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Area formula for spherical polygons via prequantization. arXiv, 2303.14555.","mla":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” ArXiv, 2303.14555, doi:10.48550/arXiv.2303.14555.","apa":"Chern, A., & Ishida, S. (n.d.). Area formula for spherical polygons via prequantization. arXiv. https://doi.org/10.48550/arXiv.2303.14555","ama":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv. doi:10.48550/arXiv.2303.14555","short":"A. Chern, S. Ishida, ArXiv (n.d.).","ieee":"A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” arXiv. ."},"date_updated":"2023-04-25T06:51:21Z","month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.14555"}],"oa":1,"acknowledgement":"The authors acknowledge Chris Wojtan for his continuous support to the present work through discussions and advice. The second author thanks Anna Sisak for a fruitful discussion on prequantum bundles. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","oa_version":"Preprint","abstract":[{"text":"We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measuring angles, the new formula mimics Green's theorem and is applicable to a wider range of degenerate spherical curves and polygons.","lang":"eng"}],"date_created":"2023-04-18T19:16:06Z","doi":"10.48550/arXiv.2303.14555","date_published":"2023-03-25T00:00:00Z","publication":"arXiv","language":[{"iso":"eng"}],"day":"25","year":"2023","publication_status":"submitted"},{"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.","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.” ACM Transactions on Graphics. Association for Computing Machinery, 2023. https://doi.org/10.1145/3605389.","ama":"Makatura L, Wang B, Chen Y-L, et al. Procedural metamaterials: A unified procedural graph for metamaterial design. ACM Transactions on Graphics. 2023;42(5). doi:10.1145/3605389","apa":"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. Association for Computing Machinery. https://doi.org/10.1145/3605389","short":"L. Makatura, B. Wang, Y.-L. Chen, B. Deng, C. Wojtan, B. Bickel, W. Matusik, ACM Transactions on Graphics 42 (2023).","ieee":"L. Makatura et al., “Procedural metamaterials: A unified procedural graph for metamaterial design,” ACM Transactions on Graphics, vol. 42, no. 5. Association for Computing Machinery, 2023.","mla":"Makatura, Liane, et al. “Procedural Metamaterials: A Unified Procedural Graph for Metamaterial Design.” ACM Transactions on Graphics, vol. 42, no. 5, 168, Association for Computing Machinery, 2023, doi:10.1145/3605389."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (in subscription journal)","author":[{"first_name":"Liane","last_name":"Makatura","full_name":"Makatura, Liane"},{"last_name":"Wang","full_name":"Wang, Bohan","first_name":"Bohan"},{"id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","first_name":"Yi-Lu","full_name":"Chen, Yi-Lu","last_name":"Chen"},{"last_name":"Deng","full_name":"Deng, Bolei","first_name":"Bolei"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","last_name":"Wojtan","first_name":"Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bickel","full_name":"Bickel, Bernd","orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","first_name":"Bernd"},{"first_name":"Wojciech","last_name":"Matusik","full_name":"Matusik, Wojciech"}],"title":"Procedural metamaterials: A unified procedural graph for metamaterial design","article_number":"168","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"year":"2023","has_accepted_license":"1","publication":"ACM Transactions on Graphics","day":"01","date_created":"2023-11-29T15:02:03Z","doi":"10.1145/3605389","date_published":"2023-10-01T00:00:00Z","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.","oa":1,"quality_controlled":"1","publisher":"Association for Computing Machinery","date_updated":"2023-12-04T08:09:05Z","ddc":["531","006"],"file_date_updated":"2023-12-04T08:04:14Z","department":[{"_id":"GradSch"},{"_id":"ChWo"},{"_id":"BeBi"}],"_id":"14628","type":"journal_article","article_type":"original","keyword":["Computer Graphics and Computer-Aided Design"],"status":"public","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"language":[{"iso":"eng"}],"file":[{"date_updated":"2023-11-29T15:16:01Z","file_size":95467870,"creator":"yichen","date_created":"2023-11-29T15:16:01Z","file_name":"tog-22-0089-File004.zip","content_type":"application/zip","access_level":"open_access","relation":"main_file","checksum":"0192f597d7a2ceaf89baddfd6190d4c8","file_id":"14630","success":1},{"date_created":"2023-11-29T15:16:01Z","file_name":"tog-22-0089-File005.zip","date_updated":"2023-11-29T15:16:01Z","file_size":103731880,"creator":"yichen","checksum":"7fb024963be81933494f38de191e4710","file_id":"14631","success":1,"content_type":"application/zip","access_level":"open_access","relation":"main_file"},{"success":1,"file_id":"14638","checksum":"b7d6829ce396e21cac9fae0ec7130a6b","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2023_ACMToG_Makatura.pdf","date_created":"2023-12-04T08:04:14Z","file_size":57067476,"date_updated":"2023-12-04T08:04:14Z","creator":"dernst"}],"issue":"5","volume":42,"abstract":[{"lang":"eng","text":"We introduce a compact, intuitive procedural graph representation for cellular metamaterials, which are small-scale, tileable structures that can be architected to exhibit many useful material properties. Because the structures’ “architectures” vary widely—with elements such as beams, thin shells, and solid bulks—it is difficult to explore them using existing representations. Generic approaches like voxel grids are versatile, but it is cumbersome to represent and edit individual structures; architecture-specific approaches address these issues, but are incompatible with one another. By contrast, our procedural graph succinctly represents the construction process for any structure using a simple skeleton annotated with spatially varying thickness. To express the highly constrained triply periodic minimal surfaces (TPMS) in this manner, we present the first fully automated version of the conjugate surface construction method, which allows novices to create complex TPMS from intuitive input. We demonstrate our representation’s expressiveness, accuracy, and compactness by constructing a wide range of established structures and hundreds of novel structures with diverse architectures and material properties. We also conduct a user study to verify our representation’s ease-of-use and ability to expand engineers’ capacity for exploration."}],"oa_version":"Published Version","intvolume":" 42","month":"10"},{"external_id":{"arxiv":["2312.12213"]},"article_processing_charge":"No","author":[{"last_name":"Ishida","full_name":"Ishida, Sadashige","first_name":"Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425"},{"first_name":"Hugo","last_name":"Lavenant","full_name":"Lavenant, Hugo"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"title":"Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation","date_updated":"2023-12-27T13:44:33Z","citation":{"ieee":"S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation,” arXiv. .","short":"S. Ishida, H. Lavenant, ArXiv (n.d.).","ama":"Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. arXiv. doi:10.48550/arXiv.2312.12213","apa":"Ishida, S., & Lavenant, H. (n.d.). Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. arXiv. https://doi.org/10.48550/arXiv.2312.12213","mla":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, 2312.12213, doi:10.48550/arXiv.2312.12213.","ista":"Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. arXiv, 2312.12213.","chicago":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2312.12213."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","type":"preprint","keyword":["Optimal transport","Hamilton-Jacobi equation","convex optimization"],"project":[{"grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"status":"public","_id":"14703","article_number":"2312.12213","date_created":"2023-12-21T10:14:37Z","date_published":"2023-12-19T00:00:00Z","doi":"10.48550/arXiv.2312.12213","year":"2023","publication_status":"submitted","publication":"arXiv","language":[{"iso":"eng"}],"day":"19","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2312.12213","open_access":"1"}],"month":"12","abstract":[{"text":"We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.","lang":"eng"}],"acknowledgement":"The authors would like to thank Chris Wojtan for his continuous support and several interesting discussions. Part of this research was performed during two visits: one of SI to the BIDSA research center at Bocconi University, and one of HL to the Institute of Science and Technology Austria. Both host institutions are warmly acknowledged for the hospital-\r\nity. HL is partially supported by the MUR-Prin 2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications to Optimization and Machine Learning”, funded by the European Union - Next Generation EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council.","oa_version":"Preprint"},{"publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"publication_status":"published","file":[{"content_type":"video/mp4","relation":"main_file","access_level":"open_access","success":1,"checksum":"1d178bb2f8011d9f5aedda6427e18c7a","file_id":"14704","file_size":511572575,"date_updated":"2023-12-21T12:26:40Z","creator":"sjeschke","file_name":"PaperVideo_final.mp4","date_created":"2023-12-21T12:26:40Z"},{"file_name":"2023_ACMToG_Jeschke.pdf","date_created":"2024-01-02T09:34:27Z","creator":"dernst","file_size":7469177,"date_updated":"2024-01-02T09:34:27Z","success":1,"file_id":"14725","checksum":"a49b2e744d5cd1276bb8b2e0ce6dc638","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"issue":"4","volume":42,"license":"https://creativecommons.org/licenses/by/4.0/","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"}],"acknowledged_ssus":[{"_id":"ScienComp"}],"oa_version":"Published Version","scopus_import":"1","month":"08","intvolume":" 42","date_updated":"2024-01-02T09:35:55Z","ddc":["000"],"department":[{"_id":"ChWo"}],"file_date_updated":"2024-01-02T09:34:27Z","_id":"14240","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","isi":1,"has_accepted_license":"1","year":"2023","day":"01","publication":"ACM Transactions on Graphics","date_published":"2023-08-01T00:00:00Z","doi":"10.1145/3592098","date_created":"2023-08-27T22:01:17Z","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.","publisher":"Association for Computing Machinery","quality_controlled":"1","oa":1,"citation":{"chicago":"Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations with Dispersive Surface Waves.” ACM Transactions on Graphics. Association for Computing Machinery, 2023. https://doi.org/10.1145/3592098.","ista":"Jeschke S, Wojtan C. 2023. Generalizing shallow water simulations with dispersive surface waves. ACM Transactions on Graphics. 42(4), 83.","mla":"Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations with Dispersive Surface Waves.” ACM Transactions on Graphics, vol. 42, no. 4, 83, Association for Computing Machinery, 2023, doi:10.1145/3592098.","ieee":"S. Jeschke and C. Wojtan, “Generalizing shallow water simulations with dispersive surface waves,” ACM Transactions on Graphics, vol. 42, no. 4. Association for Computing Machinery, 2023.","short":"S. Jeschke, C. Wojtan, ACM Transactions on Graphics 42 (2023).","apa":"Jeschke, S., & Wojtan, C. (2023). Generalizing shallow water simulations with dispersive surface waves. ACM Transactions on Graphics. Association for Computing Machinery. https://doi.org/10.1145/3592098","ama":"Jeschke S, Wojtan C. Generalizing shallow water simulations with dispersive surface waves. ACM Transactions on Graphics. 2023;42(4). doi:10.1145/3592098"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"44D6411A-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","last_name":"Jeschke","full_name":"Jeschke, Stefan"},{"orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","last_name":"Wojtan","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J"}],"article_processing_charge":"Yes (in subscription journal)","external_id":{"isi":["001044671300049"]},"title":"Generalizing shallow water simulations with dispersive surface waves","article_number":"83","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}]},{"acknowledgement":"We thank the anonymous reviewers and the members of the Visual Computing Group at ISTA for their helpful comments. 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_version":"None","acknowledged_ssus":[{"_id":"ScienComp"}],"month":"08","quality_controlled":"1","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"publication":"Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation","day":"01","publication_status":"published","year":"2023","publication_identifier":{"isbn":["9798400702686"]},"date_created":"2024-01-08T13:00:24Z","date_published":"2023-08-01T00:00:00Z","doi":"10.1145/3606037.3606836","article_number":"5","_id":"14748","status":"public","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083"}],"conference":{"end_date":"2023-08-06","location":"Los Angeles, CA, United States","start_date":"2023-08-04","name":"SCA: Symposium on Computer Animation"},"type":"conference_abstract","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"Y.-L. Chen, M. Ly, C. Wojtan, in:, Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Association for Computing Machinery, 2023.","ieee":"Y.-L. Chen, M. Ly, and C. Wojtan, “Unified treatment of contact, friction and shock-propagation in rigid body animation,” in Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Los Angeles, CA, United States, 2023.","ama":"Chen Y-L, Ly M, Wojtan C. Unified treatment of contact, friction and shock-propagation in rigid body animation. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Association for Computing Machinery; 2023. doi:10.1145/3606037.3606836","apa":"Chen, Y.-L., Ly, M., & Wojtan, C. (2023). Unified treatment of contact, friction and shock-propagation in rigid body animation. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Los Angeles, CA, United States: Association for Computing Machinery. https://doi.org/10.1145/3606037.3606836","mla":"Chen, Yi-Lu, et al. “Unified Treatment of Contact, Friction and Shock-Propagation in Rigid Body Animation.” Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 5, Association for Computing Machinery, 2023, doi:10.1145/3606037.3606836.","ista":"Chen Y-L, Ly M, Wojtan C. 2023. Unified treatment of contact, friction and shock-propagation in rigid body animation. Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA: Symposium on Computer Animation, 5.","chicago":"Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Unified Treatment of Contact, Friction and Shock-Propagation in Rigid Body Animation.” In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Association for Computing Machinery, 2023. https://doi.org/10.1145/3606037.3606836."},"date_updated":"2024-02-28T12:51:40Z","department":[{"_id":"ChWo"}],"title":"Unified treatment of contact, friction and shock-propagation in rigid body animation","article_processing_charge":"No","author":[{"last_name":"Chen","full_name":"Chen, Yi-Lu","first_name":"Yi-Lu","id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70"},{"first_name":"Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël","last_name":"Ly"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","last_name":"Wojtan","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J"}]}]