{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T08:15:15Z","timestamp":1783066515559,"version":"3.54.6"},"reference-count":62,"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-nc-nd\/4.0\/legalcode"}],"funder":[{"DOI":"10.13039\/501100010978","name":"Wallonie-Bruxelles International","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010978","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CISE 2341880"],"award-info":[{"award-number":["CISE 2341880"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"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>We present an algorithm for global knit structure planning that leverages a generalization of power diagrams to triangulated surfaces. This generalization is based on modified geodesic heat kernels and is used to quantize the curl measure of a normalized knitting time function gradient. Knit singularity positions are optimized jointly in a global fashion via an iterative Lloyd-type algorithm, leading to faster and more optimal placement of singularities than prior work, allowing for practical creation of denser knit graphs. In this denser setting, we present singularity ordering constraints that more robustly achieve helix-free knit graphs. The speed and robustness of the method is demonstrated via a diverse array of knits, and a virtual gallery of helix-free knit graphs. We also provide further demonstration of user constraints for knit singularity masking, level set alignment constraints, and apparent seam placement via curl boosting.<\/jats:p>","DOI":"10.1145\/3811401","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Surface Power Diagrams for Knit Singularity Placement"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7342-0970","authenticated-orcid":false,"given":"Rahul","family":"Mitra","sequence":"first","affiliation":[{"name":"Boston University, Boston, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9175-425X","authenticated-orcid":false,"given":"Matt\u00e9o","family":"Couplet","sequence":"additional","affiliation":[{"name":"Boston University, Boston, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7784-9929","authenticated-orcid":false,"given":"Ruichen","family":"Liu","sequence":"additional","affiliation":[{"name":"Boston University, Boston, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1258-2034","authenticated-orcid":false,"given":"Jonathan","family":"Ng","sequence":"additional","affiliation":[{"name":"VARIANT3D, Malibu, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3076-959X","authenticated-orcid":false,"given":"Ruza","family":"Markov","sequence":"additional","affiliation":[{"name":"VARIANT3D, Malibu, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-8880-2663","authenticated-orcid":false,"given":"William","family":"Batara Jeremiah Samosir","sequence":"additional","affiliation":[{"name":"VARIANT3D, Malibu, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2283-8587","authenticated-orcid":false,"given":"Megan","family":"Hofmann","sequence":"additional","affiliation":[{"name":"Northeastern University, Boston, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5084-7638","authenticated-orcid":false,"given":"Edward","family":"Chien","sequence":"additional","affiliation":[{"name":"Boston University, Boston, 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\/3290605.3300414"},{"key":"e_1_2_2_2_1","volume-title":"Translations of Mathematical Monographs","volume":"153","author":"Aranson S. Kh.","unstructured":"S. Kh. Aranson, G.R. Belitsky, and E.V. Zhuzhoma. 1996. Introduction to the Qualitative Theory of Dynamical Systems on Surfaces. Translations of Mathematical Monographs, Vol. 153. American Mathematical Society."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/0216006"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01868.x"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12014"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-016-9331-y"},{"key":"e_1_2_2_7_1","volume-title":"Proceedings of the 35th International Conference on Machine Learning (ICML) (Proceedings of Machine Learning Research","volume":"1008","author":"Claici Sebastian","year":"2018","unstructured":"Sebastian Claici, Edward Chien, and Justin Solomon. 2018. Stochastic Wasserstein Barycenters. In Proceedings of the 35th International Conference on Machine Learning (ICML) (Proceedings of Machine Learning Research, Vol. 80), Jennifer Dy and Andreas Krause (Eds.). PMLR, 999\u20131008. proceedings.mlr.press"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2504435.2504442"},{"key":"e_1_2_2_9_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2516971.2516977","article-title":"Geodesics in heat: A new approach to computing distance based on heat flow","volume":"32","author":"Crane Keenan","year":"2013","unstructured":"Keenan Crane, Clarisse Weischedel, and Max Wardetzky. 2013b. Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics (TOG) 32, 5 (2013), 1\u201311.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_2_10_1","first-page":"11","article-title":"The Heat Method for Distance","volume":"60","author":"Crane Keenan","year":"2017","unstructured":"Keenan Crane, Clarisse Weischedel, and Max Wardetzky. 2017. The Heat Method for Distance Computation. Commun. ACM 60, 11 (Oct. 2017), 90\u201399.","journal-title":"Computation. Commun. ACM"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366190"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366190"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897826.2927303"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3559400.3562005"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073676"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.5555\/1133946.1648437"},{"key":"e_1_2_2_17_1","unstructured":"Gurobi Optimization LLC. 2022. Gurobi Optimizer Reference Manual."},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3332165.3347886"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/3586183.3606789"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818078"},{"key":"e_1_2_2_21_1","article-title":"Computational Design of Knit Templates","volume":"41","author":"Jones Benjamin","year":"2021","unstructured":"Benjamin Jones, Yuxuan Mei, Haisen Zhao, Taylor Gotfrid, Jennifer Mankoff, and Adriana Schulz. 2021. Computational Design of Knit Templates. ACM Trans. Graph. 41, 2, Article 16 (Dec. 2021), 16 pages.","journal-title":"ACM Trans. Graph."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/3332165.3347879"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459752"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2767000"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-835X(99)00067-6"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592449"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687948"},{"key":"e_1_2_2_28_1","volume-title":"Computational Knitting. Lecture at SGP Graduate School","author":"Lin Jenny Han","year":"2025","unstructured":"Jenny Han Lin, Benjamin Jones, and Edward Chien. 2025. Computational Knitting. Lecture at SGP Graduate School 2025. https:\/\/school.geometryprocessing.org\/summerschool-2025\/index.html#course3 Symposium on Geometry Processing (SGP) Summer School."},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459868"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1982.1056489"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/3411764.3445780"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/3491102.3517577"},{"key":"e_1_2_2_33_1","unstructured":"James McCann. 2017. On-Demand Machine Knitting for Everyone. Lecture at Robotics Institute Seminar CMU. https:\/\/www.youtube.com\/watch?v=iEaK68VRAng"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925940"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/3721238.3730715"},{"key":"e_1_2_2_36_1","volume-title":"Singular Foliations for Knit Graph Design. In ACM SIGGRAPH 2024 Conference Papers","author":"Mitra Rahul","year":"2024","unstructured":"Rahul Mitra, Erick Jimenez Berumen, Megan Hofmann, and Edward Chien. 2024. Singular Foliations for Knit Graph Design. In ACM SIGGRAPH 2024 Conference Papers (Denver, CO, USA) (SIGGRAPH '24). Association for Computing Machinery, New York, NY, USA, Article 38, 11 pages."},{"key":"e_1_2_2_37_1","volume-title":"Helix-Free Stripes for Knit Graph Design. In ACM SIGGRAPH 2023 Conference Proceedings","author":"Mitra Rahul","year":"2023","unstructured":"Rahul Mitra, Liane Makatura, Emily Whiting, and Edward Chien. 2023. Helix-Free Stripes for Knit Graph Design. In ACM SIGGRAPH 2023 Conference Proceedings (Los Angeles, CA, USA) (SIGGRAPH '23). Association for Computing Machinery, New York, NY, USA, Article 75, 9 pages."},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530129"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964998"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459790"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/3186265"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322995"},{"key":"e_1_2_2_43_1","volume-title":"Fast Editing of Singularities in Field-Aligned Stripe Patterns. In SIGGRAPH Asia 2022 Conference Papers (Daegu, Republic of Korea) (SA '22)","author":"Noma Yuta","year":"2022","unstructured":"Yuta Noma, Nobuyuki Umetani, and Yoshihiro Kawahara. 2022. Fast Editing of Singularities in Field-Aligned Stripe Patterns. In SIGGRAPH Asia 2022 Conference Papers (Daegu, Republic of Korea) (SA '22). Association for Computing Machinery, New York, NY, USA, Article 37, 8 pages."},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1561\/2200000073"},{"key":"e_1_2_2_45_1","volume-title":"Tom Van Mele, and Philippe Block","author":"Popescu Mariana","year":"2021","unstructured":"Mariana Popescu, Matthias Rippmann, Andrew Liew, Lex Reiter, Robert J Flatt, Tom Van Mele, and Philippe Block. 2021. Structural design, digital fabrication and construction of the cable-net and knitted formwork of the KnitCandela concrete shell. In Structures, Vol. 31. Elsevier, 1287\u20131299."},{"key":"e_1_2_2_46_1","volume-title":"Tom Van Mele, and Philippe Block","author":"Popescu Mariana","year":"2020","unstructured":"Mariana Popescu, Matthias Rippmann, Tom Van Mele, and Philippe Block. 2020. KnitCandela-Challenging the construction, logistics, waste and economy of concrete-shell formworks. Fabricate 2020: Making Resilient Architecture (2020), 194\u2013201."},{"key":"e_1_2_2_47_1","unstructured":"Yixuan Qiu and Dirk Toewe. 2019. Lbfgs++. https:\/\/lbfgspp.statr.me\/"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20828-2"},{"key":"e_1_2_2_50_1","volume-title":"Knit Architecture: Exploration of Hybrid Textile Composites Through the Activation of Integrated Material Behavior.","author":"Sharmin Shahida","year":"2016","unstructured":"Shahida Sharmin and Sean Ahlquist. 2016. Knit Architecture: Exploration of Hybrid Textile Composites Through the Activation of Integrated Material Behavior."},{"key":"e_1_2_2_51_1","unstructured":"Nicholas Sharp et al. 2019b. Polyscope. www.polyscope.run"},{"key":"e_1_2_2_52_1","unstructured":"Nicholas Sharp Keenan Crane et al. 2019a. GeometryCentral: A modern C++ library of data structures and algorithms for geometry processing. https:\/\/geometry-central.net\/."},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/3243651"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459759"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3654777.3676351"},{"key":"e_1_2_2_56_1","unstructured":"Jenny Underwood. 2009. The Design of 3D Shape Knitted Preforms. Ph.D. Dissertation. RMIT University Melbourne Australia. researchbank.rmit.edu.au Doctor of Philosophy."},{"key":"e_1_2_2_57_1","unstructured":"Max Wardetzky. 2007. Discrete Differential Operators on Polyhedral Surfaces - Convergence and Approximation. Dissertation."},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201360"},{"key":"e_1_2_2_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356518"},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2021.3056101"},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185533"},{"key":"e_1_2_2_62_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\/3811401","content-type":"text\/html","content-version":"vor","intended-application":"syndication"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:15:54Z","timestamp":1783062954000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3811401"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,3]]},"references-count":62,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,7,3]]}},"alternative-id":["10.1145\/3811401"],"URL":"https:\/\/doi.org\/10.1145\/3811401","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":"2026-01-22","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"}}]}}