[{"language":[{"iso":"eng"}],"quality_controlled":"1","OA_type":"hybrid","publication":"ACM Transactions on Graphics","year":"2025","ddc":["531","006","621"],"date_published":"2025-12-04T00:00:00Z","has_accepted_license":"1","date_created":"2025-11-10T14:12:06Z","citation":{"mla":"Chen, Yi-Lu, et al. “Numerical Homogenization of Sand from Grain-Level Simulations.” <i>ACM Transactions on Graphics</i>, vol. 44, no. 6, 220, Association for Computing Machinery, 2025, doi:<a href=\"https://doi.org/10.1145/3763344\">10.1145/3763344</a>.","apa":"Chen, Y.-L., Ly, M., &#38; Wojtan, C. (2025). Numerical homogenization of sand from grain-level simulations. <i>ACM Transactions on Graphics</i>. Hong Kong, China: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3763344\">https://doi.org/10.1145/3763344</a>","chicago":"Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Numerical Homogenization of Sand from Grain-Level Simulations.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3763344\">https://doi.org/10.1145/3763344</a>.","short":"Y.-L. Chen, M. Ly, C. Wojtan, ACM Transactions on Graphics 44 (2025).","ieee":"Y.-L. Chen, M. Ly, and C. Wojtan, “Numerical homogenization of sand from grain-level simulations,” <i>ACM Transactions on Graphics</i>, vol. 44, no. 6. Association for Computing Machinery, 2025.","ama":"Chen Y-L, Ly M, Wojtan C. Numerical homogenization of sand from grain-level simulations. <i>ACM Transactions on Graphics</i>. 2025;44(6). doi:<a href=\"https://doi.org/10.1145/3763344\">10.1145/3763344</a>","ista":"Chen Y-L, Ly M, Wojtan C. 2025. Numerical homogenization of sand from grain-level simulations. ACM Transactions on Graphics. 44(6), 220."},"intvolume":"        44","article_type":"original","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"20629","creator":"yichen","checksum":"4d30ff82314e76fe411c8f8195bb6040","success":1,"access_level":"open_access","content_type":"application/pdf","date_updated":"2025-11-10T14:10:12Z","file_name":"main_paper.pdf","date_created":"2025-11-10T14:10:12Z","file_size":61708650},{"file_size":6862285,"content_type":"application/pdf","access_level":"open_access","date_created":"2025-11-10T14:10:27Z","file_name":"paper_supplemental.pdf","date_updated":"2025-11-10T14:10:27Z","file_id":"20630","checksum":"f1b6df39487866044ca7ca899d044be7","creator":"yichen","relation":"supplementary_material"},{"file_id":"20631","creator":"yichen","checksum":"04ec2a4866774673479cafe5b93d26bd","relation":"supplementary_material","file_size":164079303,"access_level":"open_access","content_type":"video/mp4","date_updated":"2025-11-10T14:10:44Z","file_name":"main_video.mp4","date_created":"2025-11-10T14:10:44Z"},{"date_created":"2025-11-10T14:10:53Z","date_updated":"2025-11-10T14:10:53Z","file_name":"extra_video.mp4","content_type":"video/mp4","access_level":"open_access","file_size":72234678,"relation":"supplementary_material","checksum":"7495e8cbcf94eb49276b4730c5886914","creator":"yichen","file_id":"20632"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"oa":1,"project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"article_number":"220","month":"12","license":"https://creativecommons.org/licenses/by-nd/4.0/","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","short":"CC BY-ND (4.0)","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png"},"author":[{"id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","orcid":"0009-0005-0723-0655","last_name":"Chen","full_name":"Chen, Yi-Lu","first_name":"Yi-Lu"},{"last_name":"Ly","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","first_name":"Mickaël","full_name":"Ly, Mickaël"},{"orcid":"0000-0001-6646-5546","last_name":"Wojtan","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","full_name":"Wojtan, Christopher J"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","day":"04","issue":"6","doi":"10.1145/3763344","abstract":[{"text":"The realistic simulation of sand, soil, powders, rubble piles, and large collections of rigid bodies is a common and important problem in the fields of computer graphics, computational physics, and engineering. Direct simulation of these individual bodies quickly becomes expensive, so we often approximate the entire group as a continuum material that can be more easily computed using tools for solving partial differential equations, like the material point method (MPM). In this paper, we present a method for automatically extracting continuum material properties from a collection of rigid\r\nbodies. We use numerical homogenization with periodic boundary conditions to simulate an effectively infinite number of rigid bodies in contact. We then record the effective stress-strain relationships from these simulations and convert them into elastic properties and yield criteria for the continuum simulations. Our experiments validate existing theoretical models like the Mohr-Coulomb yield surface by extracting material behaviors from a collection of spheres in contact. We further generalize these existing models to more exotic materials derived from diverse and non-convex shapes. We\r\nobserve complicated jamming behaviors from non-convex grains, and we introduce a new material model for materials with extremely high levels of internal friction and cohesion. We simulate these new continuum models using MPM with an improved return mapping technique. The end result is a complete system for turning an input rigid body simulation into an efficient continuum simulation with the same effective mechanical properties.","lang":"eng"}],"date_updated":"2025-12-09T14:53:32Z","volume":44,"corr_author":"1","publication_status":"published","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"file_date_updated":"2025-11-10T14:10:53Z","type":"journal_article","acknowledgement":"We thank the anonymous reviewers for their helpful comments, the members of the Visual Computing Group at ISTA for their feedback and Gauthier Rousseau for the insightful discussions. This research was supported by the Scientific Service Units (SSU) of ISTA through resources provided by Scientific Computing and was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA). ","OA_place":"publisher","scopus_import":"1","title":"Numerical homogenization of sand from grain-level simulations","_id":"20628","publisher":"Association for Computing Machinery","conference":{"location":"Hong Kong, China","name":"SIGGRAPH Asia: Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia","start_date":"2025-12-15","end_date":"2025-12-18"},"status":"public"},{"date_published":"2024-07-01T00:00:00Z","ddc":["516"],"has_accepted_license":"1","date_created":"2024-07-05T12:08:57Z","citation":{"ista":"Hafner C, Ly M, Wojtan C. 2024. Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. Transactions on Graphics. 43(4), 78.","ama":"Hafner C, Ly M, Wojtan C. Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. <i>Transactions on Graphics</i>. 2024;43(4). doi:<a href=\"https://doi.org/10.1145/3658194\">10.1145/3658194</a>","ieee":"C. Hafner, M. Ly, and C. Wojtan, “Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments,” <i>Transactions on Graphics</i>, vol. 43, no. 4. Association for Computing Machinery, 2024.","short":"C. Hafner, M. Ly, C. Wojtan, Transactions on Graphics 43 (2024).","chicago":"Hafner, Christian, Mickaël Ly, and Chris Wojtan. “Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only on Mass Moments.” <i>Transactions on Graphics</i>. Association for Computing Machinery, 2024. <a href=\"https://doi.org/10.1145/3658194\">https://doi.org/10.1145/3658194</a>.","apa":"Hafner, C., Ly, M., &#38; Wojtan, C. (2024). Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. <i>Transactions on Graphics</i>. Denver, Colorado: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3658194\">https://doi.org/10.1145/3658194</a>","mla":"Hafner, Christian, et al. “Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only on Mass Moments.” <i>Transactions on Graphics</i>, vol. 43, no. 4, 78, Association for Computing Machinery, 2024, doi:<a href=\"https://doi.org/10.1145/3658194\">10.1145/3658194</a>."},"intvolume":"        43","article_type":"original","external_id":{"isi":["001289270900045"]},"language":[{"iso":"eng"}],"quality_controlled":"1","publication":"Transactions on Graphics","year":"2024","month":"07","keyword":["Topology Optimization","Mass Moments","Computational Geometry"],"author":[{"full_name":"Hafner, Christian","first_name":"Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87","last_name":"Hafner"},{"full_name":"Ly, Mickaël","first_name":"Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","last_name":"Ly"},{"first_name":"Christopher J","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan","orcid":"0000-0001-6646-5546"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"day":"01","article_processing_charge":"Yes (via OA deal)","issue":"4","oa_version":"Published Version","file":[{"date_updated":"2024-07-05T12:05:17Z","file_name":"sif-final.pdf","date_created":"2024-07-05T12:05:17Z","access_level":"open_access","success":1,"content_type":"application/pdf","file_size":7225150,"relation":"main_file","creator":"chafner","checksum":"0dc9f5a6422b8a49a79026900f349ee5","file_id":"17204"},{"date_updated":"2024-07-05T12:06:03Z","file_name":"sif-supp-final.pdf","date_created":"2024-07-05T12:06:03Z","access_level":"open_access","content_type":"application/pdf","file_size":397262,"relation":"supplementary_material","creator":"chafner","checksum":"cde433c6a40688d5f1187fb5721f6f94","file_id":"17205"},{"creator":"chafner","checksum":"c0457a09c2ab9a1c2935c995dcc84907","title":"Submission Video","file_id":"17276","relation":"supplementary_material","file_size":170001305,"file_name":"sif-video-final.mp4","date_updated":"2024-07-17T09:29:13Z","date_created":"2024-07-17T09:29:13Z","access_level":"open_access","content_type":"video/mp4"}],"department":[{"_id":"ChWo"}],"oa":1,"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"article_number":"78","date_updated":"2025-09-08T08:29:09Z","volume":43,"corr_author":"1","publication_status":"published","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"file_date_updated":"2024-07-17T09:29:13Z","type":"journal_article","acknowledgement":"We thank Gianmarco Cherchi for his help in tailoring the Mesh Booleans code for this project, Stefan Jeschke for his help with the photographs, Malina Strugaru and Aleksei Kalinov for their help with the samples, and the anonymous reviewers as well as the members of the ISTA Visual Computing Group for their feedback. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","doi":"10.1145/3658194","abstract":[{"text":"The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found.\r\n\r\nIn this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes.\r\n\r\nThis insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.","lang":"eng"}],"status":"public","scopus_import":"1","title":"Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments","_id":"17203","publisher":"Association for Computing Machinery","conference":{"end_date":"2024-08-01","start_date":"2024-07-28","location":"Denver, Colorado"}},{"author":[{"id":"331776E2-F248-11E8-B48F-1D18A9856A87","last_name":"Synak","full_name":"Synak, Peter","first_name":"Peter"},{"full_name":"Kalinov, Aleksei","first_name":"Aleksei","id":"44b7120e-eb97-11eb-a6c2-e1557aa81d02","orcid":"0000-0003-2189-3904","last_name":"Kalinov"},{"id":"2afc607f-f128-11eb-9611-8f2a0dfcf074","last_name":"Strugaru","full_name":"Strugaru, Irina-Malina","first_name":"Irina-Malina"},{"id":"36cea3aa-f38e-11ec-8ae0-c65ae6f6098f","last_name":"Etemadihaghighi","first_name":"Arian","full_name":"Etemadihaghighi, Arian"},{"last_name":"Yang","first_name":"Huidong","full_name":"Yang, Huidong"},{"id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6646-5546","last_name":"Wojtan","first_name":"Christopher J","full_name":"Wojtan, Christopher J"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","keyword":["surface tracking","topology change","non- manifold meshes","multi-material flows","solid modeling"],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","issue":"4","isi":1,"article_processing_charge":"Yes (via OA deal)","day":"01","oa_version":"Published Version","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"oa":1,"article_number":"54","file":[{"relation":"main_file","creator":"dernst","checksum":"1917067d4b52d7729019b03560004e43","file_id":"17317","file_name":"2024_ACMToG_HeissSynak.pdf","date_updated":"2024-07-23T06:35:15Z","date_created":"2024-07-23T06:35:15Z","success":1,"access_level":"open_access","content_type":"application/pdf","file_size":48763368},{"file_id":"17221","creator":"akalinov","checksum":"a4f0e293184bfa034c0c585848806b17","relation":"main_file","file_size":48021463,"access_level":"open_access","success":1,"content_type":"video/mp4","file_name":"sdtopofixer_final.mp4","date_updated":"2024-07-10T12:23:44Z","date_created":"2024-07-10T12:23:44Z"},{"checksum":"18fc310a78ec91651148c45a8b89fa44","title":"Authors' version of the text","creator":"akalinov","file_id":"20633","relation":"preprint","file_size":48639581,"date_created":"2025-11-11T09:50:52Z","file_name":"SuperDuperTopoFixer.pdf","date_updated":"2025-11-11T09:50:52Z","content_type":"application/pdf","access_level":"open_access"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"intvolume":"        43","article_type":"original","date_published":"2024-07-01T00:00:00Z","ddc":["004"],"citation":{"mla":"Synak, Peter, et al. “Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes.” <i>ACM Transactions on Graphics</i>, vol. 43, no. 4, 54, Association for Computing Machinery, 2024, doi:<a href=\"https://doi.org/10.1145/3658223\">10.1145/3658223</a>.","apa":"Synak, P., Kalinov, A., Strugaru, I.-M., Etemadi, A., Yang, H., &#38; Wojtan, C. (2024). Multi-material mesh-based surface tracking with implicit topology changes. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3658223\">https://doi.org/10.1145/3658223</a>","chicago":"Synak, Peter, Aleksei Kalinov, Irina-Malina Strugaru, Arian Etemadi, Huidong Yang, and Chris Wojtan. “Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2024. <a href=\"https://doi.org/10.1145/3658223\">https://doi.org/10.1145/3658223</a>.","short":"P. Synak, A. Kalinov, I.-M. Strugaru, A. Etemadi, H. Yang, C. Wojtan, ACM Transactions on Graphics 43 (2024).","ieee":"P. Synak, A. Kalinov, I.-M. Strugaru, A. Etemadi, H. Yang, and C. Wojtan, “Multi-material mesh-based surface tracking with implicit topology changes,” <i>ACM Transactions on Graphics</i>, vol. 43, no. 4. Association for Computing Machinery, 2024.","ama":"Synak P, Kalinov A, Strugaru I-M, Etemadi A, Yang H, Wojtan C. Multi-material mesh-based surface tracking with implicit topology changes. <i>ACM Transactions on Graphics</i>. 2024;43(4). doi:<a href=\"https://doi.org/10.1145/3658223\">10.1145/3658223</a>","ista":"Synak P, Kalinov A, Strugaru I-M, Etemadi A, Yang H, Wojtan C. 2024. Multi-material mesh-based surface tracking with implicit topology changes. ACM Transactions on Graphics. 43(4), 54."},"date_created":"2024-07-10T12:24:00Z","has_accepted_license":"1","external_id":{"isi":["001289270900021"]},"language":[{"iso":"eng"}],"quality_controlled":"1","OA_type":"hybrid","year":"2024","publication":"ACM Transactions on Graphics","related_material":{"record":[{"status":"public","id":"18301","relation":"dissertation_contains"},{"relation":"dissertation_contains","id":"19630","status":"public"}]},"status":"public","_id":"17219","publisher":"Association for Computing Machinery","OA_place":"publisher","scopus_import":"1","title":"Multi-material mesh-based surface tracking with implicit topology changes","corr_author":"1","publication_status":"published","date_updated":"2026-01-16T09:14:23Z","volume":43,"type":"journal_article","acknowledgement":"Peter Heiss-Synak helped conceive the project, helped formulate the algorithm structure, contributed ideas and code to Sections 6 & 8, the mesh data structure, algorithm robustness and benchmarks, helped write the paper, and provided supervision and conceptual solutions throughout the project. Aleksei Kalinov contributed ideas and code to Sections 7, 8.5, and 5, the sparse grid data structure, algorithm robustness and benchmarks, optimized the performance, produced all results, most figures, and the supplementary video, helped write the text, and provided conceptual solutions throughout the project. Malina Strugaru helped implement the mesh data structure and designed re-meshing operations for non-manifold triangle meshes. Arian Etemadi developed early prototypes for ideas in Sections 8.1 and 8.3 and helped write the paper. Huidong Yang developed early prototypes for isosurface extraction and visualization. Chris Wojtan helped conceive the project, helped write the paper, and provided supervision, prototype grid data structure code, and conceptual solutions throughout the project. We thank the anonymous reviewers for their helpful comments, the members of the Visual Computing Group at ISTA for their feedback, Christopher Batty for discussions about LosTopos, and SideFX for the Houdini Education software licenses.  This research was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA).","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"file_date_updated":"2025-11-11T09:50:52Z","abstract":[{"lang":"eng","text":"We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting of millions of triangles."}],"doi":"10.1145/3658223"},{"type":"journal_article","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"intvolume":"        43","article_type":"original","publication_status":"published","date_updated":"2024-08-12T10:08:13Z","date_published":"2024-07-19T00:00:00Z","citation":{"short":"Y. Ren, J. Panetta, S. Suzuki, U. Kusupati, F. Isvoranu, M. Pauly, ACM Transactions on Graphics 43 (2024).","chicago":"Ren, Yingying, Julian Panetta, Seiichi Suzuki, Uday Kusupati, Florin Isvoranu, and Mark Pauly. “Computational Homogenization for Inverse Design of Surface-Based Inflatables.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2024. <a href=\"https://doi.org/10.1145/3658125\">https://doi.org/10.1145/3658125</a>.","apa":"Ren, Y., Panetta, J., Suzuki, S., Kusupati, U., Isvoranu, F., &#38; Pauly, M. (2024). Computational homogenization for inverse design of surface-based inflatables. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3658125\">https://doi.org/10.1145/3658125</a>","mla":"Ren, Yingying, et al. “Computational Homogenization for Inverse Design of Surface-Based Inflatables.” <i>ACM Transactions on Graphics</i>, vol. 43, no. 4, 87, Association for Computing Machinery, 2024, doi:<a href=\"https://doi.org/10.1145/3658125\">10.1145/3658125</a>.","ista":"Ren Y, Panetta J, Suzuki S, Kusupati U, Isvoranu F, Pauly M. 2024. Computational homogenization for inverse design of surface-based inflatables. ACM Transactions on Graphics. 43(4), 87.","ama":"Ren Y, Panetta J, Suzuki S, Kusupati U, Isvoranu F, Pauly M. Computational homogenization for inverse design of surface-based inflatables. <i>ACM Transactions on Graphics</i>. 2024;43(4). doi:<a href=\"https://doi.org/10.1145/3658125\">10.1145/3658125</a>","ieee":"Y. Ren, J. Panetta, S. Suzuki, U. Kusupati, F. Isvoranu, and M. Pauly, “Computational homogenization for inverse design of surface-based inflatables,” <i>ACM Transactions on Graphics</i>, vol. 43, no. 4. Association for Computing Machinery, 2024."},"volume":43,"date_created":"2024-08-12T10:03:38Z","year":"2024","publication":"ACM Transactions on Graphics","extern":"1","language":[{"iso":"eng"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"Surface-based inflatables are composed of two thin layers of nearly inextensible sheet material joined together along carefully selected fusing curves. During inflation, pressure forces separate the two sheets to maximize the enclosed volume. The fusing curves restrict this expansion, leading to a spatially varying in-plane contraction and hence metric frustration. The inflated structure settles into a 3D equilibrium that balances pressure forces with the internal elastic forces of the sheets.\r\nWe present a computational framework for analyzing and designing surface-based inflatable structures with arbitrary fusing patterns. Our approach employs numerical homogenization to characterize the behavior of parametric families of periodic inflatable patch geometries, which can then be combined to tessellate the sheet with smoothly varying patterns. We propose a novel parametrization of the underlying deformation space that allows accurate, efficient, and systematical analysis of the stretching and bending behavior of inflated patches with potentially open boundaries.\r\nWe apply our homogenization algorithm to create a database of geometrically diverse fusing patterns spanning a wide range of material properties and deformation characteristics. This database is employed in an inverse design algorithm that solves for fusing curves to best approximate a given input target surface. Local patches are selected and blended to form a global network of curves based on a geometric flattening algorithm. These fusing curves are then further optimized to minimize the distance of the deployed structure to target surface. We show that this approach offers greater flexibility to approximate given target geometries compared to previous work while significantly improving structural performance."}],"doi":"10.1145/3658125","status":"public","issue":"4","article_processing_charge":"No","day":"19","author":[{"last_name":"Ren","id":"93d68d10-3540-11ef-a265-f748a50dba3d","full_name":"Ren, Yingying","first_name":"Yingying"},{"full_name":"Panetta, Julian","first_name":"Julian","last_name":"Panetta"},{"last_name":"Suzuki","first_name":"Seiichi","full_name":"Suzuki, Seiichi"},{"last_name":"Kusupati","first_name":"Uday","full_name":"Kusupati, Uday"},{"last_name":"Isvoranu","first_name":"Florin","full_name":"Isvoranu, Florin"},{"last_name":"Pauly","full_name":"Pauly, Mark","first_name":"Mark"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","_id":"17424","article_number":"87","publisher":"Association for Computing Machinery","scopus_import":"1","title":"Computational homogenization for inverse design of surface-based inflatables","oa_version":"None"},{"quality_controlled":"1","language":[{"iso":"eng"}],"publication":"ACM Transactions on Graphics","year":"2023","citation":{"apa":"Jeschke, S., &#38; Wojtan, C. (2023). Generalizing shallow water simulations with dispersive surface waves. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3592098\">https://doi.org/10.1145/3592098</a>","mla":"Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations with Dispersive Surface Waves.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, 83, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3592098\">10.1145/3592098</a>.","short":"S. Jeschke, C. Wojtan, ACM Transactions on Graphics 42 (2023).","chicago":"Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations with Dispersive Surface Waves.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3592098\">https://doi.org/10.1145/3592098</a>.","ieee":"S. Jeschke and C. Wojtan, “Generalizing shallow water simulations with dispersive surface waves,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023.","ista":"Jeschke S, Wojtan C. 2023. Generalizing shallow water simulations with dispersive surface waves. ACM Transactions on Graphics. 42(4), 83.","ama":"Jeschke S, Wojtan C. Generalizing shallow water simulations with dispersive surface waves. <i>ACM Transactions on Graphics</i>. 2023;42(4). doi:<a href=\"https://doi.org/10.1145/3592098\">10.1145/3592098</a>"},"has_accepted_license":"1","date_created":"2023-08-27T22:01:17Z","ddc":["000"],"date_published":"2023-08-01T00:00:00Z","article_type":"original","intvolume":"        42","external_id":{"isi":["001044671300049"]},"oa_version":"Published Version","department":[{"_id":"ChWo"}],"file":[{"file_size":511572575,"success":1,"access_level":"open_access","content_type":"video/mp4","date_updated":"2023-12-21T12:26:40Z","file_name":"PaperVideo_final.mp4","date_created":"2023-12-21T12:26:40Z","file_id":"14704","creator":"sjeschke","checksum":"1d178bb2f8011d9f5aedda6427e18c7a","relation":"main_file"},{"date_created":"2024-01-02T09:34:27Z","date_updated":"2024-01-02T09:34:27Z","file_name":"2023_ACMToG_Jeschke.pdf","content_type":"application/pdf","success":1,"access_level":"open_access","file_size":7469177,"relation":"main_file","checksum":"a49b2e744d5cd1276bb8b2e0ce6dc638","creator":"dernst","file_id":"14725"}],"article_number":"83","oa":1,"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"license":"https://creativecommons.org/licenses/by/4.0/","month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"author":[{"id":"44D6411A-F248-11E8-B48F-1D18A9856A87","last_name":"Jeschke","full_name":"Jeschke, Stefan","first_name":"Stefan"},{"first_name":"Christopher J","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan","orcid":"0000-0001-6646-5546"}],"day":"01","article_processing_charge":"Yes (in subscription journal)","isi":1,"issue":"4","doi":"10.1145/3592098","abstract":[{"text":"This paper introduces a novel method for simulating large bodies of water as a height field. At the start of each time step, we partition the waves into a bulk flow (which approximately satisfies the assumptions of the shallow water equations) and surface waves (which approximately satisfy the assumptions of Airy wave theory). We then solve the two wave regimes separately using appropriate state-of-the-art techniques, and re-combine the resulting wave velocities at the end of each step. This strategy leads to the first heightfield wave model capable of simulating complex interactions between both deep and shallow water effects, like the waves from a boat wake sloshing up onto a beach, or a dam break producing wave interference patterns and eddies. We also analyze the numerical dispersion created by our method and derive an exact correction factor for waves at a constant water depth, giving us a numerically perfect re-creation of theoretical water wave dispersion patterns.","lang":"eng"}],"volume":42,"date_updated":"2025-04-14T08:01:13Z","publication_status":"published","corr_author":"1","file_date_updated":"2024-01-02T09:34:27Z","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"acknowledgement":"We thank Georg Sperl for helping with early research for this paper, Mickael Ly and Yi-Lu Chen for proofreading, and members of the ISTA Visual Computing Group for general feedback. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).\r\nThe motorboat and sailboat were modeled by Sergei and the palmtrees by YadroGames. The environment map was created by Emil Persson.","acknowledged_ssus":[{"_id":"ScienComp"}],"type":"journal_article","scopus_import":"1","title":"Generalizing shallow water simulations with dispersive surface waves","publisher":"Association for Computing Machinery","_id":"14240","status":"public"},{"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."}],"doi":"10.1145/3605389","type":"journal_article","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.","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"file_date_updated":"2023-12-04T08:04:14Z","publication_status":"published","date_updated":"2025-09-09T13:33:58Z","volume":42,"_id":"14628","publisher":"Association for Computing Machinery","title":"Procedural metamaterials: A unified procedural graph for metamaterial design","scopus_import":"1","status":"public","year":"2023","publication":"ACM Transactions on Graphics","language":[{"iso":"eng"}],"quality_controlled":"1","external_id":{"isi":["001086833300007"]},"article_type":"original","intvolume":"        42","ddc":["531","006"],"date_published":"2023-10-01T00:00:00Z","date_created":"2023-11-29T15:02:03Z","has_accepted_license":"1","citation":{"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.","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>","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.","short":"L. Makatura, B. Wang, Y.-L. Chen, B. Deng, C. Wojtan, B. Bickel, W. Matusik, ACM Transactions on Graphics 42 (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>.","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>","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>."},"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"oa":1,"article_number":"168","file":[{"access_level":"open_access","success":1,"content_type":"application/zip","date_updated":"2023-11-29T15:16:01Z","file_name":"tog-22-0089-File004.zip","date_created":"2023-11-29T15:16:01Z","file_size":95467870,"relation":"main_file","file_id":"14630","creator":"yichen","checksum":"0192f597d7a2ceaf89baddfd6190d4c8"},{"checksum":"7fb024963be81933494f38de191e4710","creator":"yichen","file_id":"14631","relation":"main_file","file_size":103731880,"date_created":"2023-11-29T15:16:01Z","date_updated":"2023-11-29T15:16:01Z","file_name":"tog-22-0089-File005.zip","content_type":"application/zip","success":1,"access_level":"open_access"},{"access_level":"open_access","success":1,"content_type":"application/pdf","date_updated":"2023-12-04T08:04:14Z","file_name":"2023_ACMToG_Makatura.pdf","date_created":"2023-12-04T08:04:14Z","file_size":57067476,"relation":"main_file","file_id":"14638","creator":"dernst","checksum":"b7d6829ce396e21cac9fae0ec7130a6b"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"},{"_id":"BeBi"}],"oa_version":"Published Version","issue":"5","isi":1,"day":"01","article_processing_charge":"Yes (in subscription journal)","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","first_name":"Yi-Lu","full_name":"Chen, Yi-Lu"},{"last_name":"Deng","full_name":"Deng, Bolei","first_name":"Bolei"},{"full_name":"Wojtan, Christopher J","first_name":"Christopher J","orcid":"0000-0001-6646-5546","last_name":"Wojtan","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bickel, Bernd","first_name":"Bernd","orcid":"0000-0001-6511-9385","last_name":"Bickel","id":"49876194-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Matusik, Wojciech","first_name":"Wojciech","last_name":"Matusik"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"10","keyword":["Computer Graphics and Computer-Aided Design"]},{"corr_author":"1","publication_status":"published","date_updated":"2025-04-15T07:43:53Z","volume":42,"acknowledged_ssus":[{"_id":"M-Shop"}],"type":"journal_article","acknowledgement":"We thank Todor Asenov and the Miba Machine Shop for their help in assembling the tattoo machine and manufacturing the substrates. We thank Geysler Rodrigues for the insightful discussions on tattooing practices from a professional artist's perspective. We thank Maria Fernanda Portugal for sharing a doctor's perspective on medical applications of tattoos. This work is graciously supported by the FWF Lise Meitner (Grant M 3319).","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"file_date_updated":"2024-04-16T05:52:18Z","abstract":[{"lang":"eng","text":"Tattoos are a highly popular medium, with both artistic and medical applications. Although the mechanical process of tattoo application has evolved historically, the results are reliant on the artisanal skill of the artist. This can be especially challenging for some skin tones, or in cases where artists lack experience. We provide the first systematic overview of tattooing as a computational fabrication technique. We built an automated tattooing rig and a recipe for the creation of silicone sheets mimicking realistic skin tones, which allowed us to create an accurate model predicting tattoo appearance. This enables several exciting applications including tattoo previewing, color retargeting, novel ink spectra optimization, color-accurate prosthetics, and more."}],"doi":"10.1145/3592432","status":"public","_id":"12984","publisher":"Association for Computing Machinery","conference":{"end_date":"2023-08-10","start_date":"2023-08-06","location":"Los Angeles, CA, United States","name":"SIGGRAPH: Computer Graphics and Interactive Techniques Conference"},"scopus_import":"1","title":"Skin-Screen: A computational fabrication framework for color tattoos","article_type":"original","intvolume":"        42","ddc":["004"],"date_published":"2023-07-26T00:00:00Z","has_accepted_license":"1","citation":{"ama":"Piovarci M, Chapiro A, Bickel B. Skin-Screen: A computational fabrication framework for color tattoos. <i>ACM Transactions on Graphics</i>. 2023;42(4). doi:<a href=\"https://doi.org/10.1145/3592432\">10.1145/3592432</a>","ista":"Piovarci M, Chapiro A, Bickel B. 2023. Skin-Screen: A computational fabrication framework for color tattoos. ACM Transactions on Graphics. 42(4), 67.","ieee":"M. Piovarci, A. Chapiro, and B. Bickel, “Skin-Screen: A computational fabrication framework for color tattoos,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023.","chicago":"Piovarci, Michael, Alexandre Chapiro, and Bernd Bickel. “Skin-Screen: A Computational Fabrication Framework for Color Tattoos.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3592432\">https://doi.org/10.1145/3592432</a>.","short":"M. Piovarci, A. Chapiro, B. Bickel, ACM Transactions on Graphics 42 (2023).","mla":"Piovarci, Michael, et al. “Skin-Screen: A Computational Fabrication Framework for Color Tattoos.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, 67, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3592432\">10.1145/3592432</a>.","apa":"Piovarci, M., Chapiro, A., &#38; Bickel, B. (2023). Skin-Screen: A computational fabrication framework for color tattoos. <i>ACM Transactions on Graphics</i>. Los Angeles, CA, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3592432\">https://doi.org/10.1145/3592432</a>"},"date_created":"2023-05-16T09:39:14Z","external_id":{"isi":["001044671300033"]},"language":[{"iso":"eng"}],"quality_controlled":"1","year":"2023","publication":"ACM Transactions on Graphics","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"author":[{"first_name":"Michael","full_name":"Piovarci, Michael","id":"62E473F4-5C99-11EA-A40E-AF823DDC885E","last_name":"Piovarci","orcid":"0000-0002-5062-4474"},{"full_name":"Chapiro, Alexandre","first_name":"Alexandre","last_name":"Chapiro"},{"last_name":"Bickel","orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","first_name":"Bernd","full_name":"Bickel, Bernd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"07","keyword":["appearance","modeling","reproduction","tattoo","skin color","gamut mapping","ink-optimization","prosthetic"],"issue":"4","isi":1,"day":"26","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","oa":1,"project":[{"grant_number":"M03319","_id":"eb901961-77a9-11ec-83b8-f5c883a62027","name":"Perception-Aware Appearance Fabrication"}],"article_number":"67","file":[{"file_name":"Piovarci2023.pdf","date_updated":"2023-05-16T09:38:25Z","date_created":"2023-05-16T09:38:25Z","access_level":"open_access","success":1,"content_type":"application/pdf","file_size":30817343,"relation":"main_file","creator":"mpiovarc","checksum":"5f0a6867689e025a661bd0b4fd90b821","file_id":"12985"},{"file_size":30281676,"date_created":"2024-04-16T05:52:18Z","date_updated":"2024-04-16T05:52:18Z","file_name":"2023_ACM_Piovarci.pdf","content_type":"application/pdf","success":1,"access_level":"open_access","checksum":"6dd371de5b517e5f184f9c2cbea4b8b3","creator":"dernst","file_id":"15324","relation":"main_file"}],"department":[{"_id":"BeBi"}]},{"isi":1,"article_processing_charge":"No","day":"26","issue":"4","month":"07","keyword":["PCB design and layout","Mesh geometry models"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"author":[{"first_name":"Marco","full_name":"Freire, Marco","last_name":"Freire"},{"last_name":"Bhargava","orcid":"0009-0007-6138-6890","id":"FF8FA64C-AA6A-11E9-99AD-50D4E5697425","first_name":"Manas","full_name":"Bhargava, Manas"},{"first_name":"Camille","full_name":"Schreck, Camille","last_name":"Schreck","id":"2B14B676-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hugron, Pierre-Alexandre","first_name":"Pierre-Alexandre","last_name":"Hugron"},{"first_name":"Bernd","full_name":"Bickel, Bernd","orcid":"0000-0001-6511-9385","last_name":"Bickel","id":"49876194-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Lefebvre, Sylvain","first_name":"Sylvain","last_name":"Lefebvre"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"GradSch"},{"_id":"BeBi"}],"file":[{"file_id":"13156","creator":"dernst","checksum":"a0b0ba3b36f43a94388e8824613d812a","relation":"main_file","file_size":78940724,"success":1,"access_level":"open_access","content_type":"application/pdf","file_name":"2023_ACMToG_Freire.pdf","date_updated":"2023-06-19T11:02:23Z","date_created":"2023-06-19T11:02:23Z"},{"file_id":"13157","checksum":"b9206bbb67af82df49b7e7cdbde3410c","creator":"dernst","relation":"main_file","file_size":34345905,"content_type":"application/pdf","access_level":"open_access","success":1,"date_created":"2023-06-20T12:20:51Z","date_updated":"2023-06-20T12:20:51Z","file_name":"2023_ACMToG_SuppMaterial_Freire.pdf"}],"oa":1,"project":[{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","call_identifier":"H2020","_id":"24F9549A-B435-11E9-9278-68D0E5697425","grant_number":"715767"}],"article_number":"142","oa_version":"Submitted Version","external_id":{"isi":["001044671300108"]},"ddc":["006"],"date_published":"2023-07-26T00:00:00Z","has_accepted_license":"1","citation":{"chicago":"Freire, Marco, Manas Bhargava, Camille Schreck, Pierre-Alexandre Hugron, Bernd Bickel, and Sylvain Lefebvre. “PCBend: Light up Your 3D Shapes with Foldable Circuit Boards.” <i>Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3592411\">https://doi.org/10.1145/3592411</a>.","short":"M. Freire, M. Bhargava, C. Schreck, P.-A. Hugron, B. Bickel, S. Lefebvre, Transactions on Graphics 42 (2023).","mla":"Freire, Marco, et al. “PCBend: Light up Your 3D Shapes with Foldable Circuit Boards.” <i>Transactions on Graphics</i>, vol. 42, no. 4, 142, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3592411\">10.1145/3592411</a>.","apa":"Freire, M., Bhargava, M., Schreck, C., Hugron, P.-A., Bickel, B., &#38; Lefebvre, S. (2023). PCBend: Light up your 3D shapes with foldable circuit boards. <i>Transactions on Graphics</i>. Los Angeles, CA, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3592411\">https://doi.org/10.1145/3592411</a>","ama":"Freire M, Bhargava M, Schreck C, Hugron P-A, Bickel B, Lefebvre S. PCBend: Light up your 3D shapes with foldable circuit boards. <i>Transactions on Graphics</i>. 2023;42(4). doi:<a href=\"https://doi.org/10.1145/3592411\">10.1145/3592411</a>","ista":"Freire M, Bhargava M, Schreck C, Hugron P-A, Bickel B, Lefebvre S. 2023. PCBend: Light up your 3D shapes with foldable circuit boards. Transactions on Graphics. 42(4), 142.","ieee":"M. Freire, M. Bhargava, C. Schreck, P.-A. Hugron, B. Bickel, and S. Lefebvre, “PCBend: Light up your 3D shapes with foldable circuit boards,” <i>Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023."},"date_created":"2023-05-22T08:37:04Z","intvolume":"        42","article_type":"original","publication":"Transactions on Graphics","year":"2023","ec_funded":1,"language":[{"iso":"eng"}],"quality_controlled":"1","status":"public","related_material":{"record":[{"relation":"dissertation_contains","id":"20276","status":"public"}]},"scopus_import":"1","title":"PCBend: Light up your 3D shapes with foldable circuit boards","_id":"13049","conference":{"location":"Los Angeles, CA, United States","name":"SIGGRAPH: Computer Graphics and Interactive Techniques Conference","start_date":"2023-08-06","end_date":"2023-08-10"},"publisher":"Association for Computing Machinery","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"file_date_updated":"2023-06-20T12:20:51Z","acknowledged_ssus":[{"_id":"M-Shop"}],"type":"journal_article","acknowledgement":"We thank the reviewers for the valuable feedback. We also thank the Miba Machine Shop at ISTA, PCBWay, and PragoBoard for helping us with fabrication and assembly. This project was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 715767 – MATERIALIZABLE).","date_updated":"2025-09-12T12:18:50Z","volume":42,"corr_author":"1","publication_status":"published","doi":"10.1145/3592411","abstract":[{"text":"We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of\r\nestablished PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. \r\nOur approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved.\r\nOur technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs.","lang":"eng"}]},{"quality_controlled":"1","language":[{"iso":"eng"}],"year":"2023","publication":"ACM Transactions on Graphics","intvolume":"        42","article_type":"original","citation":{"ieee":"F. Zhong, Y. Xu, H. Zhao, and L. Lu, “As-Continuous-As-Possible extrusion-based fabrication of surface models,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 3. Association for Computing Machinery, 2023.","ista":"Zhong F, Xu Y, Zhao H, Lu L. 2023. As-Continuous-As-Possible extrusion-based fabrication of surface models. ACM Transactions on Graphics. 42(3), 26.","ama":"Zhong F, Xu Y, Zhao H, Lu L. As-Continuous-As-Possible extrusion-based fabrication of surface models. <i>ACM Transactions on Graphics</i>. 2023;42(3). doi:<a href=\"https://doi.org/10.1145/3575859\">10.1145/3575859</a>","apa":"Zhong, F., Xu, Y., Zhao, H., &#38; Lu, L. (2023). As-Continuous-As-Possible extrusion-based fabrication of surface models. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3575859\">https://doi.org/10.1145/3575859</a>","mla":"Zhong, Fanchao, et al. “As-Continuous-As-Possible Extrusion-Based Fabrication of Surface Models.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 3, 26, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3575859\">10.1145/3575859</a>.","short":"F. Zhong, Y. Xu, H. Zhao, L. Lu, ACM Transactions on Graphics 42 (2023).","chicago":"Zhong, Fanchao, Yonglai Xu, Haisen Zhao, and Lin Lu. “As-Continuous-As-Possible Extrusion-Based Fabrication of Surface Models.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3575859\">https://doi.org/10.1145/3575859</a>."},"date_created":"2023-07-23T22:01:13Z","date_published":"2023-03-17T00:00:00Z","external_id":{"isi":["001018739600002"],"arxiv":["2201.02374"]},"arxiv":1,"oa_version":"Preprint","article_number":"26","oa":1,"department":[{"_id":"BeBi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Zhong, Fanchao","first_name":"Fanchao","last_name":"Zhong"},{"last_name":"Xu","full_name":"Xu, Yonglai","first_name":"Yonglai"},{"id":"fb7f793a-80d1-11eb-8869-d56e5b2a8ff4","orcid":"0000-0002-6389-1045","last_name":"Zhao","full_name":"Zhao, Haisen","first_name":"Haisen"},{"first_name":"Lin","full_name":"Lu, Lin","last_name":"Lu"}],"month":"03","issue":"3","article_processing_charge":"No","day":"17","isi":1,"abstract":[{"text":"In this study, we propose a computational framework for optimizing the continuity of the toolpath in fabricating surface models on an extrusion-based 3D printer. Toolpath continuity is a critical issue that influences both the quality and the efficiency of extrusion-based fabrication. Transfer moves lead to rough and bumpy surfaces, where this phenomenon worsens for materials with large viscosity, like clay. The effects of continuity on the surface models are even more severe in terms of the quality of the surface and the stability of the model. We introduce a criterion called the one–path patch (OPP) to represent a patch on the surface of the shell that can be traversed along one path by considering the constraints on fabrication. We study the properties of the OPPs and their merging operations to propose a bottom-up OPP merging procedure to decompose the given shell surface into a minimal number of OPPs, and to generate the “as-continuous-as-possible” (ACAP) toolpath. Furthermore, we augment the path planning algorithm with a curved-layer printing scheme that reduces staircase defects and improves the continuity of the toolpath by connecting multiple segments. We evaluated the ACAP algorithm on ceramic and thermoplastic materials, and the results showed that it improves the fabrication of surface models in terms of both efficiency and surface quality.","lang":"eng"}],"doi":"10.1145/3575859","publication_status":"published","volume":42,"date_updated":"2023-12-13T11:34:59Z","acknowledgement":"This work was supported in part by grants from the NSFC (61972232), Science and Technology Program of Shenzhen, China (CJGJZD20200617102202007). ","type":"journal_article","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2201.02374"}],"publisher":"Association for Computing Machinery","_id":"13265","scopus_import":"1","title":"As-Continuous-As-Possible extrusion-based fabrication of surface models","status":"public"},{"status":"public","issue":"6","article_processing_charge":"No","day":"05","author":[{"last_name":"Becker","full_name":"Becker, Quentin","first_name":"Quentin"},{"last_name":"Suzuki","first_name":"Seiichi","full_name":"Suzuki, Seiichi"},{"full_name":"Ren, Yingying","first_name":"Yingying","last_name":"Ren","id":"93d68d10-3540-11ef-a265-f748a50dba3d"},{"last_name":"Pellis","full_name":"Pellis, Davide","first_name":"Davide"},{"full_name":"Panetta, Julian","first_name":"Julian","last_name":"Panetta"},{"full_name":"Pauly, Mark","first_name":"Mark","last_name":"Pauly"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"12","_id":"17379","article_number":"173","publisher":"Association for Computing Machinery","title":"C-shells: Deployable gridshells with curved beams","scopus_import":"1","oa_version":"None","type":"journal_article","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"intvolume":"        42","article_type":"original","publication_status":"published","date_published":"2023-12-05T00:00:00Z","date_updated":"2024-08-12T09:56:32Z","date_created":"2024-08-05T06:15:06Z","volume":42,"citation":{"ieee":"Q. Becker, S. Suzuki, Y. Ren, D. Pellis, J. Panetta, and M. Pauly, “C-shells: Deployable gridshells with curved beams,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 6. Association for Computing Machinery, 2023.","ista":"Becker Q, Suzuki S, Ren Y, Pellis D, Panetta J, Pauly M. 2023. C-shells: Deployable gridshells with curved beams. ACM Transactions on Graphics. 42(6), 173.","ama":"Becker Q, Suzuki S, Ren Y, Pellis D, Panetta J, Pauly M. C-shells: Deployable gridshells with curved beams. <i>ACM Transactions on Graphics</i>. 2023;42(6). doi:<a href=\"https://doi.org/10.1145/3618366\">10.1145/3618366</a>","apa":"Becker, Q., Suzuki, S., Ren, Y., Pellis, D., Panetta, J., &#38; Pauly, M. (2023). C-shells: Deployable gridshells with curved beams. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3618366\">https://doi.org/10.1145/3618366</a>","mla":"Becker, Quentin, et al. “C-Shells: Deployable Gridshells with Curved Beams.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 6, 173, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3618366\">10.1145/3618366</a>.","short":"Q. Becker, S. Suzuki, Y. Ren, D. Pellis, J. Panetta, M. Pauly, ACM Transactions on Graphics 42 (2023).","chicago":"Becker, Quentin, Seiichi Suzuki, Yingying Ren, Davide Pellis, Julian Panetta, and Mark Pauly. “C-Shells: Deployable Gridshells with Curved Beams.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3618366\">https://doi.org/10.1145/3618366</a>."},"year":"2023","publication":"ACM Transactions on Graphics","language":[{"iso":"eng"}],"extern":"1","abstract":[{"lang":"eng","text":"We introduce a computational pipeline for simulating and designing C-shells, a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape.\r\nWe propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy.\r\nWe find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures."}],"quality_controlled":"1","doi":"10.1145/3618366"},{"issue":"4","status":"public","article_processing_charge":"No","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Vidulis, Michele","first_name":"Michele","last_name":"Vidulis"},{"first_name":"Yingying","full_name":"Ren, Yingying","last_name":"Ren","id":"93d68d10-3540-11ef-a265-f748a50dba3d"},{"last_name":"Panetta","first_name":"Julian","full_name":"Panetta, Julian"},{"last_name":"Grinspun","first_name":"Eitan","full_name":"Grinspun, Eitan"},{"last_name":"Pauly","first_name":"Mark","full_name":"Pauly, Mark"}],"month":"08","publisher":"Association for Computing Machinery","article_number":"73","_id":"17381","scopus_import":"1","title":"Computational exploration of multistable elastic knots","oa_version":"None","type":"journal_article","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"publication_status":"published","intvolume":"        42","article_type":"original","citation":{"apa":"Vidulis, M., Ren, Y., Panetta, J., Grinspun, E., &#38; Pauly, M. (2023). Computational exploration of multistable elastic knots. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3592399\">https://doi.org/10.1145/3592399</a>","mla":"Vidulis, Michele, et al. “Computational Exploration of Multistable Elastic Knots.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, 73, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3592399\">10.1145/3592399</a>.","short":"M. Vidulis, Y. Ren, J. Panetta, E. Grinspun, M. Pauly, ACM Transactions on Graphics 42 (2023).","chicago":"Vidulis, Michele, Yingying Ren, Julian Panetta, Eitan Grinspun, and Mark Pauly. “Computational Exploration of Multistable Elastic Knots.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3592399\">https://doi.org/10.1145/3592399</a>.","ieee":"M. Vidulis, Y. Ren, J. Panetta, E. Grinspun, and M. Pauly, “Computational exploration of multistable elastic knots,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023.","ista":"Vidulis M, Ren Y, Panetta J, Grinspun E, Pauly M. 2023. Computational exploration of multistable elastic knots. ACM Transactions on Graphics. 42(4), 73.","ama":"Vidulis M, Ren Y, Panetta J, Grinspun E, Pauly M. Computational exploration of multistable elastic knots. <i>ACM Transactions on Graphics</i>. 2023;42(4). doi:<a href=\"https://doi.org/10.1145/3592399\">10.1145/3592399</a>"},"date_created":"2024-08-05T06:29:22Z","volume":42,"date_published":"2023-08-01T00:00:00Z","date_updated":"2024-08-12T09:48:36Z","year":"2023","publication":"ACM Transactions on Graphics","quality_controlled":"1","abstract":[{"lang":"eng","text":"We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, these knots settle into equilibrium states that balance the forces induced by elastic deformation and self-contacts of the wire. In general, elastic knots can have many distinct equilibrium states, i.e. they are multistable mechanical systems. We propose a computational pipeline that combines randomized spatial sampling and physics simulation to efficiently find stable equilibrium states of elastic knots. Leveraging results from knot theory, we run our pipeline on thousands of different topological knot types to create an extensive data set of multistable knots. By applying a series of filters to this data, we discover new transformable knots with interesting geometric and physical properties. A further analysis across knot types reveals geometric and topological patterns, yielding constructive principles that generalize beyond the currently tabulated knot types. We show how multistable elastic knots can be used to design novel deployable structures and engaging recreational puzzles. Several physical prototypes at different scales highlight these applications and validate our simulation."}],"extern":"1","language":[{"iso":"eng"}],"doi":"10.1145/3592399"},{"day":"20","article_processing_charge":"No","isi":1,"issue":"5","keyword":["Computer Graphics","Computational Design","Computational Geometry","Shape Modeling"],"month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Hafner, Christian","first_name":"Christian","last_name":"Hafner","id":"400429CC-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bickel","orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","full_name":"Bickel, Bernd","first_name":"Bernd"}],"department":[{"_id":"BeBi"}],"file":[{"date_created":"2023-07-04T08:11:28Z","file_name":"kirchhoff-rods.pdf","date_updated":"2023-07-04T08:11:28Z","content_type":"application/pdf","access_level":"open_access","success":1,"file_size":19635168,"relation":"main_file","checksum":"4954c1cfa487725bc156dcfec872478a","creator":"chafner","file_id":"13194"},{"content_type":"application/pdf","access_level":"open_access","date_created":"2023-07-04T07:46:28Z","file_name":"supp-main.pdf","date_updated":"2023-07-04T07:46:28Z","file_size":420909,"relation":"supplementary_material","file_id":"13190","checksum":"79c9975fbc82ff71f1767331d2204cca","title":"Supplemental Material with Proofs","creator":"chafner"},{"file_size":430086,"access_level":"open_access","content_type":"application/pdf","file_name":"supp-cheat.pdf","date_updated":"2023-07-04T07:46:30Z","date_created":"2023-07-04T07:46:30Z","file_id":"13191","creator":"chafner","checksum":"4ab647e4f03c711e1e6a5fc1eb8684db","title":"Cheat Sheet for Notation","relation":"supplementary_material"},{"access_level":"open_access","content_type":"video/mp4","file_name":"kirchhoff-video-final.mp4","date_updated":"2023-07-04T07:46:39Z","date_created":"2023-07-04T07:46:39Z","file_size":268088064,"relation":"supplementary_material","file_id":"13192","creator":"chafner","title":"Supplemental Video","checksum":"c0fd9a57d012046de90c185ffa904b76"},{"relation":"supplementary_material","file_id":"13193","checksum":"71b00712b489ada2cd9815910ee180a9","title":"Matlab Source Code with Example","creator":"chafner","content_type":"application/x-zip-compressed","access_level":"open_access","date_created":"2023-07-04T07:47:10Z","file_name":"matlab-submission.zip","date_updated":"2023-07-04T07:47:10Z","file_size":25790}],"article_number":"171","oa":1,"project":[{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","call_identifier":"H2020","grant_number":"715767","_id":"24F9549A-B435-11E9-9278-68D0E5697425"}],"oa_version":"Submitted Version","external_id":{"isi":["001086833300010"]},"date_created":"2023-07-04T07:41:30Z","citation":{"ama":"Hafner C, Bickel B. The design space of Kirchhoff rods. <i>ACM Transactions on Graphics</i>. 2023;42(5). doi:<a href=\"https://doi.org/10.1145/3606033\">10.1145/3606033</a>","ista":"Hafner C, Bickel B. 2023. The design space of Kirchhoff rods. ACM Transactions on Graphics. 42(5), 171.","ieee":"C. Hafner and B. Bickel, “The design space of Kirchhoff rods,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5. Association for Computing Machinery, 2023.","chicago":"Hafner, Christian, and Bernd Bickel. “The Design Space of Kirchhoff Rods.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3606033\">https://doi.org/10.1145/3606033</a>.","short":"C. Hafner, B. Bickel, ACM Transactions on Graphics 42 (2023).","mla":"Hafner, Christian, and Bernd Bickel. “The Design Space of Kirchhoff Rods.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5, 171, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3606033\">10.1145/3606033</a>.","apa":"Hafner, C., &#38; Bickel, B. (2023). The design space of Kirchhoff rods. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3606033\">https://doi.org/10.1145/3606033</a>"},"has_accepted_license":"1","ddc":["516"],"date_published":"2023-09-20T00:00:00Z","article_type":"original","intvolume":"        42","publication":"ACM Transactions on Graphics","year":"2023","ec_funded":1,"quality_controlled":"1","language":[{"iso":"eng"}],"status":"public","related_material":{"record":[{"id":"12897","relation":"part_of_dissertation","status":"public"}]},"scopus_import":"1","title":"The design space of Kirchhoff rods","publisher":"Association for Computing Machinery","_id":"13188","file_date_updated":"2023-07-04T08:11:28Z","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"acknowledgement":"We thank the anonymous reviewers for their generous feedback, and Julian Fischer for his help in proving Proposition 1. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 715767).","type":"journal_article","acknowledged_ssus":[{"_id":"M-Shop"}],"volume":42,"date_updated":"2026-04-02T22:30:19Z","publication_status":"published","corr_author":"1","doi":"10.1145/3606033","abstract":[{"lang":"eng","text":"The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length.\r\nWe also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics."}]},{"_id":"11442","publisher":"Association for Computing Machinery","OA_place":"publisher","scopus_import":"1","title":"Closed-loop control of direct ink writing via reinforcement learning","related_material":{"link":[{"url":"https://ista.ac.at/en/news/machine-learning-3d-printing-fluids/","relation":"press_release","description":"News on ISTA website"}]},"status":"public","abstract":[{"text":"Enabling additive manufacturing to employ a wide range of novel, functional materials can be a major boost to this technology. However, making such materials printable requires painstaking trial-and-error by an expert operator,\r\nas they typically tend to exhibit peculiar rheological or hysteresis properties. Even in the case of successfully finding the process parameters, there is no guarantee of print-to-print consistency due to material differences between batches. These challenges make closed-loop feedback an attractive option where the process parameters are adjusted on-the-fly. There are several challenges for designing an efficient controller: the deposition parameters are complex and highly coupled, artifacts occur after long time horizons, simulating the deposition is computationally costly, and learning on hardware is intractable. In this work, we demonstrate the feasibility of learning a closed-loop control policy for additive manufacturing using reinforcement learning. We show that approximate, but efficient, numerical simulation is\r\nsufficient as long as it allows learning the behavioral patterns of deposition that translate to real-world experiences. In combination with reinforcement learning, our model can be used to discover control policies that outperform\r\nbaseline controllers. Furthermore, the recovered policies have a minimal sim-to-real gap. We showcase this by applying our control policy in-vivo on a single-layer, direct ink writing printer. ","lang":"eng"}],"doi":"10.1145/3528223.3530144","corr_author":"1","publication_status":"published","date_updated":"2025-09-10T09:36:45Z","volume":41,"type":"journal_article","acknowledgement":"This work is graciously supported by the following grant agencies: FWF Lise Meitner (Grant M 3319), SNSF (Grant 200502), ERC Starting Grant (MATERIALIZABLE-715767), NSF (Grant IIS-181507).\r\n","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"file_date_updated":"2022-06-28T08:32:58Z","PlanS_conform":"1","oa_version":"Submitted Version","oa":1,"project":[{"grant_number":"M03319","_id":"eb901961-77a9-11ec-83b8-f5c883a62027","name":"Perception-Aware Appearance Fabrication"},{"call_identifier":"H2020","name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","grant_number":"715767","_id":"24F9549A-B435-11E9-9278-68D0E5697425"}],"article_number":"112","department":[{"_id":"BeBi"}],"file":[{"file_id":"11467","creator":"dernst","checksum":"27f6fe41c6ff84d50445cc9b0176d45b","relation":"main_file","file_size":33994829,"access_level":"open_access","success":1,"content_type":"application/pdf","file_name":"2022_ACM_acceptedversion_Piovarci.pdf","date_updated":"2022-06-28T08:32:58Z","date_created":"2022-06-28T08:32:58Z"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"author":[{"orcid":"0000-0002-5062-4474","last_name":"Piovarci","id":"62E473F4-5C99-11EA-A40E-AF823DDC885E","first_name":"Michael","full_name":"Piovarci, Michael"},{"last_name":"Foshey","full_name":"Foshey, Michael","first_name":"Michael"},{"first_name":"Jie","full_name":"Xu, Jie","last_name":"Xu"},{"full_name":"Erps, Timothy","first_name":"Timothy","last_name":"Erps"},{"full_name":"Babaei, Vahid","first_name":"Vahid","last_name":"Babaei"},{"last_name":"Didyk","full_name":"Didyk, Piotr","first_name":"Piotr"},{"first_name":"Szymon","full_name":"Rusinkiewicz, Szymon","last_name":"Rusinkiewicz"},{"last_name":"Matusik","full_name":"Matusik, Wojciech","first_name":"Wojciech"},{"first_name":"Bernd","full_name":"Bickel, Bernd","id":"49876194-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6511-9385","last_name":"Bickel"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"06","issue":"4","isi":1,"article_processing_charge":"No","day":"01","language":[{"iso":"eng"}],"OA_type":"hybrid","quality_controlled":"1","ec_funded":1,"year":"2022","publication":"ACM Transactions on Graphics","article_type":"original","intvolume":"        41","ddc":["000"],"date_published":"2022-06-01T00:00:00Z","citation":{"chicago":"Piovarci, Michael, Michael Foshey, Jie Xu, Timothy Erps, Vahid Babaei, Piotr Didyk, Szymon Rusinkiewicz, Wojciech Matusik, and Bernd Bickel. “Closed-Loop Control of Direct Ink Writing via Reinforcement Learning.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3528223.3530144\">https://doi.org/10.1145/3528223.3530144</a>.","short":"M. Piovarci, M. Foshey, J. Xu, T. Erps, V. Babaei, P. Didyk, S. Rusinkiewicz, W. Matusik, B. Bickel, ACM Transactions on Graphics 41 (2022).","mla":"Piovarci, Michael, et al. “Closed-Loop Control of Direct Ink Writing via Reinforcement Learning.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, 112, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3528223.3530144\">10.1145/3528223.3530144</a>.","apa":"Piovarci, M., Foshey, M., Xu, J., Erps, T., Babaei, V., Didyk, P., … Bickel, B. (2022). Closed-loop control of direct ink writing via reinforcement learning. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3528223.3530144\">https://doi.org/10.1145/3528223.3530144</a>","ama":"Piovarci M, Foshey M, Xu J, et al. Closed-loop control of direct ink writing via reinforcement learning. <i>ACM Transactions on Graphics</i>. 2022;41(4). doi:<a href=\"https://doi.org/10.1145/3528223.3530144\">10.1145/3528223.3530144</a>","ista":"Piovarci M, Foshey M, Xu J, Erps T, Babaei V, Didyk P, Rusinkiewicz S, Matusik W, Bickel B. 2022. Closed-loop control of direct ink writing via reinforcement learning. ACM Transactions on Graphics. 41(4), 112.","ieee":"M. Piovarci <i>et al.</i>, “Closed-loop control of direct ink writing via reinforcement learning,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4. Association for Computing Machinery, 2022."},"date_created":"2022-06-10T06:41:47Z","has_accepted_license":"1","external_id":{"arxiv":["2201.11819"],"isi":["000830989200091"]},"arxiv":1},{"date_published":"2022-07-22T00:00:00Z","ddc":["000"],"has_accepted_license":"1","date_created":"2022-08-07T22:01:57Z","citation":{"short":"R. Chen, Z. Wang, P. Song, B. Bickel, ACM Transactions on Graphics 41 (2022).","chicago":"Chen, Rulin, Ziqi Wang, Peng Song, and Bernd Bickel. “Computational Design of High-Level Interlocking Puzzles.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3528223.3530071\">https://doi.org/10.1145/3528223.3530071</a>.","apa":"Chen, R., Wang, Z., Song, P., &#38; Bickel, B. (2022). Computational design of high-level interlocking puzzles. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3528223.3530071\">https://doi.org/10.1145/3528223.3530071</a>","mla":"Chen, Rulin, et al. “Computational Design of High-Level Interlocking Puzzles.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, 150, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3528223.3530071\">10.1145/3528223.3530071</a>.","ista":"Chen R, Wang Z, Song P, Bickel B. 2022. Computational design of high-level interlocking puzzles. ACM Transactions on Graphics. 41(4), 150.","ama":"Chen R, Wang Z, Song P, Bickel B. Computational design of high-level interlocking puzzles. <i>ACM Transactions on Graphics</i>. 2022;41(4). doi:<a href=\"https://doi.org/10.1145/3528223.3530071\">10.1145/3528223.3530071</a>","ieee":"R. Chen, Z. Wang, P. Song, and B. Bickel, “Computational design of high-level interlocking puzzles,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4. Association for Computing Machinery, 2022."},"intvolume":"        41","article_type":"original","external_id":{"isi":["000830989200018"]},"ec_funded":1,"language":[{"iso":"eng"}],"quality_controlled":"1","publication":"ACM Transactions on Graphics","year":"2022","month":"07","author":[{"last_name":"Chen","first_name":"Rulin","full_name":"Chen, Rulin"},{"full_name":"Wang, Ziqi","first_name":"Ziqi","last_name":"Wang"},{"last_name":"Song","full_name":"Song, Peng","first_name":"Peng"},{"orcid":"0000-0001-6511-9385","last_name":"Bickel","id":"49876194-F248-11E8-B48F-1D18A9856A87","full_name":"Bickel, Bernd","first_name":"Bernd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"day":"22","article_processing_charge":"No","issue":"4","oa_version":"Submitted Version","department":[{"_id":"BeBi"}],"file":[{"file_id":"11992","creator":"bbickel","checksum":"0b51651be45b1b33f2072bd5d2686c69","relation":"main_file","file_size":16896871,"success":1,"access_level":"open_access","content_type":"application/pdf","file_name":"Chen-2022-High-LevelPuzzle_authorVersion.pdf","date_updated":"2022-08-28T07:56:19Z","date_created":"2022-08-28T07:56:19Z"}],"project":[{"call_identifier":"H2020","name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","grant_number":"715767","_id":"24F9549A-B435-11E9-9278-68D0E5697425"}],"oa":1,"article_number":"150","date_updated":"2025-04-14T07:28:57Z","volume":41,"publication_status":"published","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"file_date_updated":"2022-08-28T07:56:19Z","type":"journal_article","acknowledgement":"We thank the reviewers for the valuable comments, David Gontier for sharing the source code of the baseline design approach, Christian Hafner for proofreading the paper, Keenan Crane for the 3D model of Cow, and Thingiverse for the 3D models of Moai and Owl. This work was supported by the SUTD Start-up Research Grant (Number: SRG ISTD 2019 148), the Swiss National Science Foundation (NCCR Digital Fabrication Agreement #51NF40-141853), and\r\nthe European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 715767 – MATERIALIZABLE).","doi":"10.1145/3528223.3530071","abstract":[{"text":"Interlocking puzzles are intriguing geometric games where the puzzle pieces are held together based on their geometric arrangement, preventing the puzzle from falling apart. High-level-of-difficulty, or simply high-level, interlocking puzzles are a subclass of interlocking puzzles that require multiple moves to take out the first subassembly from the puzzle. Solving a high-level interlocking puzzle is a challenging task since one has to explore many different configurations of the puzzle pieces until reaching a configuration where the first subassembly can be taken out. Designing a high-level interlocking puzzle with a user-specified level of difficulty is even harder since the puzzle pieces have to be interlocking in all the configurations before the first subassembly is taken out.\r\n\r\nIn this paper, we present a computational approach to design high-level interlocking puzzles. The core idea is to represent all possible configurations of an interlocking puzzle as well as transitions among these configurations using a rooted, undirected graph called a disassembly graph and leverage this graph to find a disassembly plan that requires a minimal number of moves to take out the first subassembly from the puzzle. At the design stage, our algorithm iteratively constructs the geometry of each puzzle piece to expand the disassembly graph incrementally, aiming to achieve a user-specified level of difficulty. We show that our approach allows efficient generation of high-level interlocking puzzles of various shape complexities, including new solutions not attainable by state-of-the-art approaches.","lang":"eng"}],"related_material":{"link":[{"url":"https://ista.ac.at/en/news/unlocking-interlocking-riddles/","relation":"press_release","description":"News on ISTA website"}]},"status":"public","title":"Computational design of high-level interlocking puzzles","scopus_import":"1","_id":"11735","publisher":"Association for Computing Machinery"},{"doi":"10.1145/3528223.3530167","abstract":[{"lang":"eng","text":"This paper introduces a methodology for inverse-modeling of yarn-level mechanics of cloth, based on the mechanical response of fabrics in the real world. We compiled a database from physical tests of several different knitted fabrics used in the textile industry. These data span different types of complex knit patterns, yarn compositions, and fabric finishes, and the results demonstrate diverse physical properties like stiffness, nonlinearity, and anisotropy.\r\n\r\nWe then develop a system for approximating these mechanical responses with yarn-level cloth simulation. To do so, we introduce an efficient pipeline for converting between fabric-level data and yarn-level simulation, including a novel swatch-level approximation for speeding up computation, and some small-but-necessary extensions to yarn-level models used in computer graphics. The dataset used for this paper can be found at http://mslab.es/projects/YarnLevelFabrics."}],"publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"acknowledgement":"We wish to thank the anonymous reviewers for their helpful comments. To develop this project, we were helped by many people both at Under Armour (Clay Dean, Randall Harward, Kyle Blakely, Craig Simile, Michael Seiz, Brooke Malone, Brittainy McFarland, Emilie Phan, Lindsey Kern, Courtney Oswald, Haley Barkley, Bob Chin, Adam Bayer, Connie Kwok, Marielle Newman, Nick Pence, Allison Hicks, Allison White, Candace Rubenstein, Jeremy Stangland, Fred Fagergren, Michael Mazzoleni, Nathaniel Berry, Manuel Frank) and SEDDI (Gabriel Cirio, Alejandro Rodríguez, Sofía Dominguez, Alicia Nicas, Elena Garcés, Daniel Rodríguez, David Pascual, Manuel Godoy, Sergio Suja, Sergio Ruiz, Roberto Condori, Alberto Martín, Graham Sullivan). We also thank the members of the Visual Computing Group at IST Austria and the Multimodal Simulation Lab at URJC for their feedback. This research was supported by the Scientific Service Units (SSU) of IST Austria through resources provided by Scientific Computing, and it was funded in part by the European Research Council (ERC Consolidator Grant 772738 TouchDesign).","type":"journal_article","acknowledged_ssus":[{"_id":"ScienComp"}],"volume":41,"date_updated":"2025-04-14T09:25:57Z","publication_status":"published","scopus_import":"1","title":"Estimation of yarn-level simulation models for production fabrics","publisher":"Association for Computing Machinery","_id":"11736","main_file_link":[{"url":"https://doi.org/10.1145/3528223.3530167","open_access":"1"}],"status":"public","related_material":{"record":[{"relation":"dissertation_contains","id":"12358","status":"public"}],"link":[{"url":"https://ista.ac.at/en/news/digital-yarn-real-socks/","relation":"press_release","description":"News on the ISTA website"}]},"publication":"ACM Transactions on Graphics","year":"2022","quality_controlled":"1","language":[{"iso":"eng"}],"external_id":{"isi":["000830989200114"]},"date_created":"2022-08-07T22:01:58Z","citation":{"ama":"Sperl G, Sánchez-Banderas RM, Li M, Wojtan C, Otaduy MA. Estimation of yarn-level simulation models for production fabrics. <i>ACM Transactions on Graphics</i>. 2022;41(4). doi:<a href=\"https://doi.org/10.1145/3528223.3530167\">10.1145/3528223.3530167</a>","ista":"Sperl G, Sánchez-Banderas RM, Li M, Wojtan C, Otaduy MA. 2022. Estimation of yarn-level simulation models for production fabrics. ACM Transactions on Graphics. 41(4), 65.","ieee":"G. Sperl, R. M. Sánchez-Banderas, M. Li, C. Wojtan, and M. A. Otaduy, “Estimation of yarn-level simulation models for production fabrics,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4. Association for Computing Machinery, 2022.","chicago":"Sperl, Georg, Rosa M. Sánchez-Banderas, Manwen Li, Chris Wojtan, and Miguel A. Otaduy. “Estimation of Yarn-Level Simulation Models for Production Fabrics.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3528223.3530167\">https://doi.org/10.1145/3528223.3530167</a>.","short":"G. Sperl, R.M. Sánchez-Banderas, M. Li, C. Wojtan, M.A. Otaduy, ACM Transactions on Graphics 41 (2022).","mla":"Sperl, Georg, et al. “Estimation of Yarn-Level Simulation Models for Production Fabrics.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, 65, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3528223.3530167\">10.1145/3528223.3530167</a>.","apa":"Sperl, G., Sánchez-Banderas, R. M., Li, M., Wojtan, C., &#38; Otaduy, M. A. (2022). Estimation of yarn-level simulation models for production fabrics. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3528223.3530167\">https://doi.org/10.1145/3528223.3530167</a>"},"date_published":"2022-07-22T00:00:00Z","article_type":"original","intvolume":"        41","department":[{"_id":"ChWo"}],"article_number":"65","oa":1,"oa_version":"Published Version","day":"22","article_processing_charge":"No","isi":1,"issue":"4","month":"07","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Sperl, Georg","first_name":"Georg","last_name":"Sperl","id":"4DD40360-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Rosa M.","full_name":"Sánchez-Banderas, Rosa M.","last_name":"Sánchez-Banderas"},{"last_name":"Li","first_name":"Manwen","full_name":"Li, Manwen"},{"first_name":"Christopher J","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan","orcid":"0000-0001-6646-5546"},{"full_name":"Otaduy, Miguel A.","first_name":"Miguel A.","last_name":"Otaduy"}]},{"scopus_import":"1","title":"Hidden degrees of freedom in implicit vortex filaments","publisher":"Association for Computing Machinery","_id":"12431","status":"public","related_material":{"record":[{"id":"20551","relation":"dissertation_contains","status":"public"}]},"doi":"10.1145/3550454.3555459","abstract":[{"text":"This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent curves implicitly with a new co-dimensional 2 level set description. Our implicit representation admits several redundant mathematical degrees of freedom in both the configuration and the dynamics of the curves, which can be tailored specifically to improve numerical robustness, in contrast to naive approaches for implicit curve dynamics that suffer from overwhelming numerical stability problems. Furthermore, we note how these hidden degrees of freedom perfectly map to a Clebsch representation in fluid dynamics. Motivated by these observations, we introduce untwisted level set functions and non-swirling dynamics which successfully regularize sources of numerical instability, particularly in the twisting modes around curve filaments. A consequence is a novel simulation method which produces stable dynamics for large numbers of interacting vortex filaments and effortlessly handles topological changes and re-connection events.","lang":"eng"}],"file_date_updated":"2023-01-30T07:15:48Z","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"acknowledgement":"We thank the visual computing group at IST Austria for their valuable discussions and feedback. Houdini Education licenses were provided by SideFX software. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","type":"journal_article","volume":41,"date_updated":"2025-11-14T12:28:38Z","publication_status":"published","department":[{"_id":"ChWo"}],"file":[{"date_created":"2023-01-30T07:15:48Z","file_name":"2022_ACM_Ishida.pdf","date_updated":"2023-01-30T07:15:48Z","content_type":"application/pdf","success":1,"access_level":"open_access","file_size":15551202,"relation":"main_file","checksum":"a2fba257fdefe0e747182be6c0f7c70c","creator":"dernst","file_id":"12433"}],"article_number":"241","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"oa":1,"oa_version":"Published Version","article_processing_charge":"No","day":"01","isi":1,"issue":"6","month":"12","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"author":[{"first_name":"Sadashige","full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100","last_name":"Ishida","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425"},{"last_name":"Wojtan","orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","full_name":"Wojtan, Christopher J"},{"last_name":"Chern","full_name":"Chern, Albert","first_name":"Albert"}],"publication":"ACM Transactions on Graphics","year":"2022","quality_controlled":"1","language":[{"iso":"eng"}],"external_id":{"isi":["000891651900061"]},"date_created":"2023-01-29T23:00:59Z","has_accepted_license":"1","citation":{"ieee":"S. Ishida, C. Wojtan, and A. Chern, “Hidden degrees of freedom in implicit vortex filaments,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6. Association for Computing Machinery, 2022.","ama":"Ishida S, Wojtan C, Chern A. Hidden degrees of freedom in implicit vortex filaments. <i>ACM Transactions on Graphics</i>. 2022;41(6). doi:<a href=\"https://doi.org/10.1145/3550454.3555459\">10.1145/3550454.3555459</a>","ista":"Ishida S, Wojtan C, Chern A. 2022. Hidden degrees of freedom in implicit vortex filaments. ACM Transactions on Graphics. 41(6), 241.","mla":"Ishida, Sadashige, et al. “Hidden Degrees of Freedom in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6, 241, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3550454.3555459\">10.1145/3550454.3555459</a>.","apa":"Ishida, S., Wojtan, C., &#38; Chern, A. (2022). Hidden degrees of freedom in implicit vortex filaments. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3550454.3555459\">https://doi.org/10.1145/3550454.3555459</a>","chicago":"Ishida, Sadashige, Chris Wojtan, and Albert Chern. “Hidden Degrees of Freedom in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3550454.3555459\">https://doi.org/10.1145/3550454.3555459</a>.","short":"S. Ishida, C. Wojtan, A. Chern, ACM Transactions on Graphics 41 (2022)."},"date_published":"2022-12-01T00:00:00Z","ddc":["000"],"article_type":"original","intvolume":"        41"},{"status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2107.12265","open_access":"1"}],"scopus_import":"1","title":"Co-optimization of design and fabrication plans for carpentry","publisher":"Association for Computing Machinery","_id":"17065","volume":41,"date_updated":"2024-08-06T07:03:14Z","publication_status":"published","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"acknowledgement":"The authors would like to thank anonymous reviewers for their helpful feedback; Haomiao Wu for her contribution to the algorithm development in the early stage of the project; Elias Baldwin, David Tsay, Alexander Lefort, and Qiyang Tan for helping the experiments.","type":"journal_article","doi":"10.1145/3508499","abstract":[{"lang":"eng","text":"Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design, instead considering families of design variations, sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts (BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs (ICEE) can keep the size of the e-graph manageable and direct the search towards promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain."}],"month":"03","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Zhao, Haisen","first_name":"Haisen","orcid":"0000-0002-6389-1045","last_name":"Zhao","id":"fb7f793a-80d1-11eb-8869-d56e5b2a8ff4"},{"last_name":"Willsey","first_name":"Max","full_name":"Willsey, Max"},{"first_name":"Amy","full_name":"Zhu, Amy","last_name":"Zhu"},{"first_name":"Chandrakana","full_name":"Nandi, Chandrakana","last_name":"Nandi"},{"full_name":"Tatlock, Zachary","first_name":"Zachary","last_name":"Tatlock"},{"last_name":"Solomon","first_name":"Justin","full_name":"Solomon, Justin"},{"last_name":"Schulz","first_name":"Adriana","full_name":"Schulz, Adriana"}],"day":"09","article_processing_charge":"No","issue":"3","oa_version":"Preprint","department":[{"_id":"BeBi"}],"article_number":"32","oa":1,"citation":{"ama":"Zhao H, Willsey M, Zhu A, et al. Co-optimization of design and fabrication plans for carpentry. <i>ACM Transactions on Graphics</i>. 2022;41(3). doi:<a href=\"https://doi.org/10.1145/3508499\">10.1145/3508499</a>","ista":"Zhao H, Willsey M, Zhu A, Nandi C, Tatlock Z, Solomon J, Schulz A. 2022. Co-optimization of design and fabrication plans for carpentry. ACM Transactions on Graphics. 41(3), 32.","ieee":"H. Zhao <i>et al.</i>, “Co-optimization of design and fabrication plans for carpentry,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 3. Association for Computing Machinery, 2022.","chicago":"Zhao, Haisen, Max Willsey, Amy Zhu, Chandrakana Nandi, Zachary Tatlock, Justin Solomon, and Adriana Schulz. “Co-Optimization of Design and Fabrication Plans for Carpentry.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3508499\">https://doi.org/10.1145/3508499</a>.","short":"H. Zhao, M. Willsey, A. Zhu, C. Nandi, Z. Tatlock, J. Solomon, A. Schulz, ACM Transactions on Graphics 41 (2022).","mla":"Zhao, Haisen, et al. “Co-Optimization of Design and Fabrication Plans for Carpentry.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 3, 32, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3508499\">10.1145/3508499</a>.","apa":"Zhao, H., Willsey, M., Zhu, A., Nandi, C., Tatlock, Z., Solomon, J., &#38; Schulz, A. (2022). Co-optimization of design and fabrication plans for carpentry. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3508499\">https://doi.org/10.1145/3508499</a>"},"date_created":"2024-05-29T06:09:23Z","date_published":"2022-03-09T00:00:00Z","intvolume":"        41","article_type":"original","arxiv":1,"external_id":{"arxiv":["2107.12265"]},"quality_controlled":"1","language":[{"iso":"eng"}],"publication":"ACM Transactions on Graphics","year":"2022"},{"month":"07","author":[{"full_name":"Ren, Yingying","first_name":"Yingying","last_name":"Ren","id":"93d68d10-3540-11ef-a265-f748a50dba3d"},{"first_name":"Uday","full_name":"Kusupati, Uday","last_name":"Kusupati"},{"full_name":"Panetta, Julian","first_name":"Julian","last_name":"Panetta"},{"first_name":"Florin","full_name":"Isvoranu, Florin","last_name":"Isvoranu"},{"last_name":"Pellis","full_name":"Pellis, Davide","first_name":"Davide"},{"last_name":"Chen","first_name":"Tian","full_name":"Chen, Tian"},{"full_name":"Pauly, Mark","first_name":"Mark","last_name":"Pauly"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"22","article_processing_charge":"No","status":"public","issue":"4","oa_version":"None","title":"Umbrella meshes: Elastic mechanisms for freeform shape deployment","scopus_import":"1","page":"1-15","_id":"17383","publisher":"Association for Computing Machinery","date_updated":"2024-08-12T09:40:49Z","date_published":"2022-07-22T00:00:00Z","volume":41,"citation":{"ama":"Ren Y, Kusupati U, Panetta J, et al. Umbrella meshes: Elastic mechanisms for freeform shape deployment. <i>ACM Transactions on Graphics</i>. 2022;41(4):1-15. doi:<a href=\"https://doi.org/10.1145/3528223.3530089\">10.1145/3528223.3530089</a>","ista":"Ren Y, Kusupati U, Panetta J, Isvoranu F, Pellis D, Chen T, Pauly M. 2022. Umbrella meshes: Elastic mechanisms for freeform shape deployment. ACM Transactions on Graphics. 41(4), 1–15.","ieee":"Y. Ren <i>et al.</i>, “Umbrella meshes: Elastic mechanisms for freeform shape deployment,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4. Association for Computing Machinery, pp. 1–15, 2022.","chicago":"Ren, Yingying, Uday Kusupati, Julian Panetta, Florin Isvoranu, Davide Pellis, Tian Chen, and Mark Pauly. “Umbrella Meshes: Elastic Mechanisms for Freeform Shape Deployment.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3528223.3530089\">https://doi.org/10.1145/3528223.3530089</a>.","short":"Y. Ren, U. Kusupati, J. Panetta, F. Isvoranu, D. Pellis, T. Chen, M. Pauly, ACM Transactions on Graphics 41 (2022) 1–15.","mla":"Ren, Yingying, et al. “Umbrella Meshes: Elastic Mechanisms for Freeform Shape Deployment.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, Association for Computing Machinery, 2022, pp. 1–15, doi:<a href=\"https://doi.org/10.1145/3528223.3530089\">10.1145/3528223.3530089</a>.","apa":"Ren, Y., Kusupati, U., Panetta, J., Isvoranu, F., Pellis, D., Chen, T., &#38; Pauly, M. (2022). Umbrella meshes: Elastic mechanisms for freeform shape deployment. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3528223.3530089\">https://doi.org/10.1145/3528223.3530089</a>"},"date_created":"2024-08-05T06:30:07Z","intvolume":"        41","article_type":"original","publication_status":"published","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"type":"journal_article","doi":"10.1145/3528223.3530089","extern":"1","language":[{"iso":"eng"}],"abstract":[{"text":"We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems.\r\nWe build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques.","lang":"eng"}],"quality_controlled":"1","publication":"ACM Transactions on Graphics","year":"2022"},{"oa_version":"None","title":"3D weaving with curved ribbons","scopus_import":"1","_id":"17384","page":"1-15","publisher":"Association for Computing Machinery","month":"08","author":[{"last_name":"Ren","id":"93d68d10-3540-11ef-a265-f748a50dba3d","first_name":"Yingying","full_name":"Ren, Yingying"},{"last_name":"Panetta","full_name":"Panetta, Julian","first_name":"Julian"},{"first_name":"Tian","full_name":"Chen, Tian","last_name":"Chen"},{"full_name":"Isvoranu, Florin","first_name":"Florin","last_name":"Isvoranu"},{"last_name":"Poincloux","full_name":"Poincloux, Samuel","first_name":"Samuel"},{"last_name":"Brandt","first_name":"Christopher","full_name":"Brandt, Christopher"},{"last_name":"Martin","full_name":"Martin, Alison","first_name":"Alison"},{"first_name":"Mark","full_name":"Pauly, Mark","last_name":"Pauly"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","article_processing_charge":"No","status":"public","issue":"4","doi":"10.1145/3450626.3459788","language":[{"iso":"eng"}],"extern":"1","quality_controlled":"1","abstract":[{"text":"Basket weaving is a traditional craft for creating curved surfaces as an interwoven array of thin, flexible, and initially straight ribbons. The three-dimensional shape of a woven structure emerges through a complex interplay of the elastic bending behavior of the ribbons and the contact forces at their crossings. Curvature can be injected by carefully placing topological singularities in the otherwise regular weaving pattern. However, shape control through topology is highly non-trivial and inherently discrete, which severely limits the range of attainable woven geometries. Here, we demonstrate how to construct arbitrary smooth free-form surface geometries by weaving carefully optimized curved ribbons. We present an optimization-based approach to solving the inverse design problem for such woven structures. Our algorithm computes the ribbons' planar geometry such that their interwoven assembly closely approximates a given target design surface in equilibrium. We systematically validate our approach through a series of physical prototypes to show a broad range of new woven geometries that is not achievable by existing methods. We anticipate our computational approach to significantly enhance the capabilities for the design of new woven structures. Facilitated by modern digital fabrication technology, we see potential applications in material science, bio- and mechanical engineering, art, design, and architecture.","lang":"eng"}],"publication":"ACM Transactions on Graphics","year":"2021","date_published":"2021-08-01T00:00:00Z","date_updated":"2024-08-12T09:38:19Z","volume":40,"citation":{"apa":"Ren, Y., Panetta, J., Chen, T., Isvoranu, F., Poincloux, S., Brandt, C., … Pauly, M. (2021). 3D weaving with curved ribbons. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3450626.3459788\">https://doi.org/10.1145/3450626.3459788</a>","mla":"Ren, Yingying, et al. “3D Weaving with Curved Ribbons.” <i>ACM Transactions on Graphics</i>, vol. 40, no. 4, Association for Computing Machinery, 2021, pp. 1–15, doi:<a href=\"https://doi.org/10.1145/3450626.3459788\">10.1145/3450626.3459788</a>.","short":"Y. Ren, J. Panetta, T. Chen, F. Isvoranu, S. Poincloux, C. Brandt, A. Martin, M. Pauly, ACM Transactions on Graphics 40 (2021) 1–15.","chicago":"Ren, Yingying, Julian Panetta, Tian Chen, Florin Isvoranu, Samuel Poincloux, Christopher Brandt, Alison Martin, and Mark Pauly. “3D Weaving with Curved Ribbons.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2021. <a href=\"https://doi.org/10.1145/3450626.3459788\">https://doi.org/10.1145/3450626.3459788</a>.","ieee":"Y. Ren <i>et al.</i>, “3D weaving with curved ribbons,” <i>ACM Transactions on Graphics</i>, vol. 40, no. 4. Association for Computing Machinery, pp. 1–15, 2021.","ista":"Ren Y, Panetta J, Chen T, Isvoranu F, Poincloux S, Brandt C, Martin A, Pauly M. 2021. 3D weaving with curved ribbons. ACM Transactions on Graphics. 40(4), 1–15.","ama":"Ren Y, Panetta J, Chen T, et al. 3D weaving with curved ribbons. <i>ACM Transactions on Graphics</i>. 2021;40(4):1-15. doi:<a href=\"https://doi.org/10.1145/3450626.3459788\">10.1145/3450626.3459788</a>"},"date_created":"2024-08-05T06:30:27Z","intvolume":"        40","article_type":"original","publication_status":"published","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"type":"journal_article"},{"volume":40,"date_updated":"2025-03-31T15:58:16Z","publication_status":"published","file_date_updated":"2021-12-17T08:13:51Z","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"acknowledgement":"We would like to thank everyone who contributed to this paper, the authors of artworks for all the examples, including @macrovec-tor_official and Wikimedia for the FLAG semaphore, and @pikisuper-star for the FIGURINE. The photos of iconic poses in the teaser were supplied by (from left to right): Mike Hewitt/Olympics Day 8 - Athletics/Gettty Images, Oneinchpunch/Basketball player training on acourt in New york city/Shutterstock, and Andrew Redington/TigerWoods/Getty Images. We also want to express our gratitude to Christian Hafner for insightful discussions, the IST Austria machine shop SSU, all proof-readers, and anonymous reviewers. This project has received funding from the European Union’s Horizon 2020 research and innovation programme, under the Marie Skłodowska-Curie grant agreement No 642841 (DISTRO), and under the European Research Council grant agreement No 715767 (MATERIALIZABLE).","acknowledged_ssus":[{"_id":"M-Shop"}],"type":"journal_article","doi":"10.1145/3453477","abstract":[{"lang":"eng","text":"This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes."}],"status":"public","title":"Computational design of planar multistable compliant structures","scopus_import":"1","publisher":"Association for Computing Machinery","_id":"9376","citation":{"ama":"Zhang R, Auzinger T, Bickel B. Computational design of planar multistable compliant structures. <i>ACM Transactions on Graphics</i>. 2021;40(5). doi:<a href=\"https://doi.org/10.1145/3453477\">10.1145/3453477</a>","ista":"Zhang R, Auzinger T, Bickel B. 2021. Computational design of planar multistable compliant structures. ACM Transactions on Graphics. 40(5), 186.","ieee":"R. Zhang, T. Auzinger, and B. Bickel, “Computational design of planar multistable compliant structures,” <i>ACM Transactions on Graphics</i>, vol. 40, no. 5. Association for Computing Machinery, 2021.","chicago":"Zhang, Ran, Thomas Auzinger, and Bernd Bickel. “Computational Design of Planar Multistable Compliant Structures.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2021. <a href=\"https://doi.org/10.1145/3453477\">https://doi.org/10.1145/3453477</a>.","short":"R. Zhang, T. Auzinger, B. Bickel, ACM Transactions on Graphics 40 (2021).","mla":"Zhang, Ran, et al. “Computational Design of Planar Multistable Compliant Structures.” <i>ACM Transactions on Graphics</i>, vol. 40, no. 5, 186, Association for Computing Machinery, 2021, doi:<a href=\"https://doi.org/10.1145/3453477\">10.1145/3453477</a>.","apa":"Zhang, R., Auzinger, T., &#38; Bickel, B. (2021). Computational design of planar multistable compliant structures. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3453477\">https://doi.org/10.1145/3453477</a>"},"date_created":"2021-05-08T17:37:08Z","has_accepted_license":"1","date_published":"2021-10-08T00:00:00Z","ddc":["000"],"article_type":"original","intvolume":"        40","external_id":{"isi":["000752079300003"]},"ec_funded":1,"quality_controlled":"1","language":[{"iso":"eng"}],"publication":"ACM Transactions on Graphics","year":"2021","keyword":["multistability","mechanism","computational design","rigidity"],"month":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"4DDBCEB0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3808-281X","last_name":"Zhang","full_name":"Zhang, Ran","first_name":"Ran"},{"orcid":"0000-0002-1546-3265","last_name":"Auzinger","id":"4718F954-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas","full_name":"Auzinger, Thomas"},{"last_name":"Bickel","orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","full_name":"Bickel, Bernd","first_name":"Bernd"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"day":"08","article_processing_charge":"No","isi":1,"issue":"5","oa_version":"Published Version","file":[{"file_id":"9377","creator":"bbickel","checksum":"8564b3118457d4c8939a8ef2b1a2f16c","relation":"main_file","file_size":18926557,"access_level":"open_access","content_type":"application/pdf","date_updated":"2021-05-08T17:36:59Z","file_name":"Multistable-authorversion.pdf","date_created":"2021-05-08T17:36:59Z"},{"success":1,"access_level":"open_access","content_type":"video/mp4","file_name":"multistable-video.mp4","date_updated":"2021-05-08T17:38:22Z","date_created":"2021-05-08T17:38:22Z","file_size":76542901,"relation":"main_file","file_id":"9378","creator":"bbickel","checksum":"3b6e874e30bfa1bfc3ad3498710145a1"},{"content_type":"application/pdf","access_level":"open_access","date_created":"2021-12-17T08:13:51Z","file_name":"multistable-supplementary material.pdf","date_updated":"2021-12-17T08:13:51Z","file_size":3367072,"relation":"supplementary_material","description":"This document provides additional results and analyzes the robustness and limitations of our approach.","file_id":"10562","checksum":"20dc3bc42e1a912a5b0247c116772098","title":"Supplementary Material for “Computational Design of Planar Multistable Compliant Structures”","creator":"bbickel"}],"department":[{"_id":"BeBi"}],"article_number":"186","project":[{"name":"Distributed 3D Object Design","call_identifier":"H2020","_id":"2508E324-B435-11E9-9278-68D0E5697425","grant_number":"642841"},{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","call_identifier":"H2020","grant_number":"715767","_id":"24F9549A-B435-11E9-9278-68D0E5697425"}],"oa":1}]