{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T06:07:14Z","timestamp":1784268434215,"version":"3.55.0"},"reference-count":61,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2024,3,23]],"date-time":"2024-03-23T00:00:00Z","timestamp":1711152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Research Grant Council of Hong Kong","award":["GRF 17210222"],"award-info":[{"award-number":["GRF 17210222"]}]},{"name":"Innovation and Technology Commission of the HKSAR Government"},{"name":"JC STEM Lab of Robotics for Soft Materials"},{"name":"The Hong Kong Jockey Club Charities Trust"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2024,4,30]]},"abstract":"<jats:p>Barrier functions are crucial for maintaining an intersection- and inversion-free simulation trajectory but existing methods, which directly use distance can restrict implementation design and performance. We present an approach to rewriting the barrier function for arriving at an efficient and robust approximation of its Hessian. The key idea is to formulate a simplicial geometric measure of contact using mesh boundary elements, from which analytic eigensystems are derived and enhanced with filtering and stiffening terms that ensure robustness with respect to the convergence of a Project-Newton solver. A further advantage of our rewriting of the barrier function is that it naturally caters to the notorious case of nearly parallel edge-edge contacts for which we also present a novel analytic eigensystem. Our approach is thus well suited for standard second-order unconstrained optimization strategies for resolving contacts, minimizing nonlinear nonconvex functions where the Hessian may be indefinite. The efficiency of our eigensystems alone yields a 3\u00d7 speedup over the standard Incremental Potential Contact (IPC) barrier formulation. We further apply our analytic proxy eigensystems to produce an entirely GPU-based implementation of IPC with significant further acceleration.<\/jats:p>","DOI":"10.1145\/3643028","type":"journal-article","created":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T12:49:45Z","timestamp":1706359785000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":25,"title":["GIPC: Fast and Stable Gauss-Newton Optimization of IPC Barrier Energy"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9147-2289","authenticated-orcid":false,"given":"Kemeng","family":"Huang","sequence":"first","affiliation":[{"name":"The University of Hong Kong, TransGP, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9489-8592","authenticated-orcid":false,"given":"Floyd M.","family":"Chitalu","sequence":"additional","affiliation":[{"name":"The University of Hong Kong, TransGP, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4446-1442","authenticated-orcid":false,"given":"Huancheng","family":"Lin","sequence":"additional","affiliation":[{"name":"The University of Hong Kong, TransGP, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2729-5860","authenticated-orcid":false,"given":"Taku","family":"Komura","sequence":"additional","affiliation":[{"name":"The University of Hong Kong, TransGP, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2024,3,23]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1833349.1778819"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3532720.3535640"},{"key":"e_1_3_4_4_1","first-page":"41","volume-title":"Proceedings of the Conference on Theory and Practice of Computer Graphics","author":"Apetrei Ciprian","year":"2014","unstructured":"Ciprian Apetrei. 2014. Fast and simple agglomerative LBVH construction. In Proceedings of the Conference on Theory and Practice of Computer Graphics, Rita Borgo and Wen Tang (Eds.). Eurographics Association, 41\u201344."},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280821"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566623"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13948"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-55860-732-3.50011-5"},{"key":"e_1_3_4_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/3096239"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459757"},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459802"},{"key":"e_1_3_4_12_1","doi-asserted-by":"crossref","unstructured":"Ming Gao Xinlei Wang Kui Wu Andre Pradhana Eftychios Sifakis Cem Yuksel and Chenfanfu Jiang. 2018. GPU optimization of material point methods. ACM Trans. Graph. 37 6 (2018).","DOI":"10.1145\/3272127.3275044"},{"key":"e_1_3_4_13_1","unstructured":"Ga\u00ebl Guennebaud Beno\u00eet Jacob et\u00a0al. 2022. Eigen v3.4. Retrieved from http:\/\/eigen.tuxfamily.org"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360622"},{"key":"e_1_3_4_15_1","unstructured":"Zizhou Huang Davi Colli Tozoni Arvi Gjoka Zachary Ferguson Teseo Schneider Daniele Panozzo and Denis Zorin. 2022. Differentiable solver for time-dependent deformation problems with contact. Retrieved from https:\/\/arxiv:cs.GR\/2205.13643"},{"key":"e_1_3_4_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1028523.1028541"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130895"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00034-1"},{"key":"e_1_3_4_20_1","first-page":"33","volume-title":"Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics (HPG\u201912)","author":"Karras Tero","year":"2012","unstructured":"Tero Karras. 2012. Maximizing parallelism in the construction of BVHs, octrees, and k-d trees. In Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics (HPG\u201912), Carsten Dachsbacher, Jacob Munkberg, and Jacopo Pantaleoni (Eds.). 33\u201337."},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1457515.1409117"},{"key":"e_1_3_4_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14111"},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323014"},{"key":"e_1_3_4_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3388769.3407490"},{"key":"e_1_3_4_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/07070111X"},{"key":"e_1_3_4_26_1","unstructured":"Lei Lan Danny M. Kaufman Minchen Li Chenfanfu Jiang and Yin Yang. 2022a. Affine body dynamics: Fast stable & intersection-free simulation of stiff materials. Retrieved from https:\/\/2201.10022"},{"key":"e_1_3_4_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530069"},{"key":"e_1_3_4_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459753"},{"key":"e_1_3_4_29_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01377.x"},{"key":"e_1_3_4_30_1","first-page":"419","volume-title":"Comput. Graph. Forum","author":"Lauterbach Christian","year":"2010","unstructured":"Christian Lauterbach, Qi Mo, and Dinesh Manocha. 2010. gProximity: Hierarchical GPU-based operations for collision and distance queries. In Comput. Graph. Forum, Vol. 29. Wiley Online Library, 419\u2013428."},{"key":"e_1_3_4_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417763"},{"key":"e_1_3_4_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392425"},{"key":"e_1_3_4_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392425"},{"key":"e_1_3_4_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459767"},{"key":"e_1_3_4_35_1","first-page":"269","volume-title":"Computer Graphics Forum","author":"Li Siwang","year":"2015","unstructured":"Siwang Li, Zherong Pan, Jin Huang, Hujun Bao, and Xiaogang Jin. 2015. Deformable objects collision handling with fast convergence. In Computer Graphics Forum, Vol. 34. Wiley Online Library, 269\u2013278."},{"key":"e_1_3_4_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555507"},{"key":"e_1_3_4_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/3338695"},{"key":"e_1_3_4_38_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2019.00554"},{"key":"e_1_3_4_39_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.142662"},{"key":"e_1_3_4_40_1","first-page":"154","volume-title":"Proceedings of the 4th International Conference on Smart City Applications (SCA\u201903)","author":"M\u00fcller Matthias","year":"2003","unstructured":"Matthias M\u00fcller, David Charypar, and Markus H. Gross. 2003. Particle-based fluid simulation for interactive applications. In Proceedings of the 4th International Conference on Smart City Applications (SCA\u201903). The Eurographics Association, 154\u2013159."},{"key":"e_1_3_4_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766907"},{"key":"e_1_3_4_42_1","volume-title":"Numerical Optimization (2nd ed.)","author":"Nocedal Jorge","year":"2006","unstructured":"Jorge Nocedal and Stephen J. Wright. 2006. Numerical Optimization (2nd ed.). Springer, New York, NY."},{"key":"e_1_3_4_43_1","first-page":"559","volume-title":"Computer Graphics Forum","author":"Otaduy Miguel A.","year":"2009","unstructured":"Miguel A. Otaduy, Rasmus Tamstorf, Denis Steinemann, and Markus Gross. 2009. Implicit contact handling for deformable objects. In Computer Graphics Forum, Vol. 28. Wiley Online Library, 559\u2013568."},{"key":"e_1_3_4_44_1","first-page":"1605","volume-title":"Computer Graphics Forum","author":"Pabst Simon","year":"2010","unstructured":"Simon Pabst, Artur Koch, and Wolfgang Stra\u00dfer. 2010. Fast and scalable cpu\/gpu collision detection for rigid and deformable surfaces. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 1605\u20131612."},{"key":"e_1_3_4_45_1","doi-asserted-by":"publisher","unstructured":"Julian Panetta. 2020. Analytic Eigensystems for Isotropic Membrane Energies. Retrieved from https:\/\/arxiv.org\/abs\/2008.10698. DOI:10.48550\/ARXIV.2008.10698","DOI":"10.48550\/ARXIV.2008.10698"},{"key":"e_1_3_4_46_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6874-5_13"},{"key":"e_1_3_4_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/3606934"},{"key":"e_1_3_4_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/2343483.2343501"},{"key":"e_1_3_4_49_1","volume-title":"Proceedings of Symposium on Computer Animation","author":"Sifakis Eftychios","year":"2008","unstructured":"Eftychios Sifakis, Sebastian Marino, and Joseph Teran. 2008. Globally coupled collision handling using volume preserving impulses. In Proceedings of Symposium on Computer Animation."},{"key":"e_1_3_4_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073208"},{"key":"e_1_3_4_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/3180491"},{"key":"e_1_3_4_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/3241041"},{"key":"e_1_3_4_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/3203188"},{"key":"e_1_3_4_54_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12851"},{"issue":"6","key":"e_1_3_4_55_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3272127.3275005","article-title":"I-Cloth: Incremental collision handling for GPU-based interactive cloth simulation","volume":"37","author":"Tang Min","year":"2018","unstructured":"Min Tang, Tongtong Wang, Zhongyuan Liu, Ruofeng Tong, and Dinesh Manocha. 2018b. I-Cloth: Incremental collision handling for GPU-based interactive cloth simulation. ACM Trans. Graph. 37, 6 (2018), 1\u201310.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_4_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073394"},{"key":"e_1_3_4_57_1","volume-title":"Iterative Methods for Solving Linear Systems on Massively Parallel Architectures","author":"Tissot Olivier","year":"2019","unstructured":"Olivier Tissot. 2019. Iterative Methods for Solving Linear Systems on Massively Parallel Architectures. Thesis. Sorbonne Universit\u00e9. Retrieved from https:\/\/theses.hal.science\/tel-02428348"},{"key":"e_1_3_4_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/3209887"},{"key":"e_1_3_4_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/3460775"},{"issue":"4","key":"e_1_3_4_60_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3450626.3459787","article-title":"GPU-based simulation of cloth wrinkles at submillimeter levels","volume":"40","author":"Wang Huamin","year":"2021","unstructured":"Huamin Wang. 2021. GPU-based simulation of cloth wrinkles at submillimeter levels. ACM Trans. Graph. 40, 4 (2021), 1\u201314.","journal-title":"ACM Trans. Graph."},{"key":"e_1_3_4_61_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13356"},{"key":"e_1_3_4_62_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530153"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3643028","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3643028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:31:21Z","timestamp":1750264281000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3643028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,23]]},"references-count":61,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4,30]]}},"alternative-id":["10.1145\/3643028"],"URL":"https:\/\/doi.org\/10.1145\/3643028","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,23]]},"assertion":[{"value":"2023-09-25","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-01-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-03-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}