{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:57:23Z","timestamp":1774022243243,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":40,"publisher":"ACM","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272429, 62025207"],"award-info":[{"award-number":["62272429, 62025207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,8,10]]},"DOI":"10.1145\/3721238.3730693","type":"proceedings-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T08:40:47Z","timestamp":1753260047000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Divide-and-Conquer Embedding"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7348-8718","authenticated-orcid":false,"given":"Yuan-Yuan","family":"Cheng","sequence":"first","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7934-6060","authenticated-orcid":false,"given":"Qing","family":"Fang","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4352-1431","authenticated-orcid":false,"given":"Ligang","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8479-0107","authenticated-orcid":false,"given":"Xiao-Ming","family":"Fu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_3_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1542362.1542401"},{"key":"e_1_3_3_2_3_1","doi-asserted-by":"crossref","unstructured":"Giuseppe\u00a0Di Battista and Fabrizio Frati. 2013. Drawing trees outerplanar graphs series-parallel graphs and planar graphs in a small area. Thirty essays on geometric graph theory (2013) 121\u2013165.","DOI":"10.1007\/978-1-4614-0110-0_9"},{"key":"e_1_3_3_2_4_1","doi-asserted-by":"crossref","unstructured":"Marcel Campen Cl\u00e1udio\u00a0T Silva and Denis Zorin. 2016. Bijective maps from simplicial foliations. ACM Transactions on Graphics (TOG) 35 4 (2016) 1\u201315.","DOI":"10.1145\/2897824.2925890"},{"key":"e_1_3_3_2_5_1","doi-asserted-by":"crossref","unstructured":"Shuangming Chai Xiao-Ming Fu Xin Hu Yang Yang and Ligang Liu. 2018. Sphere-based cut construction for planar parameterizations. Computers & Graphics 74 (2018) 66\u201375.","DOI":"10.1016\/j.cag.2018.05.007"},{"key":"e_1_3_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18469-7_12"},{"key":"e_1_3_3_2_7_1","doi-asserted-by":"crossref","unstructured":"Gianmarco Cherchi Marco Livesu Riccardo Scateni and Marco Attene. 2020. Fast and robust mesh arrangements using floating-point arithmetic. ACM Transactions on Graphics (TOG) 39 6 (2020) 1\u201316.","DOI":"10.1145\/3414685.3417818"},{"key":"e_1_3_3_2_8_1","unstructured":"Olivier Devillers Sylvain Lazard and William Lenhart. 2018. 3D snap rounding. Ph.\u00a0D. Dissertation. Inria Nancy-Grand Est."},{"key":"e_1_3_3_2_9_1","doi-asserted-by":"crossref","unstructured":"Lorenzo Diazzi Daniele Panozzo Amir Vaxman and Marco Attene. 2023. Constrained Delaunay Tetrahedrization: A Robust and Practical Approach. ACM Transactions on Graphics (TOG) 42 6 (2023) 1\u201315.","DOI":"10.1145\/3618352"},{"key":"e_1_3_3_2_10_1","doi-asserted-by":"crossref","unstructured":"Xingyi Du Noam Aigerman Qingnan Zhou Shahar\u00a0Z Kovalsky Yajie Yan Danny\u00a0M Kaufman and Tao Ju. 2020. Lifting simplices to find injectivity. ACM Trans. Graph. 39 4 (2020) 120.","DOI":"10.1145\/3386569.3392484"},{"key":"e_1_3_3_2_11_1","doi-asserted-by":"crossref","unstructured":"Rex\u00a0A Dwyer. 1987. A faster divide-and-conquer algorithm for constructing Delaunay triangulations. Algorithmica 2 1 (1987) 137\u2013151.","DOI":"10.1007\/BF01840356"},{"key":"e_1_3_3_2_12_1","doi-asserted-by":"crossref","unstructured":"Xianzhong Fang Mathieu Desbrun Hujun Bao and Jin Huang. 2022. Topocut: fast and robust planar cutting of arbitrary domains. ACM Transactions on Graphics (TOG) 41 4 (2022) 1\u201315.","DOI":"10.1145\/3528223.3530149"},{"key":"e_1_3_3_2_13_1","doi-asserted-by":"crossref","unstructured":"Ugo Finnendahl Dimitrios Bogiokas Pablo Robles\u00a0Cervantes and Marc Alexa. 2023. Efficient Embeddings in Exact Arithmetic. ACM Transactions on Graphics (TOG) 42 4 (2023) 1\u201317.","DOI":"10.1145\/3592445"},{"key":"e_1_3_3_2_14_1","doi-asserted-by":"crossref","unstructured":"Michael Floater. 2003. One-to-one piecewise linear mappings over triangulations. Math. Comp. 72 242 (2003) 685\u2013696.","DOI":"10.1090\/S0025-5718-02-01466-7"},{"key":"e_1_3_3_2_15_1","doi-asserted-by":"crossref","unstructured":"Michael\u00a0S Floater. 1997. Parametrization and smooth approximation of surface triangulations. Computer aided geometric design 14 3 (1997) 231\u2013250.","DOI":"10.1016\/S0167-8396(96)00031-3"},{"key":"e_1_3_3_2_16_1","doi-asserted-by":"crossref","unstructured":"Michael\u00a0S Floater and Kai Hormann. 2005. Surface parameterization: a tutorial and survey. Advances in multiresolution for geometric modelling (2005) 157\u2013186.","DOI":"10.1007\/3-540-26808-1_9"},{"key":"e_1_3_3_2_17_1","doi-asserted-by":"crossref","unstructured":"Xiao-Ming Fu Jian-Ping Su Zheng-Yu Zhao Qing Fang Chunyang Ye and Ligang Liu. 2021. Inversion-free geometric mapping construction: A survey. Computational Visual Media 7 (2021) 289\u2013318.","DOI":"10.1007\/s41095-021-0233-9"},{"key":"e_1_3_3_2_18_1","unstructured":"Torbj\u00f6rn Granlund. 1996. Gnu mp. The GNU Multiple Precision Arithmetic Library 2 2 (1996)."},{"key":"e_1_3_3_2_19_1","doi-asserted-by":"crossref","unstructured":"Jia-Peng Guo and Xiao-Ming Fu. 2024. Exact and Efficient Intersection Resolution for Mesh Arrangements. ACM Transactions on Graphics (TOG) 43 6 (2024) 1\u201314.","DOI":"10.1145\/3687925"},{"key":"e_1_3_3_2_20_1","unstructured":"Jia-Peng Guo Wen-Xiang Zhang Chunyang Ye and Xiao-Ming Fu. 2023. Robust Coarse Cage Construction With Small Approximation Errors. IEEE Transactions on Visualization and Computer Graphics (2023)."},{"key":"e_1_3_3_2_21_1","doi-asserted-by":"crossref","unstructured":"Kai Hormann Bruno L\u00e9vy and Alla Sheffer. 2007. Mesh parameterization: Theory and practice. (2007).","DOI":"10.1145\/1281500.1281510"},{"key":"e_1_3_3_2_22_1","doi-asserted-by":"crossref","unstructured":"Yixin Hu Qingnan Zhou Xifeng Gao Alec Jacobson Denis Zorin and Daniele Panozzo. 2018. Tetrahedral meshing in the wild. ACM Trans. Graph. 37 4 (2018) 60.","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_3_3_2_23_1","doi-asserted-by":"crossref","unstructured":"Zhongshi Jiang Scott Schaefer and Daniele Panozzo. 2017. Simplicial complex augmentation framework for bijective maps. ACM Transactions on Graphics 36 6 (2017).","DOI":"10.1145\/3130800.3130895"},{"key":"e_1_3_3_2_24_1","first-page":"89","volume-title":"Computer Graphics Forum","author":"Khanteimouri Payam","year":"2022","unstructured":"Payam Khanteimouri, Manish Mandad, and Marcel Campen. 2022. Rational B\u00e9zier Guarding. In Computer Graphics Forum , Vol.\u00a041. Wiley Online Library, 89\u201399."},{"key":"e_1_3_3_2_25_1","doi-asserted-by":"crossref","unstructured":"Vladislav Kraevoy Alla Sheffer and Craig Gotsman. 2003. Matchmaker: constructing constrained texture maps. ACM Transactions on Graphics (ToG) 22 3 (2003) 326\u2013333.","DOI":"10.1145\/882262.882271"},{"key":"e_1_3_3_2_26_1","doi-asserted-by":"crossref","unstructured":"Ligang Liu Chunyang Ye Ruiqi Ni and Xiao-Ming Fu. 2018. Progressive parameterizations. ACM Trans. Graph. 37 4 (2018) 41.","DOI":"10.1145\/3197517.3201331"},{"key":"e_1_3_3_2_27_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.15026"},{"key":"e_1_3_3_2_28_1","doi-asserted-by":"crossref","unstructured":"Marco Livesu. 2024b. Stripe embedding: Efficient maps with exact numeric computation. ACM Transactions on Graphics (TOG) 43 6 (2024) 1\u201314.","DOI":"10.1145\/3687915"},{"key":"e_1_3_3_2_29_1","doi-asserted-by":"crossref","unstructured":"Benjamin Mora. 2011. Naive ray-tracing: A divide-and-conquer approach. ACM Transactions on Graphics (TOG) 30 5 (2011) 1\u201312.","DOI":"10.1145\/2019627.2019636"},{"key":"e_1_3_3_2_30_1","doi-asserted-by":"crossref","unstructured":"Alexander Naitsat Gregory Naitzat and Yehoshua\u00a0Y Zeevi. 2021. On inversion-free mapping and distortion minimization. Journal of Mathematical Imaging and Vision 63 (2021) 974\u20131009.","DOI":"10.1007\/s10851-021-01038-y"},{"key":"e_1_3_3_2_31_1","doi-asserted-by":"crossref","unstructured":"Julius Nehring-Wirxel Philip Trettner and Leif Kobbelt. 2021. Fast exact booleans for iterated CSG using octree-embedded BSPs. Computer-Aided Design 135 (2021) 103015.","DOI":"10.1016\/j.cad.2021.103015"},{"key":"e_1_3_3_2_32_1","doi-asserted-by":"crossref","unstructured":"Sylvain Pion and Andreas Fabri. 2011. A generic lazy evaluation scheme for exact geometric computations. Science of Computer Programming 76 4 (2011) 307\u2013323.","DOI":"10.1016\/j.scico.2010.09.003"},{"key":"e_1_3_3_2_33_1","doi-asserted-by":"crossref","unstructured":"Walter Schnyder. 1989. Planar graphs and poset dimension. Order 5 (1989) 323\u2013343.","DOI":"10.1007\/BF00353652"},{"key":"e_1_3_3_2_34_1","doi-asserted-by":"crossref","unstructured":"Hanxiao Shen Zhongshi Jiang Denis Zorin and Daniele Panozzo. 2019. Progressive embedding. ACM Transactions on Graphics 38 4 (2019).","DOI":"10.1145\/3306346.3323012"},{"key":"e_1_3_3_2_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-29090-7_9"},{"key":"e_1_3_3_2_36_1","doi-asserted-by":"crossref","unstructured":"Jian-Ping Su Chunyang Ye Ligang Liu and Xiao-Ming Fu. 2020. Efficient bijective parameterizations. ACM Transactions on Graphics (TOG) 39 4 (2020) 111\u20131.","DOI":"10.1145\/3386569.3392435"},{"key":"e_1_3_3_2_37_1","doi-asserted-by":"crossref","unstructured":"Philip Trettner Julius Nehring-Wirxel and Leif Kobbelt. 2022. EMBER: exact mesh booleans via efficient & robust local arrangements. ACM Transactions on Graphics (TOG) 41 4 (2022) 1\u201315.","DOI":"10.1145\/3528223.3530181"},{"key":"e_1_3_3_2_38_1","doi-asserted-by":"crossref","unstructured":"William\u00a0Thomas Tutte. 1963. How to draw a graph. Proceedings of the London Mathematical Society 3 1 (1963) 743\u2013767.","DOI":"10.1112\/plms\/s3-13.1.743"},{"key":"e_1_3_3_2_39_1","first-page":"79","volume-title":"Computer Graphics Forum","author":"Yang Jinlin","year":"2022","unstructured":"Jinlin Yang, Shibo Liu, Shuangming Chai, Ligang Liu, and Xiao-Ming Fu. 2022. Precise High-order Meshing of 2D Domains with Rational B\u00e9zier Curves. In Computer Graphics Forum , Vol.\u00a041. Wiley Online Library, 79\u201388."},{"key":"e_1_3_3_2_40_1","doi-asserted-by":"publisher","DOI":"10.1142\/9789812831699_0011"},{"key":"e_1_3_3_2_41_1","doi-asserted-by":"crossref","unstructured":"Qingnan Zhou Eitan Grinspun Denis Zorin and Alec Jacobson. 2016. Mesh arrangements for solid geometry. ACM Transactions on Graphics (TOG) 35 4 (2016) 1\u201315.","DOI":"10.1145\/2897824.2925901"}],"event":{"name":"SIGGRAPH Conference Papers '25: Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers","location":"Vancouver BC Canada","acronym":"SIGGRAPH Conference Papers '25","sponsor":["SIGGRAPH ACM Special Interest Group on Computer Graphics and Interactive Techniques"]},"container-title":["Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3721238.3730693","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T14:57:54Z","timestamp":1774018674000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3721238.3730693"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,27]]},"references-count":40,"alternative-id":["10.1145\/3721238.3730693","10.1145\/3721238"],"URL":"https:\/\/doi.org\/10.1145\/3721238.3730693","relation":{},"subject":[],"published":{"date-parts":[[2025,7,27]]},"assertion":[{"value":"2025-07-27","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}