{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T12:32:58Z","timestamp":1766147578618,"version":"3.48.0"},"reference-count":92,"publisher":"Association for Computing Machinery (ACM)","issue":"2","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2026,4,30]]},"abstract":"<jats:p>\n                    Bounded bihramonic weights are a popular tool used to rig and deform characters for animation, to compute reduced-order simulations, and to define feature descriptors for geometry processing. They necessitate tetrahedralizing the volume bounded by the surface, introducing the possibility of meshing artifacts or tetrahedralization failure. We introduce a\n                    <jats:italic toggle=\"yes\">mesh-free<\/jats:italic>\n                    and\n                    <jats:italic toggle=\"yes\">robust<\/jats:italic>\n                    automatic skinning technique that generates weights comparable to the current state of the art, but works reliably even on open surfaces, triangle soups, and point clouds where current methods fail. We achieve this through the use of a specialized Lagrangian representation enabled by the advent of hardware ray-tracing, which circumvents the need for finite elements while optimizing the biharmonic energy and enforcing boundary conditions. The flexibility of our formulation allows us to integrate artistic control through weight painting during the optimization. We offer a thorough qualitative and quantitative evaluation of our method.\n                  <\/jats:p>","DOI":"10.1145\/3771928","type":"journal-article","created":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T11:25:38Z","timestamp":1761650738000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust Biharmonic Skinning Using Geometric Fields"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4391-8877","authenticated-orcid":false,"given":"Ana","family":"Dodik","sequence":"first","affiliation":[{"name":"MIT CSAIL","place":["USA"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0107-5704","authenticated-orcid":false,"given":"Vincent","family":"Sitzmann","sequence":"additional","affiliation":[{"name":"MIT CSAIL","place":["USA"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7701-7586","authenticated-orcid":false,"given":"Justin","family":"Solomon","sequence":"additional","affiliation":[{"name":"MIT CSAIL","place":["USA"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9741-3175","authenticated-orcid":false,"given":"Oded","family":"Stein","sequence":"additional","affiliation":[{"name":"University of Southern California","place":["USA"]},{"name":"MIT CSAIL","place":["USA"]}]}],"member":"320","published-online":{"date-parts":[[2025,12,19]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1103900.1103907"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3186565"},{"issue":"3","key":"e_1_3_4_4_1","first-page":"72\u20131\u201372\u20138","article-title":"Automatic rigging and animation of 3D characters","volume":"26","author":"Baran Ilya","year":"2007","unstructured":"Ilya Baran and Jovan Popovi\u0107. 2007. Automatic rigging and animation of 3D characters. ACM Transactions on Graphics (TOG) 26, 3 (2007), 72\u20131\u201372\u20138.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201337"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015772"},{"key":"e_1_3_4_7_1","volume-title":"Proceedings of the 12th International Conference on Learning Representations","author":"Chalapathi Nithin","year":"2024","unstructured":"Nithin Chalapathi, Yiheng Du, and Aditi S. Krishnapriyan. 2024. Scaling physics-informed hard constraints with mixture-of-experts. In Proceedings of the 12th International Conference on Learning Representations. Retrieved from https:\/\/openreview.net\/forum?id=u3dX2CEIZb"},{"key":"e_1_3_4_8_1","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Chen Honglin","year":"2023","unstructured":"Honglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng, and Peter Yichen Chen. 2023. Implicit neural spatial representations for time-dependent PDEs. In Proceedings of the International Conference on Machine Learning."},{"issue":"1","key":"e_1_3_4_9_1","article-title":"A hard-constraint wide-body physics-informed neural network model for solving multiple cases in forward problems for partial differential equations","volume":"14","author":"Chen Simin","year":"2024","unstructured":"Simin Chen, Zhixiang Liu, Wenbo Zhang, and Jinkun Yang. 2024. A hard-constraint wide-body physics-informed neural network model for solving multiple cases in forward problems for partial differential equations. Applied Sciences 14, 1 (2024).","journal-title":"Applied Sciences"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV48922.2021.01139"},{"key":"e_1_3_4_11_1","unstructured":"Aditya Chetan Guandao Yang Zichen Wang Steve Marschner and Bharath Hariharan. 2023. Accurate differential operators for hybrid neural fields. arxiv:cs.CV\/2312.05984. Retrieved from https:\/\/arxiv.org\/abs\/2312.05984"},{"key":"e_1_3_4_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.006"},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618352"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2485895.2485919"},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2321563"},{"key":"e_1_3_4_16_1","unstructured":"Franck Djeumou Cyrus Neary Eric Goubault Sylvie Putot and Ufuk Topcu. 2022. Neural networks with physics-informed architectures and constraints for dynamical systems modeling. arxiv:cs.LG\/2109.06407. Retrieved from https:\/\/arxiv.org\/abs\/2109.06407"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618403"},{"key":"e_1_3_4_18_1","volume-title":"Advances in Neural Information Processing Systems","author":"Dugas Charles","year":"2000","unstructured":"Charles Dugas, Yoshua Bengio, Fran\u00e7ois B\u00e9lisle, Claude Nadeau, and Ren\u00e9 Garcia. 2000. Incorporating second-order functional knowledge for better option pricing. In Advances in Neural Information Processing Systems. T. Leen, T. Dietterich, and V. Tresp (Eds.), Vol. 13, MIT Press. Retrieved from https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2000\/file\/44968aece94f667e4095002d140b5896-Paper.pdf"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/3478513.3480522"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/181.3.375"},{"key":"e_1_3_4_21_1","article-title":"Implicit geometric regularization for learning shapes","author":"Gropp Amos","year":"2020","unstructured":"Amos Gropp, Lior Yariv, Niv Haim, Matan Atzmon, and Yaron Lipman. 2020. Implicit geometric regularization for learning shapes. In Proceedings of the 37th International Conference on Machine Learning .","journal-title":"Proceedings of the 37th International Conference on Machine Learning"},{"key":"e_1_3_4_22_1","first-page":"1399","volume-title":"Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games","author":"Halen Henrik","year":"2021","unstructured":"Henrik Halen and K. Hayward. 2021. Global illumination based on surfels. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. 1399\u20131405."},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323011"},{"key":"e_1_3_4_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392385"},{"key":"e_1_3_4_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_3_4_26_1","unstructured":"Alec Jacobson et\u00a0al. 2021. gptoolbox: Geometry Processing Toolbox. (2021). Retrieved from http:\/\/github.com\/alecjacobson\/gptoolbox."},{"issue":"4","key":"e_1_3_4_27_1","first-page":"78:1\u201378:8","article-title":"Bounded biharmonic weights for real-time deformation","volume":"30","author":"Jacobson Alec","year":"2011","unstructured":"Alec Jacobson, Ilya Baran, Jovan Popovi\u0107, and Olga Sorkine. 2011. Bounded biharmonic weights for real-time deformation. ACM Transactions on Graphics (proceedings of ACM SIGGRAPH) 30, 4 (2011), 78:1\u201378:8.","journal-title":"ACM Transactions on Graphics (proceedings of ACM SIGGRAPH)"},{"issue":"4","key":"e_1_3_4_28_1","article-title":"Robust inside-outside segmentation using generalized winding numbers","volume":"32","author":"Jacobson Alec","year":"2013","unstructured":"Alec Jacobson, Ladislav Kavan, and Olga Sorkine. 2013. Robust inside-outside segmentation using generalized winding numbers. ACM Transactions on Graphics 32, 4 (2013).","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_3_4_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3134472.3134497"},{"key":"e_1_3_4_30_1","first-page":"1565","volume-title":"Computer Graphics Forum","author":"Jacobson Alec","year":"2010","unstructured":"Alec Jacobson, Elif Tosun, Olga Sorkine, and Denis Zorin. 2010. Mixed finite elements for variational surface modeling. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 1565\u20131574."},{"key":"e_1_3_4_31_1","first-page":"1577","volume-title":"Computer Graphics Forum","author":"Jacobson Alec","year":"2012","unstructured":"Alec Jacobson, Tino Weinkauf, and Olga Sorkine. 2012a. Smooth shape-aware functions with controlled extrema. In Computer Graphics Forum, Vol. 31. Wiley Online Library, 1577\u20131586."},{"key":"e_1_3_4_32_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03163.x"},{"key":"e_1_3_4_33_1","unstructured":"Wenzel Jakob. 2022. nanobind: tiny and efficient C++\/Python bindings. (2022). Retrieved from https:\/\/github.com\/wjakob\/nanobind."},{"key":"e_1_3_4_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073206"},{"key":"e_1_3_4_35_1","unstructured":"Timothy Jeruzalski David IW Levin Alec Jacobson Paul Lalonde Mohammad Norouzi and Andrea Tagliasacchi. 2020. NiLBS: Neural inverse linear blend skinning. arXiv:2004.05980. Retrieved from https:\/\/arxiv.org\/abs\/2004.05980"},{"issue":"3","key":"e_1_3_4_36_1","first-page":"71\u20131\u201371\u20139","article-title":"Harmonic coordinates for character articulation","volume":"26","author":"Joshi Pushkar","year":"2007","unstructured":"Pushkar Joshi, Mark Meyer, Tony DeRose, Brian Green, and Tom Sanocki. 2007. Harmonic coordinates for character articulation. ACM Transactions on Graphics (TOG) 26, 3 (2007), 71\u20131\u201371\u20139.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_3_4_37_1","first-page":"8715","volume-title":"Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition","author":"Kant Yash","year":"2023","unstructured":"Yash Kant, Aliaksandr Siarohin, Riza Alp Guler, Menglei Chai, Jian Ren, Sergey Tulyakov, and Igor Gilitschenski. 2023. Invertible neural skinning. In Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition. 8715\u20138725."},{"key":"e_1_3_4_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1409625.1409627"},{"key":"e_1_3_4_39_1","first-page":"327","volume-title":"Computer Graphics Forum","author":"Kavan Ladislav","year":"2010","unstructured":"Ladislav Kavan, Peter-Pike Sloan, and Carol O\u2019Sullivan. 2010. Fast and efficient skinning of animated meshes. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 327\u2013336."},{"key":"e_1_3_4_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592433"},{"key":"e_1_3_4_41_1","unstructured":"Diederik P. Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv:1412.6980. Retrieved from https:\/\/arxiv.org\/abs\/1412.6980"},{"key":"e_1_3_4_42_1","unstructured":"Muhammed Kocabas Jen-Hao Rick Chang James Gabriel Oncel Tuzel and Anurag Ranjan. 2023. HUGS: Human Gaussian splats. arXiv:2311.17910. Retrieved from https:\/\/arxiv.org\/abs\/2311.17910"},{"key":"e_1_3_4_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366218"},{"key":"e_1_3_4_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601161"},{"issue":"4","key":"e_1_3_4_45_1","article-title":"Direct delta mush skinning and variants","volume":"38","author":"Le Binh Huy","year":"2019","unstructured":"Binh Huy Le and J. P. Lewis. 2019. Direct delta mush skinning and variants. ACM Transactions on Graphics 38, 4 (2019), 113\u20131.","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_3_4_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459852"},{"key":"e_1_3_4_47_1","volume-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Li Zhaoshuo","year":"2023","unstructured":"Zhaoshuo Li, Thomas M\u00fcller, Alex Evans, Russell H. Taylor, Mathias Unberath, Ming-Yu Liu, and Chen-Hsuan Lin. 2023. Neuralangelo: High-fidelity neural surface reconstruction. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)."},{"key":"e_1_3_4_48_1","unstructured":"Zhouyingcheng Liao Vladislav Golyanik Marc Habermann and Christian Theobalt. 2023. VINECS: Video-based neural character skinning. arXiv:2307.00842. Retrieved from https:\/\/arxiv.org\/abs\/2307.00842"},{"issue":"4","key":"e_1_3_4_49_1","first-page":"1","article-title":"Neuroskinning: Automatic skin binding for production characters with deep graph networks","volume":"38","author":"Liu Lijuan","year":"2019","unstructured":"Lijuan Liu, Youyi Zheng, Di Tang, Yi Yuan, Changjie Fan, and Kun Zhou. 2019. Neuroskinning: Automatic skin binding for production characters with deep graph networks. ACM Transactions on Graphics (ToG) 38, 4 (2019), 1\u201312.","journal-title":"ACM Transactions on Graphics (ToG)"},{"key":"e_1_3_4_50_1","first-page":"20287","volume-title":"Proceedings of the 36th International Conference on Neural Information Processing Systems","volume":"35","author":"Liu Songming","year":"2022","unstructured":"Songming Liu, Hao Zhongkai, Chengyang Ying, Hang Su, Jun Zhu, and Ze Cheng. 2022. A unified hard-constraint framework for solving geometrically complex PDEs. In Proceedings of the 36th International Conference on Neural Information Processing Systems, Vol. 35. 20287\u201320299."},{"key":"e_1_3_4_51_1","doi-asserted-by":"publisher","DOI":"10.1137\/21M1397908"},{"key":"e_1_3_4_52_1","doi-asserted-by":"publisher","DOI":"10.1086\/112164"},{"key":"e_1_3_4_53_1","article-title":"TARig: Adaptive template-aware neural rigging for humanoid characters","author":"Ma Jing","year":"2023","unstructured":"Jing Ma and Dongliang Zhang. 2023. TARig: Adaptive template-aware neural rigging for humanoid characters. Computers & Graphics (2023).","journal-title":"Computers & Graphics"},{"key":"e_1_3_4_54_1","first-page":"679","volume-title":"Proceedings of the International Conference on 3D Vision (3DV)","author":"Ma Qianli","year":"2022","unstructured":"Qianli Ma, Jinlong Yang, Michael J. Black, and Siyu Tang. 2022. Neural point-based shape modeling of humans in challenging clothing. In Proceedings of the International Conference on 3D Vision (3DV). IEEE, 679\u2013689."},{"key":"e_1_3_4_55_1","unstructured":"Miles Macklin. 2022. Warp: A High-performance Python Framework for GPU Simulation and Graphics. Retrieved from https:\/\/github.com\/nvidia\/warp. (March2022). NVIDIA GPU Technology Conference (GTC)."},{"issue":"2","key":"e_1_3_4_56_1","first-page":"1","article-title":"Dynamic diffuse global illumination with ray-traced irradiance fields","volume":"8","author":"Majercik Zander","year":"2019","unstructured":"Zander Majercik, Jean-Philippe Guertin, Derek Nowrouzezahrai, and Morgan McGuire. 2019. Dynamic diffuse global illumination with ray-traced irradiance fields. Journal of Computer Graphics Techniques (JCGT) 8, 2 (5 June2019), 1\u201330. Retrieved fromhttp:\/\/jcgt.org\/published\/0008\/02\/01\/","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"issue":"4","key":"e_1_3_4_57_1","article-title":"Boundary value caching for walk on spheres","volume":"42","author":"Miller Bailey","year":"2023","unstructured":"Bailey Miller, Rohan Sawhney, Keenan Crane, and Ioannis Gkioulekas. 2023. Boundary value caching for walk on spheres. ACM Transactions on Graphics 42, 4 (2023).","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_3_4_58_1","article-title":"Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence","volume":"8","author":"Mohan Arvind T.","year":"2023","unstructured":"Arvind T. Mohan, Nicholas Lubbers, Misha Chertkov, and Daniel Livescu. 2023. Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence. Physical Review Fluids 8, 1 (2023), 17.","journal-title":"Physical Review Fluids"},{"key":"e_1_3_4_59_1","first-page":"18593","volume-title":"Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition","author":"Mosella-Montoro Albert","year":"2022","unstructured":"Albert Mosella-Montoro and Javier Ruiz-Hidalgo. 2022. SkinningNet: Two-stream graph convolutional neural network for skinning prediction of synthetic characters. In Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition. 18593\u201318602."},{"key":"e_1_3_4_60_1","doi-asserted-by":"publisher","DOI":"10.1137\/1109020"},{"key":"e_1_3_4_61_1","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1550\/3\/032163"},{"key":"e_1_3_4_62_1","volume-title":"Proceedings of the ACM on Computer Graphics and Interactive Techniques","volume":"4","author":"Pan Xiaoyu","year":"2021","unstructured":"Xiaoyu Pan, Jiancong Huang, Jiaming Mai, He Wang, Honglin Li, Tongkui Su, Wenjun Wang, and Xiaogang Jin. 2021. HeterSkinNet: A heterogeneous network for skin weights prediction. In Proceedings of the ACM on Computer Graphics and Interactive Techniques, Vol. 4. ACM."},{"key":"e_1_3_4_63_1","doi-asserted-by":"crossref","DOI":"10.1145\/1778765.1778803","article-title":"OptiX: A general purpose ray tracing engine","author":"Parker Steven G.","year":"2010","unstructured":"Steven G. Parker, James Bigler, Andreas Dietrich, Heiko Friedrich, Jared Hoberock, David Luebke, David McAllister, Morgan McGuire, Keith Morley, Austin Robison, and Martin Stich. 2010. OptiX: A general purpose ray tracing engine. ACM Transactions on Graphics (August2010).","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_3_4_64_1","first-page":"8024","volume-title":"Proceedings of the 33rd International Conference on Neural Information Processing Systems","author":"Paszke Adam","year":"2019","unstructured":"Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et\u00a0al. 2019. PyTorch: An imperative style, high-performance deep learning library. In Proceedings of the 33rd International Conference on Neural Information Processing Systems. Curran Associates, Inc., 8024\u20138035. Retrieved from http:\/\/papers.neurips.cc\/paper\/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf"},{"key":"e_1_3_4_65_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882319"},{"key":"e_1_3_4_66_1","volume-title":"Physically Based Rendering: From Theory to Implementation (3rd ed.)","author":"Pharr Matt","year":"2016","unstructured":"Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically Based Rendering: From Theory to Implementation (3rd ed.). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA. 1266 pages."},{"key":"e_1_3_4_67_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"e_1_3_4_68_1","unstructured":"Ruben Rodriguez-Torrado Pablo Ruiz Luis Cueto-Felgueroso Michael Cerny Green Tyler Friesen Sebastien Matringe and Julian Togelius. 2021. Physics-informed attention-based neural network for solving non-linear partial differential equations. arxiv:cs.LG\/2105.07898. Retrieved from https:\/\/arxiv.org\/abs\/2105.07898"},{"key":"e_1_3_4_69_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322970"},{"key":"e_1_3_4_70_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392374"},{"issue":"4","key":"e_1_3_4_71_1","article-title":"Walk on stars: A grid-free Monte Carlo method for PDEs with Neumann boundary conditions","volume":"42","author":"Sawhney Rohan","year":"2023","unstructured":"Rohan Sawhney, Bailey Miller, Ioannis Gkioulekas, and Keenan Crane. 2023. Walk on stars: A grid-free Monte Carlo method for PDEs with Neumann boundary conditions. ACM Transactions on Graphics 42, 4 (2023).","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_3_4_72_1","article-title":"Grid-free Monte Carlo for PDEs with spatially varying coefficients","author":"Sawhney Rohan","year":"2022","unstructured":"Rohan Sawhney, Dario Seyb, Wojciech Jarosz, and Keenan Crane. 2022. Grid-free Monte Carlo for PDEs with spatially varying coefficients. ACM Transactions on Graphics XX, X (2022).","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_3_4_73_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14069"},{"key":"e_1_3_4_74_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417839"},{"key":"e_1_3_4_75_1","doi-asserted-by":"crossref","unstructured":"Nicholas Sharp Mark Gillespie and Keenan Crane. 2021. Geometry processing with intrinsic triangulations. (2021).","DOI":"10.1145\/3450508.3464592"},{"key":"e_1_3_4_76_1","doi-asserted-by":"publisher","DOI":"10.1145\/2629697"},{"key":"e_1_3_4_77_1","volume-title":"Proceedings of the Conference on Neural Information Processing Systems","author":"Sitzmann Vincent","year":"2020","unstructured":"Vincent Sitzmann, Julien N.P. Martel, Alexander W. Bergman, David B. Lindell, and Gordon Wetzstein. 2020. Implicit neural representations with periodic activation functions. In Proceedings of the Conference on Neural Information Processing Systems."},{"key":"e_1_3_4_78_1","doi-asserted-by":"publisher","DOI":"10.1145\/3186564"},{"key":"e_1_3_4_79_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114333"},{"key":"e_1_3_4_80_1","first-page":"32","volume-title":"Computer Graphics Forum","author":"Thiery J-M","year":"2018","unstructured":"J-M Thiery and Elmar Eisemann. 2018. ARAPLBS: Robust and efficient elasticity-based optimization of weights and skeleton joints for linear blend skinning with parametrized bones. In Computer Graphics Forum, Vol. 37. Wiley Online Library, 32\u201344."},{"key":"e_1_3_4_81_1","volume-title":"Geometric Modeling Using High-order Derivatives","author":"Tosun Elif","year":"2008","unstructured":"Elif Tosun. 2008. Geometric Modeling Using High-order Derivatives. Ph.D. Dissertation. New York University."},{"key":"e_1_3_4_82_1","volume-title":"CGAL User and Reference Manual (5.6.1 ed.)","author":"Tournois Jane","year":"2024","unstructured":"Jane Tournois, Noura Faraj, Jean-Marc Thiery, and Tamy Boubekeur. 2024. Tetrahedral remeshing. In CGAL User and Reference Manual (5.6.1 ed.). CGAL Editorial Board. Retrieved from https:\/\/doc.cgal.org\/5.6.1\/Manual\/packages.html#PkgTetrahedralRemeshing"},{"key":"e_1_3_4_83_1","unstructured":"Ingo Wald. 2020. OWL - A Productivity Library for OptiX. (2020). Retrieved from http:\/\/owl-project.github.io"},{"key":"e_1_3_4_84_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982433"},{"issue":"4","key":"e_1_3_4_85_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3450626.3459801","article-title":"Fast quasi-harmonic weights for geometric data interpolation","volume":"40","author":"Wang Yu","year":"2021","unstructured":"Yu Wang and Justin Solomon. 2021. Fast quasi-harmonic weights for geometric data interpolation. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1\u201315.","journal-title":"ACM Transactions on Graphics (TOG)"},{"issue":"4","key":"e_1_3_4_86_1","first-page":"359","article-title":"Smooth regression analysis","volume":"26","author":"Watson Geoffrey S.","year":"1964","unstructured":"Geoffrey S. Watson. 1964. Smooth regression analysis. Sankhy\u0101: The Indian Journal of Statistics, Series A (1961-2002) 26, 4 (1964), 359\u2013372. Retrieved fromhttp:\/\/www.jstor.org\/stable\/25049340","journal-title":"Sankhy\u0101: The Indian Journal of Statistics, Series A (1961-2002)"},{"key":"e_1_3_4_87_1","unstructured":"Jane Wu Zhenglin Geng Hui Zhou and Ronald Fedkiw. 2020. Skinning a parameterization of three-dimensional space for neural network cloth. arXiv:2006.04874. Retrieved from https:\/\/arxiv.org\/abs\/2006.04874"},{"key":"e_1_3_4_88_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52729.2023.00849"},{"issue":"1","key":"e_1_3_4_89_1","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/MCG.2017.2801409","article-title":"Efficient  \\(C^2\\) -weighting for image warping","volume":"38","author":"Xian Chuhua","year":"2018","unstructured":"Chuhua Xian, Shuo Jin, and Charlie CL Wang. 2018. Efficient \\(C^2\\) -weighting for image warping. IEEE Computer Graphics and Applications 38, 1 (2018), 59\u201376.","journal-title":"IEEE Computer Graphics and Applications"},{"key":"e_1_3_4_90_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14505"},{"issue":"4","key":"e_1_3_4_91_1","article-title":"RigNet: Neural rigging for articulated characters","volume":"39","author":"Xu Zhan","year":"2020","unstructured":"Zhan Xu, Yang Zhou, Evangelos Kalogerakis, Chris Landreth, and Karan Singh. 2020. RigNet: Neural rigging for articulated characters. ACM Transactions on Graphics (TOG) 39, 4 (2020), 58\u20131.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_3_4_92_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.01308"},{"key":"e_1_3_4_93_1","volume-title":"Proceedings of the 37th International Conference on Neural Information Processing Systems (NIPS\u201923)","author":"Zhong Fangcheng","year":"2024","unstructured":"Fangcheng Zhong, Kyle Fogarty, Param Hanji, Tianhao Wu, Alejandro Sztrajman, Andrew Spielberg, Andrea Tagliasacchi, Petra Bosilj, and Cengiz Oztireli. 2024. Neural fields with hard constraints of arbitrary differential order. In Proceedings of the 37th International Conference on Neural Information Processing Systems (NIPS\u201923). Curran Associates Inc., Red Hook, NY, USA, Article 992, 26 pages."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3771928","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T12:28:08Z","timestamp":1766147288000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3771928"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,19]]},"references-count":92,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4,30]]}},"alternative-id":["10.1145\/3771928"],"URL":"https:\/\/doi.org\/10.1145\/3771928","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2025,12,19]]},"assertion":[{"value":"2024-12-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}