[{"date_updated":"2026-04-28T10:56:30Z","keyword":["l’Hopital theorem","complex functions"],"file_date_updated":"2026-04-28T10:53:27Z","file":[{"file_name":"2026_arXiv_2602.09958.pdf","file_id":"21771","content_type":"application/pdf","relation":"main_file","file_size":867109,"date_updated":"2026-04-28T10:53:27Z","access_level":"open_access","date_created":"2026-04-28T10:53:27Z","checksum":"6a76591c723d3e949ad5afa9f7dbb2ee","creator":"dernst","success":1}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2026","publication_status":"submitted","_id":"21737","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"oa_version":"Preprint","oa":1,"author":[{"full_name":"Chern, Albert","last_name":"Chern","first_name":"Albert"},{"last_name":"Ishida","first_name":"Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100"}],"external_id":{"arxiv":["2602.09958"]},"abstract":[{"text":"In calculus, l'Hopital's rule provides a simple way to evaluate the limits of quotient functions when both the numerator and denominator vanish. But what happens when we move beyond real functions on a real interval? In this article, we study when the quotient of two complex-valued functions in higher dimension can be defined continuously at the points where both functions vanish. Surprisingly, the answer is far subtler than in the real-valued setting. We provide a complete characterization for the continuity of the quotient function. We also point out why extending this result to smoother quotients remains an intriguing challenge.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"OA_type":"green","title":"L'Hopital rules for complex-valued functions in higher dimensions","ddc":["510"],"corr_author":"1","status":"public","has_accepted_license":"1","date_created":"2026-04-15T16:28:24Z","arxiv":1,"doi":"10.48550/ARXIV.2602.09958","acknowledgement":"This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA) and the National Science Foundation CAREER Award 2239062.\r\n","day":"10","type":"preprint","article_number":"2602.09958","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2026-02-10T00:00:00Z","citation":{"ama":"Chern A, Ishida S. L’Hopital rules for complex-valued functions in higher dimensions. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2602.09958\">10.48550/ARXIV.2602.09958</a>","ieee":"A. Chern and S. Ishida, “L’Hopital rules for complex-valued functions in higher dimensions,” <i>arXiv</i>. .","chicago":"Chern, Albert, and Sadashige Ishida. “L’Hopital Rules for Complex-Valued Functions in Higher Dimensions.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2602.09958\">https://doi.org/10.48550/ARXIV.2602.09958</a>.","mla":"Chern, Albert, and Sadashige Ishida. “L’Hopital Rules for Complex-Valued Functions in Higher Dimensions.” <i>ArXiv</i>, 2602.09958, doi:<a href=\"https://doi.org/10.48550/ARXIV.2602.09958\">10.48550/ARXIV.2602.09958</a>.","ista":"Chern A, Ishida S. L’Hopital rules for complex-valued functions in higher dimensions. arXiv, 2602.09958.","apa":"Chern, A., &#38; Ishida, S. (n.d.). L’Hopital rules for complex-valued functions in higher dimensions. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2602.09958\">https://doi.org/10.48550/ARXIV.2602.09958</a>","short":"A. Chern, S. Ishida, ArXiv (n.d.)."},"publication":"arXiv","article_processing_charge":"No","language":[{"iso":"eng"}],"OA_place":"repository","license":"https://creativecommons.org/licenses/by/4.0/","month":"02"},{"intvolume":"        36","article_number":"45","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ama":"Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. <i>Journal of Nonlinear Science</i>. 2026;36(2). doi:<a href=\"https://doi.org/10.1007/s00332-026-10266-8\">10.1007/s00332-026-10266-8</a>","chicago":"Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures on the Space of Space Curves.” <i>Journal of Nonlinear Science</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00332-026-10266-8\">https://doi.org/10.1007/s00332-026-10266-8</a>.","ieee":"M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space of space curves,” <i>Journal of Nonlinear Science</i>, vol. 36, no. 2. Springer Nature, 2026.","mla":"Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.” <i>Journal of Nonlinear Science</i>, vol. 36, no. 2, 45, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00332-026-10266-8\">10.1007/s00332-026-10266-8</a>.","ista":"Bauer M, Ishida S, Michor PW. 2026. Symplectic structures on the space of space curves. Journal of Nonlinear Science. 36(2), 45.","apa":"Bauer, M., Ishida, S., &#38; Michor, P. W. (2026). Symplectic structures on the space of space curves. <i>Journal of Nonlinear Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00332-026-10266-8\">https://doi.org/10.1007/s00332-026-10266-8</a>","short":"M. Bauer, S. Ishida, P.W. Michor, Journal of Nonlinear Science 36 (2026)."},"date_published":"2026-04-15T00:00:00Z","publication":"Journal of Nonlinear Science","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","OA_place":"publisher","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"04","title":"Symplectic structures on the space of space curves","issue":"2","OA_type":"hybrid","scopus_import":"1","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"ddc":["510"],"status":"public","has_accepted_license":"1","date_created":"2026-04-16T07:29:17Z","arxiv":1,"doi":"10.1007/s00332-026-10266-8","acknowledgement":"The authors are grateful to Boris Khesin for valuable comments on the MW symplectic structure and S. Ishida thanks Albert Chern for insightful discussions on space curves and Chris Wojtan for his continuous support. M. Bauer was partially supported by NSF grant DMS-1953244 and by the Binational Science Foundation (BSF). S. Ishida was partially supported by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council. Some figures were generated by the software Houdini and its education license was provided by SideFX. Open access funding provided by University of Vienna.","day":"15","type":"journal_article","_id":"21743","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083"}],"oa_version":"Published Version","article_type":"original","oa":1,"external_id":{"arxiv":["2407.19908"]},"author":[{"first_name":"Martin","last_name":"Bauer","full_name":"Bauer, Martin"},{"full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","first_name":"Sadashige","last_name":"Ishida"},{"full_name":"Michor, Peter W.","last_name":"Michor","first_name":"Peter W."}],"abstract":[{"text":"We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden–Weinstein structure. Our method integrates the Liouville 1-form of the Marsden–Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures.","lang":"eng"}],"PlanS_conform":"1","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"date_updated":"2026-04-28T09:59:01Z","file_date_updated":"2026-04-28T09:55:32Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17361"}]},"file":[{"file_name":"2026_JourNonlinearScience_Bauer.pdf","file_id":"21770","content_type":"application/pdf","relation":"main_file","file_size":1108518,"date_updated":"2026-04-28T09:55:32Z","access_level":"open_access","date_created":"2026-04-28T09:55:32Z","checksum":"760de2631b6fd7d57bcd5115ed36c0a2","creator":"dernst","success":1}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2026","volume":36,"publication_status":"published"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","creator":"dpalmer","date_created":"2026-05-29T12:53:25Z","checksum":"384524659fbaf3b9da80c3852ba835af","file_name":"main.pdf","file_size":39491071,"date_updated":"2026-05-29T12:53:25Z","content_type":"application/pdf","file_id":"21922","relation":"main_file"}],"publication_status":"accepted","year":"2026","date_updated":"2026-06-02T06:26:52Z","file_date_updated":"2026-05-29T12:53:25Z","abstract":[{"text":"A variety of problems in geometry processing boil down to finding the most\r\nparallel field relative to a connection. Instances of this prototypical problem\r\nshow up in computing direction fields and stripe patterns, quadrilateral\r\nmeshing, and visualization of fluid flows. When the class of allowed fields\r\nincludes those with topological defects, a relaxation is required to make\r\nthe problem well-posed. We observe that these problems can be viewed\r\nas synchronization problems, which admit a natural semidefinite relaxation.\r\nWe propose a unified method of solving all these problems via the efficient\r\nBurer-Monteiro factorization method. Geometrically, this amounts to lifting the field values to a higher-dimensional manifold, naturally resolving\r\nthe singular nature of defects. Practically, we show that our convex relaxation method achieves better and more reliable optima than previous work\r\nemploying alternative relaxations","lang":"eng"}],"author":[{"full_name":"Pacheco-Tallaj, Natalia","first_name":"Natalia","last_name":"Pacheco-Tallaj"},{"full_name":"Couplet, Matteo","last_name":"Couplet","first_name":"Matteo"},{"full_name":"Chien, Edward","first_name":"Edward","last_name":"Chien"},{"orcid":"0000-0002-1931-5673","full_name":"Palmer, David","id":"6574708f-2fd3-11f0-89e2-ae42ebc712a4","first_name":"David","last_name":"Palmer"}],"department":[{"_id":"ChWo"}],"oa_version":"Accepted Version","_id":"21921","oa":1,"date_created":"2026-05-29T12:53:59Z","doi":"10.1145/3799902.3811225","status":"public","has_accepted_license":"1","type":"conference","day":"01","acknowledgement":"The authors thank Steven J. Gortler and Nicolas Boumal for interesting discussions.\r\nDavid Palmer acknowledges the generous support of the NSF\r\nMSPRF under award #2303403 during his time at Harvard University.\r\nNatalia Pacheco-Tallaj was supported by the NSF DGE-2141064.\r\nMattéo Couplet was supported by Wallonie-Bruxelles International","OA_type":"green","title":"Synchronizing fields with singularities","ddc":["000"],"corr_author":"1","publication_identifier":{"eisbn":["9798400725548"]},"article_processing_charge":"No","quality_controlled":"1","publication":"SIGGRAPH Conference Papers","month":"06","language":[{"iso":"eng"}],"OA_place":"repository","publisher":"ACM","date_published":"2026-06-01T00:00:00Z","citation":{"mla":"Pacheco-Tallaj, Natalia, et al. “Synchronizing Fields with Singularities.” <i>SIGGRAPH Conference Papers</i>, ACM, doi:<a href=\"https://doi.org/10.1145/3799902.3811225\">10.1145/3799902.3811225</a>.","ama":"Pacheco-Tallaj N, Couplet M, Chien E, Palmer D. Synchronizing fields with singularities. In: <i>SIGGRAPH Conference Papers</i>. ACM. doi:<a href=\"https://doi.org/10.1145/3799902.3811225\">10.1145/3799902.3811225</a>","chicago":"Pacheco-Tallaj, Natalia, Matteo Couplet, Edward Chien, and David Palmer. “Synchronizing Fields with Singularities.” In <i>SIGGRAPH Conference Papers</i>. ACM, n.d. <a href=\"https://doi.org/10.1145/3799902.3811225\">https://doi.org/10.1145/3799902.3811225</a>.","ieee":"N. Pacheco-Tallaj, M. Couplet, E. Chien, and D. Palmer, “Synchronizing fields with singularities,” in <i>SIGGRAPH Conference Papers</i>, Los Angeles, CA, United States.","short":"N. Pacheco-Tallaj, M. Couplet, E. Chien, D. Palmer, in:, SIGGRAPH Conference Papers, ACM, n.d.","ista":"Pacheco-Tallaj N, Couplet M, Chien E, Palmer D. Synchronizing fields with singularities. SIGGRAPH Conference Papers. SIGGRAPH: International Conference and Exhibition on Computer Graphics and Interactive Techniques.","apa":"Pacheco-Tallaj, N., Couplet, M., Chien, E., &#38; Palmer, D. (n.d.). Synchronizing fields with singularities. In <i>SIGGRAPH Conference Papers</i>. Los Angeles, CA, United States: ACM. <a href=\"https://doi.org/10.1145/3799902.3811225\">https://doi.org/10.1145/3799902.3811225</a>"},"conference":{"name":"SIGGRAPH: International Conference and Exhibition on Computer Graphics and Interactive Techniques","end_date":"2026-07-23","start_date":"2026-07-19","location":"Los Angeles, CA, United States"}},{"abstract":[{"text":"The appearance of simulated natural phenomena heavily depends on the way surfaces are textured. However, applying texture maps to dynamic deformable surfaces presents a significant challenge, due to ever-shifting differences in length scales involved. When these surfaces move and advect the texture along with them, their final appearance degrades as deformed regions dramatically distort their texture map. Modifications to the texture directly at the pixel level in response to the deformation may introduce ghosting artifacts and look unnatural. In the real world, the appearance of surface details on a deforming material changes through the interplay of physical processes such as rupturing, exposure of internal structure, or wrinkling. Motivated by these behaviors, in this work we explore how physical principles can guide the texturing methods based on the measure of surface deformation.\r\nWe present two novel wave-based procedural texturing algorithms which reproduce common physical properties like advection and self-similarity, enabling the plausible animation of deforming objects with extreme texture map distortions. Our algorithms are fully procedural, require no actual physics simulation, and store no state or history of deformation besides the input UV map, making them highly parallelizable on the GPU and efficient enough for real-time applications. We show the versatility of the method by animating physical phenomena with extreme deformations such as flowing lava, stretching putty and outpouring sludge.","lang":"eng"}],"acknowledged_ssus":[{"_id":"ScienComp"}],"author":[{"id":"44b7120e-eb97-11eb-a6c2-e1557aa81d02","orcid":"0000-0003-2189-3904","full_name":"Kalinov, Aleksei","last_name":"Kalinov","first_name":"Aleksei"},{"last_name":"Ly","first_name":"Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël"},{"id":"400429CC-F248-11E8-B48F-1D18A9856A87","full_name":"Hafner, Christian","last_name":"Hafner","first_name":"Christian"},{"orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"oa_version":"Accepted Version","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083"}],"_id":"21923","oa":1,"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_size":77337231,"date_updated":"2026-05-29T13:19:33Z","relation":"main_file","file_id":"21924","content_type":"video/mp4","file_name":"tog454-article154-supplemental.mp4","success":1,"creator":"akalinov","checksum":"ea165bf731ddd3045f83878dcb833672","date_created":"2026-05-29T13:19:33Z","access_level":"open_access"},{"creator":"akalinov","success":1,"date_created":"2026-05-29T13:19:37Z","checksum":"6274cfb15ea5ba7324b74afc7b0d9629","access_level":"open_access","date_updated":"2026-05-29T13:19:37Z","file_size":226633977,"content_type":"video/mp4","file_id":"21925","relation":"main_file","file_name":"tog454-article154-video.mp4"},{"success":1,"creator":"akalinov","checksum":"9d41b322a7876be9a3311017b9973183","date_created":"2026-05-29T13:19:33Z","access_level":"open_access","file_size":6793867,"date_updated":"2026-05-29T13:19:33Z","relation":"main_file","content_type":"application/pdf","file_id":"21926","file_name":"tog454-article154-supplemental.pdf"},{"file_name":"tog454-article154-main-1.pdf","file_size":84173392,"date_updated":"2026-05-29T13:19:36Z","content_type":"application/pdf","file_id":"21927","relation":"main_file","access_level":"open_access","creator":"akalinov","success":1,"date_created":"2026-05-29T13:19:36Z","checksum":"51bc60d2de867fbfa570652dec7993b4"}],"publication_status":"inpress","volume":45,"year":"2026","keyword":["Procedural animation"],"date_updated":"2026-06-02T08:56:50Z","file_date_updated":"2026-05-29T13:19:37Z","article_processing_charge":"Yes","quality_controlled":"1","publication":"ACM Transactions on Graphics","month":"07","language":[{"iso":"eng"}],"publisher":"ACM","OA_place":"publisher","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_number":"154","intvolume":"        45","date_published":"2026-07-01T00:00:00Z","citation":{"short":"A. Kalinov, M. Ly, C. Hafner, C. Wojtan, ACM Transactions on Graphics 45 (n.d.).","apa":"Kalinov, A., Ly, M., Hafner, C., &#38; Wojtan, C. (n.d.). Physics-inspired procedural texturing of extremely deformable surfaces. <i>ACM Transactions on Graphics</i>. Los Angeles, CA, United States: ACM. <a href=\"https://doi.org/10.1145/3811353\">https://doi.org/10.1145/3811353</a>","ista":"Kalinov A, Ly M, Hafner C, Wojtan C. Physics-inspired procedural texturing of extremely deformable surfaces. ACM Transactions on Graphics. 45(4), 154.","mla":"Kalinov, Aleksei, et al. “Physics-Inspired Procedural Texturing of Extremely Deformable Surfaces.” <i>ACM Transactions on Graphics</i>, vol. 45, no. 4, 154, ACM, doi:<a href=\"https://doi.org/10.1145/3811353\">10.1145/3811353</a>.","ieee":"A. Kalinov, M. Ly, C. Hafner, and C. Wojtan, “Physics-inspired procedural texturing of extremely deformable surfaces,” <i>ACM Transactions on Graphics</i>, vol. 45, no. 4. ACM.","chicago":"Kalinov, Aleksei, Mickaël Ly, Christian Hafner, and Chris Wojtan. “Physics-Inspired Procedural Texturing of Extremely Deformable Surfaces.” <i>ACM Transactions on Graphics</i>. ACM, n.d. <a href=\"https://doi.org/10.1145/3811353\">https://doi.org/10.1145/3811353</a>.","ama":"Kalinov A, Ly M, Hafner C, Wojtan C. Physics-inspired procedural texturing of extremely deformable surfaces. <i>ACM Transactions on Graphics</i>. 45(4). doi:<a href=\"https://doi.org/10.1145/3811353\">10.1145/3811353</a>"},"conference":{"start_date":"2026-07-19","location":"Los Angeles, CA, United States","name":"SIGGRAPH: International Conference and Exhibition on Computer Graphics and Interactive Techniques","end_date":"2026-07-23"},"doi":"10.1145/3811353","date_created":"2026-05-29T13:25:16Z","has_accepted_license":"1","status":"public","type":"journal_article","day":"01","acknowledgement":"We thank the anonymous reviewers for their helpful comments, the members of the Visual Computing Group at ISTA for their feedback. We also thank Jonathan Gagnon for their help with running the Lapped Textures codes and SideFX for the Houdini Education software licenses.\r\nImages in Fig. 2 by Kisoulou and Vultured on Unsplash, Michal Jarmoluk and Public Domain Pictures from Pixabay and Hawai‘i Volcanoes NPS on flickr. 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_type":"hybrid","issue":"4","title":"Physics-inspired procedural texturing of extremely deformable surfaces","corr_author":"1","ddc":["006"],"publication_identifier":{"issn":["0730-0301"]}},{"date_updated":"2026-04-16T08:29:34Z","supervisor":[{"id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","last_name":"Wojtan","first_name":"Christopher J"}],"file_date_updated":"2025-04-30T15:49:16Z","degree_awarded":"PhD","alternative_title":["ISTA Thesis"],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","file":[{"file_id":"19633","content_type":"application/x-zip-compressed","relation":"source_file","date_updated":"2025-04-30T14:02:25Z","file_size":60670543,"file_name":"Thesis_source_Heiss_Synak.zip","date_created":"2025-04-30T14:02:25Z","checksum":"f00b519c27529daa0c3b2d4102b4fa7b","creator":"cchlebak","access_level":"closed"},{"creator":"cchlebak","checksum":"6e40a2fd3b1b881af1385670854a682e","date_created":"2025-04-30T14:02:42Z","access_level":"open_access","date_updated":"2025-04-30T15:49:16Z","file_size":21319043,"relation":"main_file","content_type":"application/pdf","file_id":"19634","file_name":"Thesis_PDFA_Heiss_Synak.pdf"}],"related_material":{"record":[{"id":"8135","relation":"part_of_dissertation","status":"public"},{"id":"17219","relation":"part_of_dissertation","status":"public"},{"id":"8384","relation":"part_of_dissertation","status":"public"}]},"publication_status":"published","year":"2025","oa_version":"Published Version","ec_funded":1,"_id":"19630","project":[{"call_identifier":"H2020","grant_number":"638176","_id":"2533E772-B435-11E9-9278-68D0E5697425","name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales"},{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"},{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales","call_identifier":"H2020","_id":"2533E772-B435-11E9-9278-68D0E5697425","grant_number":"638176"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"oa":1,"page":"106","abstract":[{"lang":"eng","text":"This thesis consists of three chapters, each corresponding to one publication. While each of these projects tackles a topic in a different area of research, they all share a common thread in the type of topological structure they handle - a partition of space into volumes separated by interfaces that meet in non-manifold junctions.\r\n\r\nIn Chapter 2, we study clusters of soap bubbles from a simulation perspective. In particular, we develop a surface-only algorithm that couples large scale motion and shape deformation of soap bubble clusters with the small scale evolution of the thin film's thickness, which is responsible for visual phenomena like surface vortices, Newton's interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. We model film thickness as a reduced degree of freedom in the Navier-Stokes equations and from them derive three sets of equations governing normal and tangential motion of the soap film surface, as well as the evolution of the thin film thickness. We discretize these equations on a non-manifold triangle mesh, extending and adapting operators to handle complex topology. We also present an incompressible fluid solver for 2.5D films and an advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film.\r\n\r\nIn Chapter 3, we introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts mesh defects, such as overlaps, self-intersections, and inversions 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, such as those presented in Chapter 2, but with an order of magnitude more interacting bubbles than what we could achieve before, and Boolean unions of non-manifold meshes consisting of millions of triangles.\r\n\r\nLastly, in Chapter 4, we utilize developments in the theory of random geometric complexes facilitated by observations from Discrete Morse theory. We survey the methods and results obtained with this new approach, and discuss some of its shortcomings. We use simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics."}],"acknowledged_ssus":[{"_id":"ScienComp"}],"author":[{"last_name":"Synak","first_name":"Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87","full_name":"Synak, Peter"}],"department":[{"_id":"ChWo"},{"_id":"GradSch"}],"title":"Methods for fluid simulation, surface tracking, and statistics of non-manifold structures","ddc":["519","006"],"corr_author":"1","publication_identifier":{"issn":["2663-337X"]},"doi":"10.15479/AT-ISTA-19630","date_created":"2025-04-29T09:39:34Z","has_accepted_license":"1","status":"public","type":"dissertation","day":"29","acknowledgement":"The project in Chapter 2 has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No. 638176. The project in Chapter 3 was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA). The project in Chapter 4 has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 78818 Alpha and No 638176). It was also partially supported by the DFG Collaborative Research Center TRR 109, 'Discretization in Geometry and Dynamics', through grant no. I02979-N35 of the Austrian Science Fund (FWF). Thank you for providing funds to support my work.","date_published":"2025-04-29T00:00:00Z","citation":{"mla":"Synak, Peter. <i>Methods for Fluid Simulation, Surface Tracking, and Statistics of Non-Manifold Structures</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-19630\">10.15479/AT-ISTA-19630</a>.","chicago":"Synak, Peter. “Methods for Fluid Simulation, Surface Tracking, and Statistics of Non-Manifold Structures.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-19630\">https://doi.org/10.15479/AT-ISTA-19630</a>.","ieee":"P. Synak, “Methods for fluid simulation, surface tracking, and statistics of non-manifold structures,” Institute of Science and Technology Austria, 2025.","ama":"Synak P. Methods for fluid simulation, surface tracking, and statistics of non-manifold structures. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-19630\">10.15479/AT-ISTA-19630</a>","short":"P. Synak, Methods for Fluid Simulation, Surface Tracking, and Statistics of Non-Manifold Structures, Institute of Science and Technology Austria, 2025.","apa":"Synak, P. (2025). <i>Methods for fluid simulation, surface tracking, and statistics of non-manifold structures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-19630\">https://doi.org/10.15479/AT-ISTA-19630</a>","ista":"Synak P. 2025. Methods for fluid simulation, surface tracking, and statistics of non-manifold structures. Institute of Science and Technology Austria."},"article_processing_charge":"No","month":"04","language":[{"iso":"eng"}],"OA_place":"publisher","publisher":"Institute of Science and Technology Austria"},{"alternative_title":["ISTA Thesis"],"degree_awarded":"PhD","file_date_updated":"2025-11-10T08:45:05Z","supervisor":[{"orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"},{"last_name":"Chern","first_name":"Albert","full_name":"Chern, Albert"}],"date_updated":"2026-04-07T12:02:23Z","year":"2025","publication_status":"published","related_material":{"record":[{"id":"12846","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"12431"},{"status":"public","relation":"part_of_dissertation","id":"17361"},{"status":"public","relation":"part_of_dissertation","id":"20580"}]},"file":[{"access_level":"open_access","date_created":"2025-11-01T18:26:14Z","checksum":"4eef80afcb67691cbb6549c4756fa534","creator":"sishida","file_name":"Thesis_tex.zip","file_id":"20583","content_type":"application/zip","relation":"source_file","file_size":72487812,"date_updated":"2025-11-01T18:26:14Z"},{"checksum":"1e5a557900bf2dce01966b211b15d0fe","date_created":"2025-11-10T08:45:05Z","success":1,"creator":"sishida","access_level":"open_access","relation":"main_file","file_id":"20623","content_type":"application/pdf","date_updated":"2025-11-10T08:45:05Z","file_size":8945141,"file_name":"Thesis_Sadashige_Ishida_PDFA.pdf"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","page":"141","oa":1,"_id":"20551","ec_funded":1,"project":[{"call_identifier":"H2020","grant_number":"638176","_id":"2533E772-B435-11E9-9278-68D0E5697425","name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales"},{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083"}],"oa_version":"Published Version","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"author":[{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","orcid":"0000-0002-3121-3100","full_name":"Ishida, Sadashige","last_name":"Ishida","first_name":"Sadashige"}],"acknowledged_ssus":[{"_id":"CampIT"}],"abstract":[{"text":"The space of codimension-2 shapes, such as curves in 3D and surfaces in 4D, is an infinite-dimensional manifold. This thesis explores geometric structures and dynamics on this space, with emphasis on their implications for physics, particularly hydrodynamics.\r\n\r\nOur investigation ranges from theoretical studies of infinite-dimensional symplectic and prequantum geometry to numerical computation of the time evolution of shapes. The thesis presents four main contributions.\r\n\r\nIn the first part, we introduce implicit representations of codimension-2 shapes using a class of complex-valued functions, and prove that the space of these implicit representations forms a prequantum bundle over the codimension-2 shape space. This reveals a new geometric interpretation of the canonical symplectic structure on the codimension-2 shape space.\r\n\r\nIn the second part, we use implicit representations to develop a simulation method for the dynamics of space curves. To handle chaotic systems such as vortex filaments in hydrodynamics, we exploit the infinite degrees of freedom, hidden in both the configuration and dynamics of implicit representations.\r\n\r\nIn the third part, we introduce new symplectic structures on the space of space curves, which generalize the only previously known symplectic structure on this space, allowing for new Hamiltonian dynamics of space curves.\r\n\r\nIn the fourth part, we apply a symplectic viewpoint to a differential geometric problem with practical applications. We derive a new area formula for spherical polygons via prequantization. ","lang":"eng"}],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-070-1"]},"corr_author":"1","ddc":["516"],"title":"Symplectic-prequantum structures and dynamics on the codimension-2 shape space","acknowledgement":"Projects contained in this thesis were financially supported in part by the\r\nEuropean Research Council with grants 1. ERC Consolidator Grant 101045083 CoDiNA,\r\nand 2. the European Union’s Horizon 2020 research and innovation programme under grant\r\nagreement No. 638176.","day":"31","type":"dissertation","status":"public","has_accepted_license":"1","date_created":"2025-10-27T10:28:52Z","doi":"10.15479/AT-ISTA-20551","citation":{"short":"S. Ishida, Symplectic-Prequantum Structures and Dynamics on the Codimension-2 Shape Space, Institute of Science and Technology Austria, 2025.","ista":"Ishida S. 2025. Symplectic-prequantum structures and dynamics on the codimension-2 shape space. Institute of Science and Technology Austria.","apa":"Ishida, S. (2025). <i>Symplectic-prequantum structures and dynamics on the codimension-2 shape space</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-20551\">https://doi.org/10.15479/AT-ISTA-20551</a>","mla":"Ishida, Sadashige. <i>Symplectic-Prequantum Structures and Dynamics on the Codimension-2 Shape Space</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20551\">10.15479/AT-ISTA-20551</a>.","ama":"Ishida S. Symplectic-prequantum structures and dynamics on the codimension-2 shape space. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20551\">10.15479/AT-ISTA-20551</a>","ieee":"S. Ishida, “Symplectic-prequantum structures and dynamics on the codimension-2 shape space,” Institute of Science and Technology Austria, 2025.","chicago":"Ishida, Sadashige. “Symplectic-Prequantum Structures and Dynamics on the Codimension-2 Shape Space.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-20551\">https://doi.org/10.15479/AT-ISTA-20551</a>."},"date_published":"2025-10-31T00:00:00Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Institute of Science and Technology Austria","OA_place":"publisher","language":[{"iso":"eng"}],"month":"10","article_processing_charge":"No"},{"status":"public","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"20551"}]},"arxiv":1,"date_created":"2025-10-30T18:36:56Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2507.11727","open_access":"1"}],"doi":"10.48550/ARXIV.2507.11727","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","year":"2025","publication_status":"draft","day":"15","type":"preprint","date_updated":"2026-04-07T12:02:23Z","title":"Implicit representations of codimension-2 submanifolds and their prequantum structure","corr_author":"1","publication":"arXiv","external_id":{"arxiv":["2507.11727"]},"author":[{"last_name":"Chern","first_name":"Albert","full_name":"Chern, Albert"},{"last_name":"Ishida","first_name":"Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100"}],"article_processing_charge":"No","abstract":[{"text":"This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. This reveals a prequantum bundle structure over the space of submanifolds, equipped with the well-known Marsden-Weinstein symplectic structure. This bundle allows a new physical interpretation of the Marsden-Weinstein structure as the curvature of a connection form, which measures the average of volumes swept by the deformation of the S^1-family of hypersurfaces, defined as the phases of a complex function implicitly representing a submanifold.","lang":"eng"}],"OA_place":"repository","language":[{"iso":"eng"}],"month":"07","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"_id":"20580","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa_version":"Preprint","citation":{"short":"A. Chern, S. Ishida, ArXiv (n.d.).","ista":"Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">10.48550/ARXIV.2507.11727</a>.","apa":"Chern, A., &#38; Ishida, S. (n.d.). Implicit representations of codimension-2 submanifolds and their prequantum structure. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">https://doi.org/10.48550/ARXIV.2507.11727</a>","mla":"Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2 Submanifolds and Their Prequantum Structure.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">10.48550/ARXIV.2507.11727</a>.","ama":"Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">10.48550/ARXIV.2507.11727</a>","chicago":"Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2 Submanifolds and Their Prequantum Structure.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">https://doi.org/10.48550/ARXIV.2507.11727</a>.","ieee":"A. Chern and S. Ishida, “Implicit representations of codimension-2 submanifolds and their prequantum structure,” <i>arXiv</i>. ."},"oa":1,"date_published":"2025-07-15T00:00:00Z"},{"OA_type":"hybrid","title":"Numerical homogenization of sand from grain-level simulations","issue":"6","corr_author":"1","ddc":["531","006","621"],"scopus_import":"1","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"doi":"10.1145/3763344","date_created":"2025-11-10T14:12:06Z","status":"public","has_accepted_license":"1","day":"04","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). ","tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"article_number":"220","intvolume":"        44","date_published":"2025-12-04T00:00:00Z","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>.","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.","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>.","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>","short":"Y.-L. Chen, M. Ly, C. Wojtan, ACM Transactions on Graphics 44 (2025).","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>","ista":"Chen Y-L, Ly M, Wojtan C. 2025. Numerical homogenization of sand from grain-level simulations. ACM Transactions on Graphics. 44(6), 220."},"conference":{"name":"SIGGRAPH Asia: Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia","end_date":"2025-12-18","start_date":"2025-12-15","location":"Hong Kong, China"},"article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","publication":"ACM Transactions on Graphics","license":"https://creativecommons.org/licenses/by-nd/4.0/","month":"12","language":[{"iso":"eng"}],"publisher":"Association for Computing Machinery","OA_place":"publisher","date_updated":"2025-12-09T14:53:32Z","file_date_updated":"2025-11-10T14:10:53Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","success":1,"creator":"yichen","checksum":"4d30ff82314e76fe411c8f8195bb6040","date_created":"2025-11-10T14:10:12Z","file_name":"main_paper.pdf","file_size":61708650,"date_updated":"2025-11-10T14:10:12Z","relation":"main_file","content_type":"application/pdf","file_id":"20629"},{"date_updated":"2025-11-10T14:10:27Z","file_size":6862285,"content_type":"application/pdf","file_id":"20630","relation":"supplementary_material","file_name":"paper_supplemental.pdf","creator":"yichen","date_created":"2025-11-10T14:10:27Z","checksum":"f1b6df39487866044ca7ca899d044be7","access_level":"open_access"},{"file_name":"main_video.mp4","file_size":164079303,"date_updated":"2025-11-10T14:10:44Z","relation":"supplementary_material","file_id":"20631","content_type":"video/mp4","access_level":"open_access","creator":"yichen","checksum":"04ec2a4866774673479cafe5b93d26bd","date_created":"2025-11-10T14:10:44Z"},{"content_type":"video/mp4","file_id":"20632","relation":"supplementary_material","file_size":72234678,"date_updated":"2025-11-10T14:10:53Z","file_name":"extra_video.mp4","date_created":"2025-11-10T14:10:53Z","checksum":"7495e8cbcf94eb49276b4730c5886914","creator":"yichen","access_level":"open_access"}],"publication_status":"published","volume":44,"year":"2025","oa_version":"Published Version","project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"_id":"20628","oa":1,"article_type":"original","abstract":[{"lang":"eng","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."}],"author":[{"full_name":"Chen, Yi-Lu","orcid":"0009-0005-0723-0655","id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","first_name":"Yi-Lu","last_name":"Chen"},{"last_name":"Ly","first_name":"Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}]},{"author":[{"first_name":"Arian","last_name":"Etemadihaghighi","full_name":"Etemadihaghighi, Arian","id":"36cea3aa-f38e-11ec-8ae0-c65ae6f6098f"}],"abstract":[{"text":"Physics simulation in computer graphics can bring triangle meshes into topologically invalid states. The method in this thesis contributed to Heiss-Synak* and Kalinov* et al. [2024] who devised a non-manifold hybrid surface tracker—a surface tracker that repairs explicit non-manifold triangle meshes with the help of the implicit domain. Specifically, this thesis provides an algorithm for filling the holes that are left after removing problematic parts of the mesh.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"_id":"18301","oa_version":"Published Version","page":"39","oa":1,"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"17219"}]},"file":[{"creator":"aetemadi","success":1,"date_created":"2024-10-24T14:34:42Z","checksum":"80fb7923e229ad9d39253d7c8a8083d0","access_level":"open_access","date_updated":"2024-10-24T14:34:42Z","file_size":8914218,"file_id":"18469","content_type":"application/pdf","relation":"main_file","file_name":"thesis-arian-etemadi.pdf"},{"access_level":"closed","creator":"aetemadi","date_created":"2024-10-24T14:34:54Z","checksum":"1c02586ed7d441d5ec441867650568d1","file_name":"thesis-arian-etemadi-latex-source.zip","date_updated":"2024-10-24T14:34:54Z","file_size":9802650,"content_type":"application/x-zip-compressed","file_id":"18470","relation":"source_file"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","year":"2024","publication_status":"published","date_updated":"2026-04-07T13:02:36Z","keyword":["surface tracking","non-manifold","hole-filling","topology change","multi-material","solid-modeling"],"alternative_title":["ISTA Master's Thesis"],"degree_awarded":"MS","file_date_updated":"2024-10-24T14:34:54Z","supervisor":[{"first_name":"Christopher J","last_name":"Wojtan","orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","publisher":"Institute of Science and Technology Austria","OA_place":"publisher","language":[{"iso":"eng"}],"month":"10","license":"https://creativecommons.org/licenses/by-sa/4.0/","tmp":{"name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","image":"/images/cc_by_sa.png","short":"CC BY-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"citation":{"apa":"Etemadi, A. (2024). <i>Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18301\">https://doi.org/10.15479/at:ista:18301</a>","ista":"Etemadi A. 2024. Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking. Institute of Science and Technology Austria.","short":"A. Etemadi, Filling the Holes of Non-Manifold Self-Intersecting Meshes for Implicit Topology Changes in Surface Tracking, Institute of Science and Technology Austria, 2024.","ama":"Etemadi A. Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18301\">10.15479/at:ista:18301</a>","ieee":"A. Etemadi, “Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking,” Institute of Science and Technology Austria, 2024.","chicago":"Etemadi, Arian. “Filling the Holes of Non-Manifold Self-Intersecting Meshes for Implicit Topology Changes in Surface Tracking.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18301\">https://doi.org/10.15479/at:ista:18301</a>.","mla":"Etemadi, Arian. <i>Filling the Holes of Non-Manifold Self-Intersecting Meshes for Implicit Topology Changes in Surface Tracking</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18301\">10.15479/at:ista:18301</a>."},"date_published":"2024-10-15T00:00:00Z","status":"public","has_accepted_license":"1","date_created":"2024-10-11T19:52:20Z","doi":"10.15479/at:ista:18301","day":"15","type":"dissertation","title":"Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking","publication_identifier":{"issn":["2791-4585"]},"ddc":["000"],"corr_author":"1"},{"citation":{"short":"S. Ishida, H. Lavenant, Foundations of Computational Mathematics (2024).","apa":"Ishida, S., &#38; Lavenant, H. (2024). Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>Foundations of Computational Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-024-09686-3\">https://doi.org/10.1007/s10208-024-09686-3</a>","ista":"Ishida S, Lavenant H. 2024. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. Foundations of Computational Mathematics.","mla":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>Foundations of Computational Mathematics</i>, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s10208-024-09686-3\">10.1007/s10208-024-09686-3</a>.","ama":"Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>Foundations of Computational Mathematics</i>. 2024. doi:<a href=\"https://doi.org/10.1007/s10208-024-09686-3\">10.1007/s10208-024-09686-3</a>","chicago":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10208-024-09686-3\">https://doi.org/10.1007/s10208-024-09686-3</a>.","ieee":"S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation,” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2024."},"date_published":"2024-11-11T00:00:00Z","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Foundations of Computational Mathematics","month":"11","publisher":"Springer Nature","OA_place":"publisher","language":[{"iso":"eng"}],"title":"Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation","OA_type":"hybrid","scopus_import":"1","publication_identifier":{"eissn":["1615-3383"],"issn":["1615-3375"]},"ddc":["000"],"corr_author":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s10208-024-09686-3"}],"doi":"10.1007/s10208-024-09686-3","arxiv":1,"date_created":"2023-12-21T10:14:37Z","status":"public","day":"11","type":"journal_article","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 hospitality. 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":"Published Version","project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"_id":"14703","oa":1,"article_type":"original","abstract":[{"lang":"eng","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."}],"external_id":{"isi":["001352503300001"],"arxiv":["2312.12213"]},"author":[{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","orcid":"0000-0002-3121-3100","full_name":"Ishida, Sadashige","last_name":"Ishida","first_name":"Sadashige"},{"full_name":"Lavenant, Hugo","last_name":"Lavenant","first_name":"Hugo"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"keyword":["Optimal transport","Hamilton-Jacobi equation","convex optimization"],"date_updated":"2026-06-18T17:37:10Z","isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","year":"2024"},{"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"author":[{"full_name":"Chern, Albert","last_name":"Chern","first_name":"Albert"},{"first_name":"Sadashige","last_name":"Ishida","full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425"}],"external_id":{"isi":["001342265800009"],"arxiv":["2303.14555"]},"abstract":[{"lang":"eng","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."}],"article_type":"original","page":"782-796","oa":1,"_id":"12846","project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"oa_version":"Preprint","volume":8,"year":"2024","publication_status":"published","related_material":{"record":[{"id":"20551","relation":"dissertation_contains","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"date_updated":"2026-04-07T12:02:22Z","language":[{"iso":"eng"}],"OA_place":"repository","publisher":"Society for Industrial and Applied Mathematics","month":"09","publication":"SIAM Journal on Applied Algebra and Geometry","article_processing_charge":"No","quality_controlled":"1","date_published":"2024-09-23T00:00:00Z","citation":{"ama":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. <i>SIAM Journal on Applied Algebra and Geometry</i>. 2024;8(3):782-796. doi:<a href=\"https://doi.org/10.1137/23M1565255\">10.1137/23M1565255</a>","ieee":"A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” <i>SIAM Journal on Applied Algebra and Geometry</i>, vol. 8, no. 3. Society for Industrial and Applied Mathematics, pp. 782–796, 2024.","chicago":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>SIAM Journal on Applied Algebra and Geometry</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/23M1565255\">https://doi.org/10.1137/23M1565255</a>.","mla":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>SIAM Journal on Applied Algebra and Geometry</i>, vol. 8, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 782–96, doi:<a href=\"https://doi.org/10.1137/23M1565255\">10.1137/23M1565255</a>.","apa":"Chern, A., &#38; Ishida, S. (2024). Area formula for spherical polygons via prequantization. <i>SIAM Journal on Applied Algebra and Geometry</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/23M1565255\">https://doi.org/10.1137/23M1565255</a>","ista":"Chern A, Ishida S. 2024. Area formula for spherical polygons via prequantization. SIAM Journal on Applied Algebra and Geometry. 8(3), 782–796.","short":"A. Chern, S. Ishida, SIAM Journal on Applied Algebra and Geometry 8 (2024) 782–796."},"intvolume":"         8","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"acknowledgement":"This work was funded by European Research Council Consolidator grant 101045083 CoDiNA and National Science Foundation CAREER award 2239062. Some figures in the article were generated by the software Houdini and its education license was provided by SideFX. The authors acknowledge anonymous referees for their reviews and insightful suggestions, and Chris Wojtan for his continuous support through discussions. The second author thanks Anna Sisak for a fruitful discussion on prequantum bundles.","day":"23","type":"journal_article","status":"public","has_accepted_license":"1","date_created":"2023-04-18T19:16:06Z","arxiv":1,"doi":"10.1137/23M1565255","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2303.14555"}],"ddc":["516"],"corr_author":"1","publication_identifier":{"eissn":["2470-6566"]},"scopus_import":"1","OA_type":"green","issue":"3","title":"Area formula for spherical polygons via prequantization"},{"scopus_import":"1","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"corr_author":"1","ddc":["516"],"issue":"4","title":"Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments","type":"journal_article","day":"01","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","date_created":"2024-07-05T12:08:57Z","has_accepted_license":"1","status":"public","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.","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>","short":"C. Hafner, M. Ly, C. Wojtan, Transactions on Graphics 43 (2024).","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>","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>.","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.","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>."},"date_published":"2024-07-01T00:00:00Z","conference":{"end_date":"2024-08-01","location":"Denver, Colorado","start_date":"2024-07-28"},"intvolume":"        43","article_number":"78","month":"07","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Transactions on Graphics","file_date_updated":"2024-07-17T09:29:13Z","keyword":["Topology Optimization","Mass Moments","Computational Geometry"],"date_updated":"2025-09-08T08:29:09Z","publication_status":"published","volume":43,"year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"file":[{"access_level":"open_access","date_created":"2024-07-05T12:05:17Z","checksum":"0dc9f5a6422b8a49a79026900f349ee5","creator":"chafner","success":1,"file_name":"sif-final.pdf","file_id":"17204","content_type":"application/pdf","relation":"main_file","date_updated":"2024-07-05T12:05:17Z","file_size":7225150},{"creator":"chafner","date_created":"2024-07-05T12:06:03Z","checksum":"cde433c6a40688d5f1187fb5721f6f94","access_level":"open_access","file_size":397262,"date_updated":"2024-07-05T12:06:03Z","content_type":"application/pdf","file_id":"17205","relation":"supplementary_material","file_name":"sif-supp-final.pdf"},{"file_name":"sif-video-final.mp4","date_updated":"2024-07-17T09:29:13Z","file_size":170001305,"title":"Submission Video","relation":"supplementary_material","file_id":"17276","content_type":"video/mp4","access_level":"open_access","creator":"chafner","checksum":"c0457a09c2ab9a1c2935c995dcc84907","date_created":"2024-07-17T09:29:13Z"}],"oa":1,"article_type":"original","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"}],"_id":"17203","department":[{"_id":"ChWo"}],"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"}],"external_id":{"isi":["001289270900045"]},"author":[{"last_name":"Hafner","first_name":"Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87","full_name":"Hafner, Christian"},{"id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël","last_name":"Ly","first_name":"Mickaël"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}]},{"title":"Primal-dual non-smooth friction for rigid body animation","scopus_import":"1","publication_identifier":{"isbn":["9798400705250"]},"corr_author":"1","ddc":["621","531","006"],"doi":"10.1145/3641519.3657485","date_created":"2024-07-10T11:06:20Z","has_accepted_license":"1","status":"public","type":"conference","day":"01","acknowledgement":"We thank Vincent Acary for his help with Siconos, as well as the anonymous reviewers and the members of the Visual Computing Group at ISTA for their helpful comments. This research was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA).","citation":{"ama":"Chen Y-L, Ly M, Wojtan C. Primal-dual non-smooth friction for rigid body animation. In: <i>Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24</i>. Association for Computing Machinery; 2024. doi:<a href=\"https://doi.org/10.1145/3641519.3657485\">10.1145/3641519.3657485</a>","ieee":"Y.-L. Chen, M. Ly, and C. Wojtan, “Primal-dual non-smooth friction for rigid body animation,” in <i>Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24</i>, Denver, United States, 2024.","chicago":"Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Primal-Dual Non-Smooth Friction for Rigid Body Animation.” In <i>Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24</i>. Association for Computing Machinery, 2024. <a href=\"https://doi.org/10.1145/3641519.3657485\">https://doi.org/10.1145/3641519.3657485</a>.","mla":"Chen, Yi-Lu, et al. “Primal-Dual Non-Smooth Friction for Rigid Body Animation.” <i>Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24</i>, Association for Computing Machinery, 2024, doi:<a href=\"https://doi.org/10.1145/3641519.3657485\">10.1145/3641519.3657485</a>.","ista":"Chen Y-L, Ly M, Wojtan C. 2024. Primal-dual non-smooth friction for rigid body animation. Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24. SIGGRAPH: Computer Graphics and Interactive Techniques Conference.","apa":"Chen, Y.-L., Ly, M., &#38; Wojtan, C. (2024). Primal-dual non-smooth friction for rigid body animation. In <i>Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24</i>. Denver, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3641519.3657485\">https://doi.org/10.1145/3641519.3657485</a>","short":"Y.-L. Chen, M. Ly, C. Wojtan, in:, Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers ’24, Association for Computing Machinery, 2024."},"date_published":"2024-07-01T00:00:00Z","conference":{"name":"SIGGRAPH: Computer Graphics and Interactive Techniques Conference","end_date":"2024-08-01","location":"Denver, United States","start_date":"2024-07-28"},"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers '24","month":"07","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"keyword":["physical simulation","frictional contact","rigid body mechanics","non-smooth dynamics"],"date_updated":"2025-09-08T08:54:38Z","file_date_updated":"2024-07-10T11:03:58Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"file":[{"access_level":"open_access","checksum":"b8b203ed09e3995ba0d7e6a76288663a","date_created":"2024-07-10T11:03:14Z","success":1,"creator":"yichen","file_name":"sig24_friction_authors.pdf","relation":"main_file","content_type":"application/pdf","file_id":"17215","date_updated":"2024-07-10T11:03:14Z","file_size":47309472},{"date_created":"2024-07-10T11:03:12Z","checksum":"89d81b397b4b6469d828808a68b70820","creator":"yichen","success":1,"access_level":"open_access","content_type":"application/pdf","file_id":"17216","relation":"main_file","date_updated":"2024-07-10T11:03:12Z","file_size":10518286,"file_name":"sig24_friction_supplementary.pdf"},{"relation":"main_file","file_id":"17217","content_type":"video/mp4","file_size":71789192,"date_updated":"2024-07-10T11:03:51Z","file_name":"friction_paper_extra_video_finished.mp4","checksum":"7123deed34a5456810e7b5336a31c657","date_created":"2024-07-10T11:03:51Z","success":1,"creator":"yichen","access_level":"open_access"},{"checksum":"e606fc1ae8f2610ce3b4421566800b45","date_created":"2024-07-10T11:03:58Z","success":1,"creator":"yichen","access_level":"open_access","relation":"main_file","content_type":"video/mp4","file_id":"17218","date_updated":"2024-07-10T11:03:58Z","file_size":280610763,"file_name":"friction_paper_video_finished.mp4"}],"publication_status":"published","year":"2024","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"}],"_id":"17214","oa":1,"abstract":[{"lang":"eng","text":"Current numerical algorithms for simulating friction fall in one of two camps: smooth solvers sacrifice the stable treatment of static friction in exchange for fast convergence, and non-smooth solvers accurately compute friction at convergence rates that are often prohibitive for large graphics applications. We introduce a novel bridge between these two ideas that computes static and dynamic friction stably and efficiently. Our key idea is to convert the highly constrained non-smooth problem into an unconstrained smooth problem using logarithmic barriers that converges to the exact solution as accuracy increases. We phrase the problem as an interior point primal-dual problem that can be solved efficiently with Newton iteration. We observe quadratic convergence despite the non-smooth nature of the original problem, and our method is well-suited for large systems of tightly packed objects with many contact points. We demonstrate the efficacy of our method with stable piles of grains and stacks of objects, complex granular flows, and robust interlocking assemblies of rigid bodies."}],"external_id":{"isi":["001282218200091"]},"author":[{"first_name":"Yi-Lu","last_name":"Chen","full_name":"Chen, Yi-Lu","id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70"},{"full_name":"Ly, Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","first_name":"Mickaël","last_name":"Ly"},{"id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","last_name":"Wojtan","first_name":"Christopher J"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"}]},{"citation":{"short":"P. Synak, A. Kalinov, I.-M. Strugaru, A. Etemadi, H. Yang, C. Wojtan, ACM Transactions on Graphics 43 (2024).","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.","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>","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>.","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>","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>.","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."},"date_published":"2024-07-01T00:00:00Z","intvolume":"        43","article_number":"54","tmp":{"short":"CC BY-NC-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png"},"OA_place":"publisher","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"month":"07","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","publication":"ACM Transactions on Graphics","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"ddc":["004"],"corr_author":"1","issue":"4","title":"Multi-material mesh-based surface tracking with implicit topology changes","OA_type":"hybrid","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).","type":"journal_article","day":"01","status":"public","has_accepted_license":"1","date_created":"2024-07-10T12:24:00Z","doi":"10.1145/3658223","article_type":"original","oa":1,"_id":"17219","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"oa_version":"Published Version","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"external_id":{"isi":["001289270900021"]},"author":[{"last_name":"Synak","first_name":"Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87","full_name":"Synak, Peter"},{"last_name":"Kalinov","first_name":"Aleksei","id":"44b7120e-eb97-11eb-a6c2-e1557aa81d02","full_name":"Kalinov, Aleksei","orcid":"0000-0003-2189-3904"},{"first_name":"Irina-Malina","last_name":"Strugaru","full_name":"Strugaru, Irina-Malina","id":"2afc607f-f128-11eb-9611-8f2a0dfcf074"},{"last_name":"Etemadihaghighi","first_name":"Arian","id":"36cea3aa-f38e-11ec-8ae0-c65ae6f6098f","full_name":"Etemadihaghighi, Arian"},{"full_name":"Yang, Huidong","last_name":"Yang","first_name":"Huidong"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}],"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2025-11-11T09:50:52Z","date_updated":"2026-04-07T13:02:36Z","keyword":["surface tracking","topology change","non- manifold meshes","multi-material flows","solid modeling"],"year":"2024","volume":43,"publication_status":"published","related_material":{"record":[{"id":"19630","relation":"dissertation_contains","status":"public"},{"status":"public","relation":"dissertation_contains","id":"18301"}]},"file":[{"access_level":"open_access","date_created":"2024-07-23T06:35:15Z","checksum":"1917067d4b52d7729019b03560004e43","creator":"dernst","success":1,"file_name":"2024_ACMToG_HeissSynak.pdf","file_id":"17317","content_type":"application/pdf","relation":"main_file","date_updated":"2024-07-23T06:35:15Z","file_size":48763368},{"access_level":"open_access","date_created":"2024-07-10T12:23:44Z","checksum":"a4f0e293184bfa034c0c585848806b17","creator":"akalinov","success":1,"file_name":"sdtopofixer_final.mp4","content_type":"video/mp4","file_id":"17221","relation":"main_file","date_updated":"2024-07-10T12:23:44Z","file_size":48021463},{"file_size":48639581,"date_updated":"2025-11-11T09:50:52Z","title":"Authors' version of the text","relation":"preprint","content_type":"application/pdf","file_id":"20633","file_name":"SuperDuperTopoFixer.pdf","creator":"akalinov","checksum":"18fc310a78ec91651148c45a8b89fa44","date_created":"2025-11-11T09:50:52Z","access_level":"open_access"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"keyword":["space of space curves","symplectic stuctures"],"title":"Symplectic structures on the space of space curves","date_updated":"2026-04-28T09:59:01Z","date_created":"2024-08-01T06:34:08Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2407.19908","open_access":"1"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","arxiv":1,"doi":"10.48550/arXiv.2407.19908","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"20551"},{"id":"21743","status":"public","relation":"later_version"}]},"status":"public","day":"29","type":"preprint","publication_status":"draft","acknowledgement":"The authors are grateful to Boris Khesin for valuable comments on the MW symplectic structure and S. Ishida thanks Albert Chern for insightful discussions on space curves and Chris Wojtan for his continuous support. M. Bauer was partially supported by NSF grant DMS-1953244 and by the Binational Science Foundation (BSF). S. Ishida was partially supported by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council. Some figures were generated by the software Houdini and its education license was provided by SideFX.","year":"2024","oa_version":"Preprint","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"_id":"17361","date_published":"2024-07-29T00:00:00Z","oa":1,"citation":{"mla":"Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2407.19908\">10.48550/arXiv.2407.19908</a>.","ama":"Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2407.19908\">10.48550/arXiv.2407.19908</a>","chicago":"Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures on the Space of Space Curves.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2407.19908\">https://doi.org/10.48550/arXiv.2407.19908</a>.","ieee":"M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space of space curves,” <i>arXiv</i>. .","short":"M. Bauer, S. Ishida, P.W. Michor, ArXiv (n.d.).","apa":"Bauer, M., Ishida, S., &#38; Michor, P. W. (n.d.). Symplectic structures on the space of space curves. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2407.19908\">https://doi.org/10.48550/arXiv.2407.19908</a>","ista":"Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2407.19908\">10.48550/arXiv.2407.19908</a>."},"abstract":[{"lang":"eng","text":"We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1-form of the Marsden-Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures."}],"article_processing_charge":"No","author":[{"last_name":"Bauer","first_name":"Martin","full_name":"Bauer, Martin"},{"full_name":"Ishida, Sadashige","orcid":"0000-0002-3121-3100","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","first_name":"Sadashige","last_name":"Ishida"},{"last_name":"Michor","first_name":"Peter W.","full_name":"Michor, Peter W."}],"external_id":{"arxiv":["2407.19908"]},"publication":"arXiv","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"month":"07","language":[{"iso":"eng"}],"OA_place":"repository"},{"issue":"5","title":"Procedural metamaterials: A unified procedural graph for metamaterial design","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"scopus_import":"1","ddc":["531","006"],"date_created":"2023-11-29T15:02:03Z","doi":"10.1145/3605389","has_accepted_license":"1","status":"public","type":"journal_article","day":"01","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.","article_number":"168","intvolume":"        42","citation":{"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>.","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>","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>.","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).","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.","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>"},"date_published":"2023-10-01T00:00:00Z","quality_controlled":"1","article_processing_charge":"Yes (in subscription journal)","publication":"ACM Transactions on Graphics","month":"10","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"keyword":["Computer Graphics and Computer-Aided Design"],"date_updated":"2025-09-09T13:33:58Z","file_date_updated":"2023-12-04T08:04:14Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"file":[{"file_name":"tog-22-0089-File004.zip","file_size":95467870,"date_updated":"2023-11-29T15:16:01Z","content_type":"application/zip","file_id":"14630","relation":"main_file","access_level":"open_access","creator":"yichen","success":1,"date_created":"2023-11-29T15:16:01Z","checksum":"0192f597d7a2ceaf89baddfd6190d4c8"},{"file_size":103731880,"date_updated":"2023-11-29T15:16:01Z","relation":"main_file","file_id":"14631","content_type":"application/zip","file_name":"tog-22-0089-File005.zip","success":1,"creator":"yichen","checksum":"7fb024963be81933494f38de191e4710","date_created":"2023-11-29T15:16:01Z","access_level":"open_access"},{"file_name":"2023_ACMToG_Makatura.pdf","relation":"main_file","file_id":"14638","content_type":"application/pdf","file_size":57067476,"date_updated":"2023-12-04T08:04:14Z","access_level":"open_access","checksum":"b7d6829ce396e21cac9fae0ec7130a6b","date_created":"2023-12-04T08:04:14Z","success":1,"creator":"dernst"}],"publication_status":"published","volume":42,"year":"2023","oa_version":"Published Version","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"_id":"14628","oa":1,"article_type":"original","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."}],"external_id":{"isi":["001086833300007"]},"author":[{"full_name":"Makatura, Liane","first_name":"Liane","last_name":"Makatura"},{"full_name":"Wang, Bohan","first_name":"Bohan","last_name":"Wang"},{"last_name":"Chen","first_name":"Yi-Lu","id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","full_name":"Chen, Yi-Lu"},{"first_name":"Bolei","last_name":"Deng","full_name":"Deng, Bolei"},{"orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"},{"full_name":"Bickel, Bernd","orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","first_name":"Bernd","last_name":"Bickel"},{"first_name":"Wojciech","last_name":"Matusik","full_name":"Matusik, Wojciech"}],"department":[{"_id":"GradSch"},{"_id":"ChWo"},{"_id":"BeBi"}]},{"year":"2023","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).","publication_status":"published","day":"01","type":"conference_abstract","related_material":{"record":[{"id":"15292","relation":"other","status":"public"}]},"status":"public","doi":"10.1145/3606037.3606836","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-01-08T13:00:24Z","publication_identifier":{"isbn":["9798400702686"]},"corr_author":"1","date_updated":"2025-04-14T12:58:27Z","title":"Unified treatment of contact, friction and shock-propagation in rigid body animation","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"month":"08","department":[{"_id":"ChWo"}],"publication":"Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation","author":[{"first_name":"Yi-Lu","last_name":"Chen","full_name":"Chen, Yi-Lu","id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70"},{"last_name":"Ly","first_name":"Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël"},{"id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","last_name":"Wojtan","first_name":"Christopher J"}],"quality_controlled":"1","acknowledged_ssus":[{"_id":"ScienComp"}],"article_processing_charge":"No","conference":{"location":"Los Angeles, CA, United States","start_date":"2023-08-04","name":"SCA: Symposium on Computer Animation","end_date":"2023-08-06"},"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.","apa":"Chen, Y.-L., Ly, M., &#38; Wojtan, C. (2023). Unified treatment of contact, friction and shock-propagation in rigid body animation. In <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>. Los Angeles, CA, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3606037.3606836\">https://doi.org/10.1145/3606037.3606836</a>","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.","mla":"Chen, Yi-Lu, et al. “Unified Treatment of Contact, Friction and Shock-Propagation in Rigid Body Animation.” <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>, 5, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3606037.3606836\">10.1145/3606037.3606836</a>.","ama":"Chen Y-L, Ly M, Wojtan C. Unified treatment of contact, friction and shock-propagation in rigid body animation. In: <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>. Association for Computing Machinery; 2023. doi:<a href=\"https://doi.org/10.1145/3606037.3606836\">10.1145/3606037.3606836</a>","ieee":"Y.-L. Chen, M. Ly, and C. Wojtan, “Unified treatment of contact, friction and shock-propagation in rigid body animation,” in <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>, Los Angeles, CA, United States, 2023.","chicago":"Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Unified Treatment of Contact, Friction and Shock-Propagation in Rigid Body Animation.” In <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3606037.3606836\">https://doi.org/10.1145/3606037.3606836</a>."},"date_published":"2023-08-01T00:00:00Z","_id":"14748","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":"5","oa_version":"None"},{"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"author":[{"full_name":"Chen, Yi-Lu","id":"0b467602-dbcd-11ea-9d1d-ed480aa46b70","first_name":"Yi-Lu","last_name":"Chen"},{"last_name":"Ly","first_name":"Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}],"abstract":[{"text":"We present a rigid body animation technique which prevents solids from interpenetrating, dissipates energy through friction, and propagates shocks through contacts. We employ the Alternating Direction Method of Multipliers (ADMM) to couple non-smooth Coulomb friction with impact propagation, allowing efficient and accurate non-smooth dynamics along with a correct transmission of impacts through assemblies of rigid bodies. We further extend our method to model adhesion, dynamic friction and lubricated contact.","lang":"eng"}],"oa":1,"project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083"}],"_id":"15292","oa_version":"None","year":"2023","publication_status":"published","file":[{"access_level":"open_access","checksum":"88bdef929ca262ee0eefae0bbc649139","date_created":"2024-04-03T14:58:24Z","success":1,"creator":"yichen","file_name":"video.mp4","relation":"main_file","content_type":"video/mp4","file_id":"15293","date_updated":"2024-04-03T14:58:24Z","file_size":58770929},{"success":1,"creator":"yichen","checksum":"c06881ba847da365a74ac09c953eaffd","date_created":"2024-04-03T14:58:23Z","access_level":"open_access","date_updated":"2024-04-03T14:58:23Z","file_size":3951968,"relation":"main_file","file_id":"15294","content_type":"application/pdf","file_name":"frictionPoster_clean.pdf"}],"related_material":{"record":[{"id":"14748","status":"public","relation":"other"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2024-04-03T14:58:24Z","date_updated":"2025-04-14T12:58:27Z","language":[{"iso":"eng"}],"publisher":"ACM","month":"08","publication":"Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation","article_processing_charge":"No","conference":{"name":"SCA: Symposium on Computer Animation","end_date":"2023-08-06","start_date":"2023-08-04","location":"Los Angeles, CA, United States"},"date_published":"2023-08-01T00:00:00Z","citation":{"short":"Y.-L. Chen, M. Ly, C. Wojtan, Unified Treatment of Contact, Friction and Shock-Propagation in Rigid Body Animation, ACM, 2023.","ista":"Chen Y-L, Ly M, Wojtan C. 2023. Unified treatment of contact, friction and shock-propagation in rigid body animation, ACM,p.","apa":"Chen, Y.-L., Ly, M., &#38; Wojtan, C. (2023). <i>Unified treatment of contact, friction and shock-propagation in rigid body animation</i>. <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>. 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ACM, 2023.","ama":"Chen Y-L, Ly M, Wojtan C. <i>Unified Treatment of Contact, Friction and Shock-Propagation in Rigid Body Animation</i>. ACM; 2023. doi:<a href=\"https://doi.org/10.1145/3606037.3606836\">10.1145/3606037.3606836</a>"},"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)","type":"conference_poster","day":"01","status":"public","has_accepted_license":"1","doi":"10.1145/3606037.3606836","date_created":"2024-04-03T14:57:23Z","corr_author":"1","ddc":["005","531"],"title":"Unified treatment of contact, friction and shock-propagation in rigid body animation"},{"external_id":{"isi":["001044671300049"]},"author":[{"first_name":"Stefan","last_name":"Jeschke","full_name":"Jeschke, Stefan","id":"44D6411A-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}],"acknowledged_ssus":[{"_id":"ScienComp"}],"abstract":[{"lang":"eng","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."}],"department":[{"_id":"ChWo"}],"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"_id":"14240","oa_version":"Published Version","article_type":"original","oa":1,"file":[{"success":1,"creator":"sjeschke","checksum":"1d178bb2f8011d9f5aedda6427e18c7a","date_created":"2023-12-21T12:26:40Z","access_level":"open_access","date_updated":"2023-12-21T12:26:40Z","file_size":511572575,"relation":"main_file","file_id":"14704","content_type":"video/mp4","file_name":"PaperVideo_final.mp4"},{"date_updated":"2024-01-02T09:34:27Z","file_size":7469177,"content_type":"application/pdf","file_id":"14725","relation":"main_file","file_name":"2023_ACMToG_Jeschke.pdf","creator":"dernst","success":1,"date_created":"2024-01-02T09:34:27Z","checksum":"a49b2e744d5cd1276bb8b2e0ce6dc638","access_level":"open_access"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","volume":42,"publication_status":"published","date_updated":"2025-04-14T08:01:13Z","file_date_updated":"2024-01-02T09:34:27Z","publication":"ACM Transactions on Graphics","quality_controlled":"1","article_processing_charge":"Yes (in subscription journal)","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"month":"08","intvolume":"        42","article_number":"83","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"short":"S. Jeschke, C. Wojtan, ACM Transactions on Graphics 42 (2023).","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>","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.” <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>.","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.","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>.","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>"},"date_published":"2023-08-01T00:00:00Z","status":"public","has_accepted_license":"1","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.","day":"01","type":"journal_article","issue":"4","title":"Generalizing shallow water simulations with dispersive surface waves","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"scopus_import":"1","corr_author":"1","ddc":["000"]},{"date_published":"2022-05-01T00:00:00Z","citation":{"mla":"Schreck, Camille, and Chris Wojtan. “Coupling 3D Liquid Simulation with 2D Wave Propagation for Large Scale Water Surface Animation Using the Equivalent Sources Method.” <i>Computer Graphics Forum</i>, vol. 41, no. 2, Wiley, 2022, pp. 343–53, doi:<a href=\"https://doi.org/10.1111/cgf.14478\">10.1111/cgf.14478</a>.","ama":"Schreck C, Wojtan C. Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method. <i>Computer Graphics Forum</i>. 2022;41(2):343-353. doi:<a href=\"https://doi.org/10.1111/cgf.14478\">10.1111/cgf.14478</a>","chicago":"Schreck, Camille, and Chris Wojtan. “Coupling 3D Liquid Simulation with 2D Wave Propagation for Large Scale Water Surface Animation Using the Equivalent Sources Method.” <i>Computer Graphics Forum</i>. Wiley, 2022. <a href=\"https://doi.org/10.1111/cgf.14478\">https://doi.org/10.1111/cgf.14478</a>.","ieee":"C. Schreck and C. Wojtan, “Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method,” <i>Computer Graphics Forum</i>, vol. 41, no. 2. Wiley, pp. 343–353, 2022.","short":"C. Schreck, C. Wojtan, Computer Graphics Forum 41 (2022) 343–353.","ista":"Schreck C, Wojtan C. 2022. Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method. Computer Graphics Forum. 41(2), 343–353.","apa":"Schreck, C., &#38; Wojtan, C. (2022). Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method. <i>Computer Graphics Forum</i>. Wiley. <a href=\"https://doi.org/10.1111/cgf.14478\">https://doi.org/10.1111/cgf.14478</a>"},"intvolume":"        41","month":"05","language":[{"iso":"eng"}],"publisher":"Wiley","article_processing_charge":"No","quality_controlled":"1","publication":"Computer Graphics Forum","corr_author":"1","scopus_import":"1","publication_identifier":{"eissn":["1467-8659"],"issn":["0167-7055"]},"title":"Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method","issue":"2","type":"journal_article","day":"01","acknowledgement":"We wish to thank the anonymous reviewers and the members of the Visual Computing Group at IST Austria and MFX Team at INRIA for their valuable feedback. This research was supported by the Scientific Service Units (SSU) of IST Austria through resources provided by Scientific Computing. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 638176.","main_file_link":[{"open_access":"1","url":"https://hal.archives-ouvertes.fr/hal-03641349/"}],"date_created":"2022-06-05T22:01:49Z","doi":"10.1111/cgf.14478","status":"public","oa":1,"page":"343-353","article_type":"original","oa_version":"Submitted Version","ec_funded":1,"_id":"11432","project":[{"_id":"2533E772-B435-11E9-9278-68D0E5697425","grant_number":"638176","call_identifier":"H2020","name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales"}],"department":[{"_id":"ChWo"}],"abstract":[{"lang":"eng","text":"This paper proposes a method for simulating liquids in large bodies of water by coupling together a water surface wave simulator with a 3D Navier-Stokes simulator. The surface wave simulation uses the equivalent sources method (ESM) to efficiently animate large bodies of water with precisely controllable wave propagation behavior. The 3D liquid simulator animates complex non-linear fluid behaviors like splashes and breaking waves using off-the-shelf simulators using FLIP or the level set method with semi-Lagrangian advection.\r\nWe combine the two approaches by using the 3D solver to animate localized non-linear behaviors, and the 2D wave solver to animate larger regions with linear surface physics. We use the surface motion from the 3D solver as boundary conditions for 2D surface wave simulator, and we use the velocity and surface heights from the 2D surface wave simulator as boundary conditions for the 3D fluid simulation. We also introduce a novel technique for removing visual artifacts caused by numerical errors in 3D fluid solvers: we use experimental data to estimate the artificial dispersion caused by the 3D solver and we then carefully tune the wave speeds of the 2D solver to match it, effectively eliminating any differences in wave behavior across the boundary. To the best of our knowledge, this is the first time such a empirically driven error compensation approach has been used to remove coupling errors from a physics simulator.\r\nOur coupled simulation approach leverages the strengths of each simulation technique, animating large environments with seamless transitions between 2D and 3D physics."}],"acknowledged_ssus":[{"_id":"ScienComp"}],"author":[{"last_name":"Schreck","first_name":"Camille","id":"2B14B676-F248-11E8-B48F-1D18A9856A87","full_name":"Schreck, Camille"},{"full_name":"Wojtan, Christopher J","orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","last_name":"Wojtan"}],"external_id":{"isi":["000802723900027"]},"date_updated":"2024-10-22T09:58:19Z","publication_status":"published","year":"2022","volume":41,"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}]