{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T20:34:56Z","timestamp":1771533296368,"version":"3.50.1"},"reference-count":43,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:00:00Z","timestamp":1559865600000},"content-version":"vor","delay-in-days":37,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[2019,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Dissection puzzles require assembling a common set of pieces into multiple distinct forms. Existing works focus on creating 2D dissection puzzles that form primitive or naturalistic shapes. Unlike 2D dissection puzzles that could be supported on a tabletop surface, 3D dissection puzzles are preferable to be steady by themselves for each assembly form. In this work, we aim at computationally designing <jats:italic>steady 3D dissection puzzles<\/jats:italic>. We address this challenging problem with three key contributions. First, we take two voxelized shapes as inputs and dissect them into a common set of puzzle pieces, during which we allow slightly modifying the input shapes, preferably on their internal volume, to preserve the external appearance. Second, we formulate a formal model of generalized interlocking for connecting pieces into a steady assembly using both their geometric arrangements and friction. Third, we modify the geometry of each dissected puzzle piece based on the formal model such that each assembly form is steady accordingly. We demonstrate the effectiveness of our approach on a wide variety of shapes, compare it with the state\u2010of\u2010the\u2010art on 2D and 3D examples, and fabricate some of our designed puzzles to validate their steadiness.<\/jats:p>","DOI":"10.1111\/cgf.13638","type":"journal-article","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T14:31:53Z","timestamp":1559917913000},"page":"291-303","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Computational Design of Steady 3D Dissection Puzzles"],"prefix":"10.1111","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0377-1022","authenticated-orcid":false,"given":"Keke","family":"Tang","sequence":"first","affiliation":[{"name":"Cyberspace Institute of Advanced Technology, Guangzhou University"},{"name":"University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Song","sequence":"additional","affiliation":[{"name":"EPFL"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofei","family":"Wang","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bailin","family":"Deng","sequence":"additional","affiliation":[{"name":"Cardiff University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi\u2010Wing","family":"Fu","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ligang","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,6,7]]},"reference":[{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9305-9"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185543"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13327"},{"key":"e_1_2_9_5_2","volume-title":"Tentamen juventutem. Typis Collegii Refomatorum per Josephum et Simeonem Kali","author":"Bolyai F.","year":"1832"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366149"},{"issue":"52","key":"e_1_2_9_7_2","first-page":"2593","article-title":"Rectilinear glasscut dissections of rectangles to squares","volume":"1","author":"Czyzowicz J.","year":"2007","journal-title":"Applied Mathematical Sciences"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181377"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/2537852"},{"key":"e_1_2_9_10_2","volume-title":"The Canterbury Puzzles, and Other Curious Problems","author":"Dudeney H. E.","year":"1907"},{"issue":"6","key":"e_1_2_9_11_2","first-page":"182:1","article-title":"Approximate dissections","volume":"36","author":"Duncan N.","year":"2017","journal-title":"ACM Trans. on Graph. (SIGGRAPH Asia)"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511574917"},{"key":"e_1_2_9_13_2","volume-title":"Hinged Dissections: Swinging and Twisting","author":"Frederickson G. N.","year":"2002"},{"key":"e_1_2_9_14_2","unstructured":"FredericksonG. N.: Symmetry and structure in twist-hinged dissections of polygonal rings and polygonal anti-rings.Proc. Bridges Donostia: Mathematics Music Art Architecture Culture(2007) 21\u201328. 2"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-007-0697-0"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1080\/07468342.2008.11922302"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.4169\/002557009X478346"},{"key":"e_1_2_9_18_2","volume-title":"Ernest Irving Freese's Geometric Transformations: The Man, The Manuscript, The Magnificent Dissections!","author":"Frederickson G. N.","year":"2017"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1145\/2766892"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1833.10.228"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925900"},{"key":"e_1_2_9_22_2","doi-asserted-by":"crossref","unstructured":"HuangY.-J. ChanS.-Y. LinW.-C. ChuangS.-Y.: Making and animating transformable 3D models.Computers & Graphics (Proc. of CAD\/Graphics)54 (2016) 127\u2013134. 2","DOI":"10.1016\/j.cag.2015.07.014"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.4171\/EM\/26"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005292125553"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366148"},{"key":"e_1_2_9_26_2","volume-title":"Recreational Problems in Geometric Dissections and How to Solve Them","author":"Lindgren H.","year":"1972"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1145\/2766912"},{"issue":"6","key":"e_1_2_9_28_2","first-page":"190:1","article-title":"Construction and fabrication of reversible shape transforms","volume":"37","author":"Li S.","year":"2018","journal-title":"ACM Trans. on Graph. (SIGGRAPH Asia)"},{"key":"e_1_2_9_29_2","first-page":"103","article-title":"On geometric dissections and transformations","volume":"1","author":"Perigal H.","year":"1872","journal-title":"Messenger of Mathematics (second series)"},{"key":"e_1_2_9_30_2","volume-title":"The complete illustrated guide to joinery","author":"Rogowski G.","year":"2002"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925876"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366147"},{"issue":"6","key":"e_1_2_9_33_2","first-page":"174:1","article-title":"Reconfigurable interlocking furniture","volume":"36","author":"Song P.","year":"2017","journal-title":"ACM Trans. on Graph. (SIGGRAPH Asia)"},{"key":"e_1_2_9_34_2","doi-asserted-by":"crossref","unstructured":"SongP. FuZ. LiuL. FuC.-W.: Printing 3D objects with interlocking parts.Comp. Aided Geom. Des. 35-36(2015) 137\u2013148. 3 4","DOI":"10.1016\/j.cagd.2015.03.020"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1145\/2766961"},{"key":"e_1_2_9_36_2","unstructured":"TheobaldG.:Solid dissections 2018.http:\/\/gavin-theobald.uk\/HTML\/3D.html.1"},{"issue":"6","key":"e_1_2_9_37_2","first-page":"191:1","article-title":"DESIA: A general framework for designing interlocking assemblies","volume":"37","author":"Wang Z.","year":"2018","journal-title":"ACM Trans. on Graph. (SIGGRAPH Asia)"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964992"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13267"},{"key":"e_1_2_9_40_2","doi-asserted-by":"publisher","DOI":"10.1145\/3054740"},{"issue":"8","key":"e_1_2_9_41_2","first-page":"2","article-title":"Computational design of transformables","volume":"37","author":"Yuan Y.","year":"2018","journal-title":"Computer Graphics Forum (SCA)"},{"key":"e_1_2_9_42_2","doi-asserted-by":"crossref","unstructured":"ZhangY. BalkcomD.: Interlocking structure assembly with voxels. InIEEE\/RSJ Intl. Conf. on Intelligent Robots and Systems(2016) pp.2173\u20132180. 3 4","DOI":"10.1109\/IROS.2016.7759341"},{"key":"e_1_2_9_43_2","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601173"},{"key":"e_1_2_9_44_2","unstructured":"ZhouY. WangR.: An algorithm for creating geometric dissection puzzles. InBridges Towson: Mathematics Music Art Architecture Culture(2012) pp.49\u201356. 1 2 10 11"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.13638","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/cgf.13638","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.13638","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T01:57:22Z","timestamp":1693360642000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cgf.13638"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["10.1111\/cgf.13638"],"URL":"https:\/\/doi.org\/10.1111\/cgf.13638","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5]]},"assertion":[{"value":"2019-06-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}