name":"Bernd","id":"49876194-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Wojciech","full_name":"Matusik, Wojciech","last_name":"Matusik"}],"year":"2023","type":"journal_article","volume":42,"title":"Procedural metamaterials: A unified procedural graph for metamaterial design","quality_controlled":"1","date_published":"2023-10-01T00:00:00Z","article_processing_charge":"Yes (in subscription journal)","acknowledgement":"The authors thank Mina Konaković Luković and Michael Foshey for their early contributions to this project, David Palmer and Paul Zhang for their insightful discussions about minimal surfaces and the CSCM, Julian Panetta for providing the Elastic Textures code, and Hannes Hergeth for his feedback and support. 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.","doi":"10.1145/3605389","_id":"14628","has_accepted_license":"1","intvolume":"        42","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","keyword":["Computer Graphics and Computer-Aided Design"],"article_number":"168","date_updated":"2023-12-04T08:09:05Z","ddc":["531","006"],"publication_status":"published"}