{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T08:17:17Z","timestamp":1783066637053,"version":"3.54.6"},"reference-count":79,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:00:00Z","timestamp":1783036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"name":"NSF","award":["2301040"],"award-info":[{"award-number":["2301040"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>While yarn-level garments offer rich dynamic details and compelling visual realism compared to triangle-based models, their wide adoption is hindered by the immense computational cost due to the presence of a large number of degrees of freedom (DOFs). This paper proposes a novel simulation framework designed to enhance the performance and stability for numerical simulation of nonlinear, non-convex, and high-resolution knitwear. Our method generalizes the Douglas-Rachford Splitting (DRS) scheme to resolve the non-convex coupling between stretching, shearing, bending, twisting, and contacting at each yarn thread. A key contribution is a nested decomposition strategy that decouples the non-convex variational energy into independent and convex sub-problems. Such convexification improves solver robustness and removes the necessity for frequent line searches. We provide a theoretically grounded strategy for metric selection for each sub-problem, derived from an analysis of the convergence guarantee of DRS. Consequently, our method achieves close-to-optimal convergence along the nonlinear iterations rather than relying on ad-hoc parameter tuning. The paper also clarifies a formal connection between our generalized DRS and the ADMM (Alternating Direction Method of Multipliers) framework, extending the applicability of our analysis to a broader set of constrained dynamics problems. Experimental results demonstrate that our method robustly handles complex knitwear simulation scenes with superior efficiency, stability, and physical fidelity compared to existing methods. With a matrix-free GPU parallelization, our method allows an interactive simulation rate of knitwear of multi-million DOFs.<\/jats:p>","DOI":"10.1145\/3811277","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Interactive Yarn-level Knitwear with Nested Douglas-Rachford Splitting"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1134-0442","authenticated-orcid":false,"given":"Chun","family":"Yuan","sequence":"first","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0067-0242","authenticated-orcid":false,"given":"Zixuan","family":"Lu","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6917-5007","authenticated-orcid":false,"given":"Haoyang","family":"Shi","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7393-5486","authenticated-orcid":false,"given":"Dewen","family":"Guo","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8153-2337","authenticated-orcid":false,"given":"Huamin","family":"Wang","sequence":"additional","affiliation":[{"name":"Style3D Research, Hangzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3506-0583","authenticated-orcid":false,"given":"Chenfanfu","family":"Jiang","sequence":"additional","affiliation":[{"name":"UCLA, Los Angeles, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9348-526X","authenticated-orcid":false,"given":"Zherong","family":"Pan","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Seattle, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3326-7943","authenticated-orcid":false,"given":"Kui","family":"Wu","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Los Angeles, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7645-5931","authenticated-orcid":false,"given":"Yin","family":"Yang","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3340260"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778853"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1399504.1360662"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01381.x"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1142012"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566623"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13915"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461962"},{"key":"e_1_2_2_11_1","series-title":"SIAM review 31, 1","volume-title":"Fourier analysis of iterative methods for elliptic pr","author":"Chan Tony F","year":"1989","unstructured":"Tony F Chan and Howard C Elman. 1989. Fourier analysis of iterative methods for elliptic pr. SIAM review 31, 1 (1989), 20\u201349."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731205"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731208"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661279"},{"key":"e_1_2_2_15_1","volume-title":"Yarn-level cloth simulation with sliding persistent contacts","author":"Cirio Gabriel","year":"2016","unstructured":"Gabriel Cirio, Jorge Lopez-Moreno, and Miguel A Otaduy. 2016. Yarn-level cloth simulation with sliding persistent contacts. IEEE transactions on visualization and computer graphics 23, 2 (2016), 1152\u20131162."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392439"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591551"},{"key":"e_1_2_2_18_1","volume-title":"Decision sciences","author":"Deb Kalyanmoy","unstructured":"Kalyanmoy Deb, Karthik Sindhya, and Jussi Hakanen. 2016. Multi-objective optimization. In Decision sciences. CRC Press, USA, 161\u2013200."},{"key":"e_1_2_2_19_1","volume-title":"Direct Position-Based Solver for Stiff Rods. Computer Graphics Forum 37 (03","author":"Deul Crispin","year":"2018","unstructured":"Crispin Deul, Tassilo Kugelstadt, Marcel Weiler, and Jan Bender. 2018. Direct Position-Based Solver for Stiff Rods. Computer Graphics Forum 37 (03 2018)."},{"key":"e_1_2_2_20_1","volume-title":"On the Douglas\u2014Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical programming 55","author":"Eckstein Jonathan","year":"1992","unstructured":"Jonathan Eckstein and Dimitri P Bertsekas. 1992. On the Douglas\u2014Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical programming 55 (1992), 293\u2013318."},{"key":"e_1_2_2_21_1","volume-title":"Multiscale finite element methods: theory and applications","author":"Efendiev Yalchin","unstructured":"Yalchin Efendiev and Thomas Y Hou. 2009. Multiscale finite element methods: theory and applications. Vol. 4. Springer Science & Business Media."},{"key":"e_1_2_2_22_1","volume-title":"Neural-Assisted Homog-enization of Yarn-Level Cloth. In ACM SIGGRAPH 2024 Conference Papers","author":"Feng Xudong","year":"2024","unstructured":"Xudong Feng, Huamin Wang, Yin Yang, and Weiwei Xu. 2024. Neural-Assisted Homog-enization of Yarn-Level Cloth. In ACM SIGGRAPH 2024 Conference Papers (Denver, CO, USA) (SIGGRAPH '24). Association for Computing Machinery, New York, NY, USA, Article 80, 10 pages."},{"key":"e_1_2_2_23_1","volume-title":"Metric selection in Douglas-Rachford splitting and ADMM. arXiv preprint arXiv:1410.8479 0, 0","author":"Giselsson Pontus","year":"2014","unstructured":"Pontus Giselsson and Stephen Boyd. 2014. Metric selection in Douglas-Rachford splitting and ADMM. arXiv preprint arXiv:1410.8479 0, 0 (2014), 16 pages."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2564160"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/3340258"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5682"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592143"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/3658176"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3721238.3730618"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/3606937"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731184"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/2485895.2485913"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073623"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1399504.1360664"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778842"},{"key":"e_1_2_2_36_1","volume-title":"Breen","author":"Kapllani Levi","year":"2021","unstructured":"Levi Kapllani, Chelsea Amanatides, Genevieve Dion, Vadim Shapiro, and David E. Breen. 2021. TopoKnit: A Process-Oriented Representation for Modeling the Topology of Yarns in Weft-Knitted Textiles. Graph. Models 118, C (Nov. 2021), 19 pages."},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/3332165.3347879"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459752"},{"key":"e_1_2_2_39_1","volume-title":"Ray tracing complex scenes. ACM SIGGRAPH computer graphics 20, 4","author":"Kay Timothy L","year":"1986","unstructured":"Timothy L Kay and James T Kajiya. 1986. Ray tracing complex scenes. ACM SIGGRAPH computer graphics 20, 4 (1986), 269\u2013278."},{"key":"e_1_2_2_40_1","volume-title":"Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation","author":"Kugelstadt T.","unstructured":"T. Kugelstadt and E. Sch\u00f6mer. 2016. Position and orientation based Cosserat rods. In Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation (Zurich, Switzerland) (SCA '16). Eurographics Association, Goslar, DEU, 169\u2013178."},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592104"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530069"},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275105"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392425"},{"key":"e_1_2_2_45_1","volume-title":"Subspace-Preconditioned GPU Projective Dynamics with Contact for Cloth Simulation. In SIGGRAPH Asia 2023 Conference Papers","author":"Li Xuan","year":"2023","unstructured":"Xuan Li, Yu Fang, Lei Lan, Huamin Wang, Yin Yang, Minchen Li, and Chenfanfu Jiang. 2023. Subspace-Preconditioned GPU Projective Dynamics with Contact for Cloth Simulation. In SIGGRAPH Asia 2023 Conference Papers (Sydney, NSW, Australia) (SA '23). Association for Computing Machinery, New York, NY, USA, Article 1, 12 pages."},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/3411764.3445780"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/3491102.3517577"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/2994258.2994272"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/2994258.2994272"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925940"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/3721238.3730715"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322995"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14081"},{"key":"e_1_2_2_54_1","volume-title":"ADMM supseteq projective dynamics: Fast simulation of hyperelastic models with dynamic constraints","author":"Overby Matthew","year":"2017","unstructured":"Matthew Overby, George E Brown, Jie Li, and Rahul Narain. 2017. ADMM supseteq projective dynamics: Fast simulation of hyperelastic models with dynamic constraints. IEEE transactions on visualization and computer graphics 23, 10 (2017), 2222\u20132234."},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00594"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130814"},{"key":"e_1_2_2_57_1","doi-asserted-by":"crossref","unstructured":"Yousef Saad. 2003. Iterative methods for sparse linear systems. SIAM.","DOI":"10.1137\/1.9780898718003"},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360663"},{"key":"e_1_2_2_59_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13519"},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392412"},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459816"},{"key":"e_1_2_2_62_1","volume-title":"Proceedings of the 2007 ACM SIGGRAPH\/Eurographics Symposium on Computer Animation","author":"Spillmann J.","unstructured":"J. Spillmann and M. Teschner. 2007. CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects. In Proceedings of the 2007 ACM SIGGRAPH\/Eurographics Symposium on Computer Animation (San Diego, California) (SCA '07). Eurographics Association, Goslar, DEU, 63\u201372."},{"key":"e_1_2_2_63_1","unstructured":"Matthias Teschner Bruno Heidelberger Matthias M\u00fcller C. Pomerantes and Markus Gross. 2003. Optimized Spatial Hashing for Collision Detection of Deformable Objects. In Vision Modeling and Visualization."},{"key":"e_1_2_2_64_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1163993"},{"key":"e_1_2_2_65_1","doi-asserted-by":"publisher","DOI":"10.1145\/3654777.3676351"},{"key":"e_1_2_2_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/3613904.3642799"},{"key":"e_1_2_2_67_1","volume-title":"Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation","author":"Umetani Nobuyuki","year":"2015","unstructured":"Nobuyuki Umetani, Ryan Schmidt, and Jos Stam. 2015. Position-Based Elastic Rods. In Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation (Copenhagen, Denmark) (SCA '14). Eurographics Association, Goslar, DEU, 21\u201330."},{"key":"e_1_2_2_68_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601199"},{"key":"e_1_2_2_69_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818063"},{"key":"e_1_2_2_70_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2980236"},{"key":"e_1_2_2_71_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14133"},{"key":"e_1_2_2_72_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201360"},{"key":"e_1_2_2_73_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356556"},{"key":"e_1_2_2_74_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2021.3056101"},{"key":"e_1_2_2_75_1","doi-asserted-by":"publisher","DOI":"10.1137\/0917013"},{"key":"e_1_2_2_76_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687911"},{"key":"e_1_2_2_77_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185533"},{"key":"e_1_2_2_78_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14701"},{"key":"e_1_2_2_79_1","volume-title":"An Integrated Design Pipeline for Tactile Sensing Robotic Manipulators. In 2022 International Conference on Robotics and Automation (ICRA)","author":"Zlokapa Lara","year":"2022","unstructured":"Lara Zlokapa, Yiyue Luo, Jie Xu, Michael Foshey, Kui Wu, Pulkit Agrawal, and Wojciech Matusik. 2022. An Integrated Design Pipeline for Tactile Sensing Robotic Manipulators. In 2022 International Conference on Robotics and Automation (ICRA) (Philadelphia, PA, USA). IEEE Press, New York, NY, USA, 3136\u20133142."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/abs\/10.1145\/3811277","content-type":"text\/html","content-version":"vor","intended-application":"syndication"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:33:04Z","timestamp":1783063984000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3811277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,3]]},"references-count":79,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,7,3]]}},"alternative-id":["10.1145\/3811277"],"URL":"https:\/\/doi.org\/10.1145\/3811277","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,3]]},"assertion":[{"value":"2026-01-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-03-27","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}