{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T16:18:57Z","timestamp":1782317937213,"version":"3.54.5"},"reference-count":64,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T00:00:00Z","timestamp":1731974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China,","doi-asserted-by":"crossref","award":["2021YFB1715900"],"award-info":[{"award-number":["2021YFB1715900"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272277"],"award-info":[{"award-number":["62272277"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U23A20312"],"award-info":[{"award-number":["U23A20312"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62072284"],"award-info":[{"award-number":["62072284"]}],"id":[{"id":"10.13039\/501100001809","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":[[2024,12,19]]},"abstract":"<jats:p>Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points\/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh.<\/jats:p>\n          <jats:p>\n            This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising\n            <jats:italic>n<\/jats:italic>\n            triangles, the final distance field for accommodating the offset surface is determined by minimizing these\n            <jats:italic>n<\/jats:italic>\n            triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.\n          <\/jats:p>","DOI":"10.1145\/3687920","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T15:46:04Z","timestamp":1732031164000},"page":"1-16","update-policy":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["PCO: Precision-Controllable Offset Surfaces with Sharp Features"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0009-0009-1953-5594","authenticated-orcid":false,"given":"Lei","family":"Wang","sequence":"first","affiliation":[{"name":"Shandong University, Qingdao, China"},{"name":"School of Computer Science and Technology, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0009-0000-5862-5845","authenticated-orcid":false,"given":"Xudong","family":"Wang","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-2079-275X","authenticated-orcid":false,"given":"Pengfei","family":"Wang","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-0835-3316","authenticated-orcid":false,"given":"Shuangmin","family":"Chen","sequence":"additional","affiliation":[{"name":"Qingdao University of Science and Technology, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0001-8452-8723","authenticated-orcid":false,"given":"Shiqing","family":"Xin","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0003-2137-205X","authenticated-orcid":false,"given":"Jiong","family":"Guo","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-2284-3952","authenticated-orcid":false,"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, State of Texas, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-1231-3392","authenticated-orcid":false,"given":"Changhe","family":"Tu","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2020.102856"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2017.05.011"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601130"},{"key":"e_1_2_1_4_1","volume-title":"Computer Graphics Forum","author":"Campen Marcel","unstructured":"Marcel Campen and Leif Kobbelt. 2010a. Exact and robust (self-) intersections for polygonal meshes. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 397--406."},{"key":"e_1_2_1_5_1","volume-title":"Computer Graphics Forum","author":"Campen Marcel","unstructured":"Marcel Campen and Leif Kobbelt. 2010b. Polygonal boundary evaluation of minkowski sums and swept volumes. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 1613--1622."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/220279.220311"},{"key":"e_1_2_1_7_1","volume-title":"Uniform offsetting of polygonal model based on layered depth-normal images. Computer-aided design 43, 1","author":"Chen Yong","year":"2011","unstructured":"Yong Chen and Charlie CL Wang. 2011. Uniform offsetting of polygonal model based on layered depth-normal images. Computer-aided design 43, 1 (2011), 31--46."},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","first-page":"2970","DOI":"10.1109\/TVCG.2019.2945961","article-title":"Half-space power diagrams and discrete surface offsets","volume":"26","author":"Chen Zhen","year":"2019","unstructured":"Zhen Chen, Daniele Panozzo, and Jeremie Dumas. 2019. Half-space power diagrams and discrete surface offsets. IEEE Transactions on Visualization and Computer Graphics 26, 10 (2019), 2970--2981.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190153"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530176"},{"key":"e_1_2_1_11_1","volume-title":"Computer Graphics Forum","author":"Ehmann Stephen A","unstructured":"Stephen A Ehmann and Ming C Lin. 2001. Accurate and fast proximity queries between polyhedra using convex surface decomposition. In Computer Graphics Forum, Vol. 20. Wiley Online Library, 500--511."},{"key":"e_1_2_1_12_1","first-page":"3","article-title":"Listing all maximal cliques in large sparse real-world graphs","volume":"18","author":"Eppstein David","year":"2013","unstructured":"David Eppstein, Maarten L\u00f6ffler, and Darren Strash. 2013. Listing all maximal cliques in large sparse real-world graphs. Journal of Experimental Algorithmics (JEA) 18 (2013), 3--1.","journal-title":"Journal of Experimental Algorithmics (JEA)"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.5555\/1648395.1648507"},{"key":"e_1_2_1_14_1","unstructured":"Ga\u00ebl Guennebaud Beno\u00eet Jacob et al. 2010. Eigen v3. https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/eigen.tuxfamily.org."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-008-9219-6"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1987.4767941"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_2_1_18_1","volume-title":"Surface reconstruction from point clouds: A survey and a benchmark. arXiv preprint arXiv:2205.02413","author":"Huang Zhangjin","year":"2022","unstructured":"Zhangjin Huang, Yuxin Wen, Zihao Wang, Jinjuan Ren, and Kui Jia. 2022. Surface reconstruction from point clouds: A survey and a benchmark. arXiv preprint arXiv:2205.02413 (2022)."},{"key":"e_1_2_1_19_1","doi-asserted-by":"crossref","unstructured":"Alec Jacobson Daniele Panozzo et al. 2018. libigl: A simple C++ geometry processing library. https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/libigl.github.io\/.","DOI":"10.1145\/3134472.3134497"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417769"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566586"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383265"},{"key":"e_1_2_1_23_1","volume-title":"ABC: A Big CAD Model Dataset For Geometric Deep Learning. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR).","author":"Koch Sebastian","year":"2019","unstructured":"Sebastian Koch, Albert Matveev, Zhongshi Jiang, Francis Williams, Alexey Artemov, Evgeny Burnaev, Marc Alexa, Denis Zorin, and Daniele Panozzo. 2019. ABC: A Big CAD Model Dataset For Geometric Deep Learning. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2015.04.012"},{"key":"e_1_2_1_25_1","volume-title":"Charlie CL Wang, and Yong Chen","author":"Leung Yuen-Shan","year":"2013","unstructured":"Yuen-Shan Leung, Charlie CL Wang, and Yong Chen. 2013. GPU-Based Super-union for Minkowski Sum. Computer-Aided Design & Applications 10, 3 (2013)."},{"key":"e_1_2_1_26_1","volume-title":"Proceedings of the 27th annual conference on Computer graphics and interactive techniques. 131--144","author":"Levoy Marc","year":"2000","unstructured":"Marc Levoy, Kari Pulli, Brian Curless, Szymon Rusinkiewicz, David Koller, Lucas Pereira, Matt Ginzton, Sean Anderson, James Davis, Jeremy Ginsberg, et al. 2000. The digital Michelangelo project: 3D scanning of large statues. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques. 131--144."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1839778.1839783"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2011.06.022"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2013.08.021"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2008.06.006"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2008.10.008"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2010.2066563"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/37402.37422"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2014.09.017"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2017.07.003"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/218013.218057"},{"key":"e_1_2_1_37_1","volume-title":"Robust free space computation for curved planar bodies","author":"Milenkovic Victor","year":"2013","unstructured":"Victor Milenkovic, Elisha Sacks, and Steven Trac. 2013. Robust free space computation for curved planar bodies. IEEE transactions on automation science and engineering 10, 4 (2013), 875--883."},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2003.1196006"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00025"},{"key":"e_1_2_1_40_1","volume-title":"Computer Graphics Forum","author":"Pavi\u0107 Darko","unstructured":"Darko Pavi\u0107 and Leif Kobbelt. 2008. High-resolution volumetric computation of offset surfaces with feature preservation. In Computer Graphics Forum, Vol. 27. Wiley Online Library, 165--174."},{"key":"e_1_2_1_41_1","first-page":"3","article-title":"Minkowski sum boundary surfaces of 3D-objects","volume":"69","author":"Peternell Martin","year":"2007","unstructured":"Martin Peternell and Tibor Steiner. 2007. Minkowski sum boundary surfaces of 3D-objects. Graphical Models 69, 3--4 (2007), 180--190.","journal-title":"Graphical Models"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(92)90059-J"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530152"},{"key":"e_1_2_1_44_1","volume-title":"2004 IEEE Symposium on","volume":"46","author":"Qu Huamin","year":"2004","unstructured":"Huamin Qu, Nan Zhang, Ran Shao, Arie Kaufman, and Klaus Mueller. 2004. Feature preserving distance fields. In 2004 IEEE Symposium on Volume Visualization and Graphics. IEEE, 39--46."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2011.06.015"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/PCCGA.2004.1348336"},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/3610548.3618196"},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417778"},{"key":"e_1_2_1_49_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3528223.3530155","article-title":"Spelunking the deep: Guaranteed queries on general neural implicit surfaces via range analysis","volume":"41","author":"Sharp Nicholas","year":"2022","unstructured":"Nicholas Sharp and Alec Jacobson. 2022. Spelunking the deep: Guaranteed queries on general neural implicit surfaces via range analysis. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1--16.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/1186562.1015816"},{"key":"e_1_2_1_51_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2023.103608"},{"key":"e_1_2_1_52_1","doi-asserted-by":"crossref","unstructured":"Matthias Teschner Stefan Kimmerle Bruno Heidelberger Gabriel Zachmann Laks Raghupathi Arnulph Fuhrmann M-P Cani Fran\u00e7ois Faure Nadia Magnenat-Thalmann Wolfgang Strasser et al. 2005. Collision detection for deformable objects. In Computer graphics forum Vol. 24. Wiley Online Library 61--81.","DOI":"10.1111\/j.1467-8659.2005.00829.x"},{"key":"e_1_2_1_53_1","unstructured":"The CGAL Project. 2024. CGAL User and Reference Manual (5.6.1 ed.). CGAL Editorial Board. https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doc.cgal.org\/5.6.1\/Manual\/packages.html"},{"key":"e_1_2_1_54_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1145\/15886.15887","article-title":"Real-time shaded NC milling display","volume":"20","author":"Hook Tim Van","year":"1986","unstructured":"Tim Van Hook. 1986. Real-time shaded NC milling display. ACM SIGGRAPH Computer Graphics 20, 4 (1986), 15--20.","journal-title":"ACM SIGGRAPH Computer Graphics"},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057464"},{"key":"e_1_2_1_56_1","volume-title":"12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings. IEEE, 392--401","author":"Varadhan Gokul","year":"2004","unstructured":"Gokul Varadhan and Dinesh Manocha. 2004. Accurate Minkowski sum approximation of polyhedral models. In 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings. IEEE, 392--401."},{"key":"e_1_2_1_57_1","first-page":"114","article-title":"Exact and efficient polyhedral envelope containment check","volume":"39","author":"Wang Bolun","year":"2020","unstructured":"Bolun Wang, Teseo Schneider, Yixin Hu, Marco Attene, and Daniele Panozzo. 2020. Exact and efficient polyhedral envelope containment check. ACM Trans. Graph. 39, 4 (2020), 114.","journal-title":"ACM Trans. Graph."},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.5555\/2396897.2396940"},{"key":"e_1_2_1_59_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2004.10.001"},{"key":"e_1_2_1_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555453"},{"key":"e_1_2_1_61_1","volume-title":"Zheng Ma, et al.","author":"Zhang Lulu","year":"2021","unstructured":"Lulu Zhang, Tao Luo, Yaoyu Zhang, Zhi-Qin John Xu, Zheng Ma, et al. 2021. MOD-Net: A machine learning approach via model-operator-data network for solving PDEs. arXiv preprint arXiv:2107.03673 (2021)."},{"key":"e_1_2_1_62_1","volume-title":"Thingi10k: A dataset of 10,000 3d-printing models. arXiv preprint arXiv:1605.04797","author":"Zhou Qingnan","year":"2016","unstructured":"Qingnan Zhou and Alec Jacobson. 2016. Thingi10k: A dataset of 10,000 3d-printing models. arXiv preprint arXiv:1605.04797 (2016)."},{"key":"e_1_2_1_63_1","doi-asserted-by":"crossref","unstructured":"Daniel Zint Nissim Maruani Mael Rouxel-Labb\u00e9 and Pierre Alliez. 2023. Feature-Preserving Offset Mesh Generation from Topology-Adapted Octrees. In Computer Graphics Forum. 12.","DOI":"10.1111\/cgf.14906"},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592439"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/dl.acm.org\/doi\/10.1145\/3687920","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/dl.acm.org\/doi\/pdf\/10.1145\/3687920","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:09:57Z","timestamp":1750295397000},"score":1,"resource":{"primary":{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/dl.acm.org\/doi\/10.1145\/3687920"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,19]]},"references-count":64,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,12,19]]}},"alternative-id":["10.1145\/3687920"],"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1145\/3687920","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,19]]},"assertion":[{"value":"2024-11-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}