{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:48:32Z","timestamp":1774021712266,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":48,"publisher":"ACM","funder":[{"name":"Khoury College of Computer Sciences","award":["330345"],"award-info":[{"award-number":["330345"]}]},{"DOI":"10.13039\/100014600","name":"MathWorks","doi-asserted-by":"publisher","award":["687671"],"award-info":[{"award-number":["687671"]}],"id":[{"id":"10.13039\/100014600","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\/3721238.3730681","type":"proceedings-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T08:40:47Z","timestamp":1753260047000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Escher Tile Deformation via Closed-Form Solution"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9044-2130","authenticated-orcid":false,"given":"Crane He","family":"Chen","sequence":"first","affiliation":[{"name":"Industrial Light & Magic, San Francisco, California, USA and Northeastern University, Boston, MA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3996-6588","authenticated-orcid":false,"given":"Vladimir","family":"Kim","sequence":"additional","affiliation":[{"name":"Adobe Research, Seattle, WA, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_3_3_2_2_1","unstructured":"Noam Aigerman and Thibault Groueix. 2023. Generative Escher Meshes. arXiv preprint arXiv:https:\/\/arXiv.org\/abs\/2309.14564 (2023)."},{"key":"e_1_3_3_2_3_1","doi-asserted-by":"crossref","unstructured":"Noam Aigerman Shahar\u00a0Z Kovalsky and Yaron Lipman. 2017. Spherical orbifold tu e embeddings. ACM Trans. Graph. 36 4 (2017) 90.","DOI":"10.1145\/3072959.3073615"},{"key":"e_1_3_3_2_4_1","doi-asserted-by":"crossref","unstructured":"Noam Aigerman and Yaron Lipman. 2015. Orbifold tutte embeddings. ACM Trans. Graph. 34 6 (2015) 190\u20131.","DOI":"10.1145\/2816795.2818099"},{"key":"e_1_3_3_2_5_1","doi-asserted-by":"crossref","unstructured":"Noam Aigerman and Yaron Lipman. 2016. Hyperbolic orbifold tutte embeddings. ACM Trans. Graph. 35 6 (2016) 217\u20131.","DOI":"10.1145\/2980179.2982412"},{"key":"e_1_3_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/079"},{"key":"e_1_3_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/563732.1138362"},{"key":"e_1_3_3_2_8_1","unstructured":"Anton Bakker Doris Schattschneider Herman Tulleken Jonathan Bailey Markus Krisam. 2021. Conway\u2019s Magic Pen. http:\/\/www.conwaysmagicalpen.com\/"},{"key":"e_1_3_3_2_9_1","unstructured":"Nikos\u00a0D. Bagis. 2015. On the Complete Evaluation of Jacobi Theta Functions. arxiv:https:\/\/arXiv.org\/abs\/1503.01141\u00a0[math.NT]"},{"key":"e_1_3_3_2_10_1","doi-asserted-by":"crossref","unstructured":"Rulin Chen Ziqi Wang Peng Song and Bernd Bickel. 2022. Computational design of high-level interlocking puzzles. ACM Transactions on Graphics (TOG) 41 4 (2022) 1\u201315.","DOI":"10.1145\/3528223.3530071"},{"key":"e_1_3_3_2_11_1","doi-asserted-by":"crossref","unstructured":"Gregory\u00a0S Chirikjian Yu Zhou and Jackrit Suthakorn. 2002. Self-replicating robots for lunar development. IEEE\/ASME transactions on mechatronics 7 4 (2002) 462\u2013472.","DOI":"10.1109\/TMECH.2002.806232"},{"key":"e_1_3_3_2_12_1","doi-asserted-by":"publisher","DOI":"10.1201\/b21368"},{"key":"e_1_3_3_2_13_1","doi-asserted-by":"crossref","unstructured":"Qiaodong Cui Victor Rong Desai Chen and Wojciech Matusik. 2023. Dense Interlocking-Free and Scalable Spectral Packing of Generic 3D Objects. ACM Trans. Graph. 42 4 (2023) 141\u20131.","DOI":"10.1145\/3592126"},{"key":"e_1_3_3_2_14_1","doi-asserted-by":"crossref","unstructured":"Fernando De\u00a0Goes and Doug\u00a0L James. 2017. Regularized kelvinlets: sculpting brushes based on fundamental solutions of elasticity. ACM Transactions on Graphics (TOG) 36 4 (2017) 1\u201311.","DOI":"10.1145\/3072959.3073595"},{"key":"e_1_3_3_2_15_1","doi-asserted-by":"crossref","unstructured":"Fernando De\u00a0Goes and Doug\u00a0L James. 2018. Dynamic Kelvinlets: secondary motions based on fundamental solutions of elastodynamics. ACM Transactions on Graphics (TOG) 37 4 (2018) 1\u201310.","DOI":"10.1145\/3197517.3201280"},{"key":"e_1_3_3_2_16_1","unstructured":"Tom Goertzen. 2024. Constructing interlocking assemblies with crystallographic symmetries. arXiv preprint arXiv:https:\/\/arXiv.org\/abs\/2405.15080 (2024)."},{"key":"e_1_3_3_2_17_1","volume-title":"Tilings and patterns","author":"Gr\u00fcnbaum Branko","year":"1987","unstructured":"Branko Gr\u00fcnbaum and Geoffrey\u00a0Colin Shephard. 1987. Tilings and patterns. Courier Dover Publications."},{"key":"e_1_3_3_2_18_1","doi-asserted-by":"crossref","unstructured":"Alexander Guerten. 2020. KUHKUBUS-3D-Escher-tessellations. Journal of Mathematics and the Arts 14 1-2 (2020) 69\u201371.","DOI":"10.1080\/17513472.2020.1734519"},{"key":"e_1_3_3_2_19_1","doi-asserted-by":"crossref","unstructured":"Alec Jacobson Ilya Baran Jovan Popovic and Olga Sorkine. 2011. Bounded biharmonic weights for real-time deformation. ACM Trans. Graph. 30 4 (2011) 78.","DOI":"10.1145\/2010324.1964973"},{"key":"e_1_3_3_2_20_1","unstructured":"Jeff Weeks. 1991. KaleidoTile. https:\/\/www.geometrygames.org\/KaleidoTile\/index.html"},{"key":"e_1_3_3_2_21_1","volume-title":"Plans, Elevations, Sections and Details of the Alhambra","author":"Jones Owen","year":"1842","unstructured":"Owen Jones. 1842. Plans, Elevations, Sections and Details of the Alhambra. Owen Jones and Jules Goury, London."},{"key":"e_1_3_3_2_22_1","doi-asserted-by":"publisher","DOI":"10.5479\/sil.387695.39088012147732"},{"key":"e_1_3_3_2_23_1","doi-asserted-by":"publisher","DOI":"10.5555\/1696513"},{"key":"e_1_3_3_2_24_1","first-page":"39","volume-title":"Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture","author":"Kaplan Craig\u00a0S","year":"2008","unstructured":"Craig\u00a0S Kaplan. 2008. Metamorphosis in Escher\u2019s art. In Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture. 39\u201346."},{"key":"e_1_3_3_2_25_1","first-page":"95","volume-title":"Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture","author":"Kaplan Craig\u00a0S","year":"2010","unstructured":"Craig\u00a0S Kaplan. 2010. Curve evolution schemes for parquet deformations. In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture. 95\u2013102."},{"key":"e_1_3_3_2_26_1","volume-title":"Graphics Interface","author":"Kaplan Craig\u00a0S.","year":"2004","unstructured":"Craig\u00a0S. Kaplan and D. Salesin. 2004a. Dihedral Escherization. In Graphics Interface. https:\/\/api.semanticscholar.org\/CorpusID:18798031"},{"key":"e_1_3_3_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345022"},{"key":"e_1_3_3_2_28_1","doi-asserted-by":"crossref","unstructured":"Craig\u00a0S Kaplan and David\u00a0H Salesin. 2004b. Islamic star patterns in absolute geometry. ACM Transactions on Graphics (TOG) 23 2 (2004) 97\u2013119.","DOI":"10.1145\/990002.990003"},{"key":"e_1_3_3_2_29_1","first-page":"483","volume-title":"Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture","author":"Lee Kevin","year":"2015","unstructured":"Kevin Lee. 2015. Algorithms for morphing escher-like tessellations. In Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture. 483\u2013486."},{"key":"e_1_3_3_2_30_1","doi-asserted-by":"crossref","unstructured":"Shih-Syun Lin Charles\u00a0C Morace Chao-Hung Lin Li-Fong Hsu and Tong-Yee Lee. 2017. Generation of escher arts with dual perception. IEEE transactions on visualization and computer graphics 24 2 (2017) 1103\u20131113.","DOI":"10.1109\/TVCG.2017.2660488"},{"key":"e_1_3_3_2_31_1","doi-asserted-by":"crossref","unstructured":"Yuichi Nagata and Shinji Imahori. 2021. Escherization with Large Deformations Based on As-Rigid-As-Possible Shape Modeling. ACM Transactions on Graphics (TOG) 41 2 (2021) 1\u201316.","DOI":"10.1145\/3487017"},{"key":"e_1_3_3_2_32_1","doi-asserted-by":"crossref","unstructured":"Peichang Ouyang Kwok\u00a0Wai Chung Alain Nicolas and Krzysztof Gdawiec. 2021. Self-similar fractal drawings inspired by MC Escher\u2019s print Square Limit. ACM Transactions on Graphics (TOG) 40 3 (2021) 1\u201334.","DOI":"10.1145\/3456298"},{"key":"e_1_3_3_2_33_1","doi-asserted-by":"crossref","unstructured":"Peichang Ouyang and Robert\u00a0W Fathauer. 2014. Beautiful math part 2: aesthetic patterns based on fractal tilings. IEEE Computer Graphics and applications 34 1 (2014) 68\u201376.","DOI":"10.1109\/MCG.2014.6"},{"key":"e_1_3_3_2_34_1","doi-asserted-by":"crossref","unstructured":"Peichang Ouyang Krzysztof Gdawiec Alain Nicolas David Bailey and Kwok\u00a0Wai Chung. 2022. Interlocking spiral drawings inspired by MC Escher\u2019s print whirlpools. ACM Transactions on Graphics 42 2 (2022) 1\u201317.","DOI":"10.1145\/3560711"},{"key":"e_1_3_3_2_35_1","doi-asserted-by":"crossref","unstructured":"Jonathan Palacios and Eugene Zhang. 2007. Rotational symmetry field design on surfaces. ACM Transactions on Graphics (TOG) 26 3 (2007) 55\u2013es.","DOI":"10.1145\/1276377.1276446"},{"key":"e_1_3_3_2_36_1","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780195090864.001.0001"},{"key":"e_1_3_3_2_37_1","doi-asserted-by":"crossref","unstructured":"Nicolas Ray Wan\u00a0Chiu Li Bruno L\u00e9vy Alla Sheffer and Pierre Alliez. 2006. Periodic global parameterization. ACM Transactions on Graphics (TOG) 25 4 (2006) 1460\u20131485.","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_3_3_2_38_1","doi-asserted-by":"crossref","unstructured":"JF Rigby. 1991. Napoleon Escher and tessellations. Mathematics Magazine 64 4 (1991) 242\u2013246.","DOI":"10.1080\/0025570X.1991.11977614"},{"key":"e_1_3_3_2_39_1","doi-asserted-by":"crossref","unstructured":"Lawrence Roy Prashant Kumar Sanaz Golbabaei Yue Zhang and Eugene Zhang. 2017. Interactive design and visualization of branched covering spaces. IEEE Transactions on Visualization and Computer Graphics 24 1 (2017) 843\u2013852.","DOI":"10.1109\/TVCG.2017.2744038"},{"key":"e_1_3_3_2_40_1","doi-asserted-by":"crossref","unstructured":"Doris Schattschneider. 1980. Will it tile? Try the Conway criterion! Mathematics Magazine 53 4 (1980) 224\u2013233.","DOI":"10.1080\/0025570X.1980.11976859"},{"key":"e_1_3_3_2_41_1","volume-title":"M.C. Escher: Visions of Symmetry","author":"Schattschneider Doris","year":"2004","unstructured":"Doris Schattschneider. 2004. M.C. Escher: Visions of Symmetry. Harry N. Abrams."},{"key":"e_1_3_3_2_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657466"},{"key":"e_1_3_3_2_43_1","unstructured":"David Smith Joseph\u00a0Samuel Myers Craig\u00a0S Kaplan and Chaim Goodman-Strauss. 2023. An aperiodic monotile. arXiv preprint arXiv:https:\/\/arXiv.org\/abs\/2303.10798 (2023)."},{"key":"e_1_3_3_2_44_1","unstructured":"Walter\u00a0F. Smith. 2002. The Bravais Lattices Song. https:\/\/www.physicssongs.org\/bravais.htm Accessed: 2024-07-07."},{"key":"e_1_3_3_2_45_1","first-page":"109","volume-title":"Symposium on Geometry processing","author":"Sorkine Olga","year":"2007","unstructured":"Olga Sorkine and Marc Alexa. 2007. As-rigid-as-possible surface modeling. In Symposium on Geometry processing , Vol.\u00a04. Citeseer, 109\u2013116."},{"key":"e_1_3_3_2_46_1","volume-title":"The Geometry and Topology of Three-Manifolds","author":"Thurston William","year":"1978","unstructured":"William Thurston. 1978-1981. The Geometry and Topology of Three-Manifolds. Princeton University lecture notes."},{"key":"e_1_3_3_2_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/3005358.3005368"},{"key":"e_1_3_3_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280948"},{"key":"e_1_3_3_2_49_1","doi-asserted-by":"crossref","unstructured":"Jinta Zheng Eugene Zhang and Yue Zhang. 2023. Interactive Design and Optics-Based Visualization of Arbitrary Non-Euclidean Kaleidoscopic Orbifolds. IEEE Transactions on Visualization and Computer Graphics 30 1 (2023) 1292\u20131301.","DOI":"10.1109\/TVCG.2023.3326927"}],"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\/3721238.3730681","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T14:55:37Z","timestamp":1774018537000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3721238.3730681"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,27]]},"references-count":48,"alternative-id":["10.1145\/3721238.3730681","10.1145\/3721238"],"URL":"https:\/\/doi.org\/10.1145\/3721238.3730681","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"}}]}}