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Designing these assemblies is a complex problem, since it requires a compatible decomposition of shapes with correspondence across forms, and a planning of well-matched joints to connect parts in each form. This paper presents computational methods as tools to assist the design and construction of reconfigurable assemblies, typically for furniture. There are three key contributions in this work. First, we present the compatible decomposition as a weakly-constrained dissection problem, and derive its solution based on a dynamic bipartite graph to construct parts across multiple forms; particularly, we optimize the parts reuse and preserve the geometric semantics. Second, we develop a joint connection graph to model the solution space of reconfigurable assemblies with part and joint compatibility across different forms. Third, we formulate the backward interlocking and multi-key interlocking models, with which we iteratively plan the joints consistently over multiple forms. We show the applicability of our approach by constructing reconfigurable furniture of various complexities, extend it with recursive connections to generate extensible and hierarchical structures, and fabricate a number of results using 3D printing, 2D laser cutting, and woodworking.<\/jats:p>","DOI":"10.1145\/3130800.3130803","type":"journal-article","created":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T16:25:08Z","timestamp":1511367908000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":42,"title":["Reconfigurable interlocking furniture"],"prefix":"10.1145","volume":"36","author":[{"given":"Peng","family":"Song","sequence":"first","affiliation":[{"name":"University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Wing","family":"Fu","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yueming","family":"Jin","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongfei","family":"Xu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ligang","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pheng-Ann","family":"Heng","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong and Shenzhen Institutes of Advanced Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Cohen-Or","sequence":"additional","affiliation":[{"name":"Tel Aviv University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2017,11,20]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/3116263.3116421"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12723"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185543"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366149"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508400"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/199404.199437"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181377"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461953"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982402"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130831"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511574917"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766892"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925900"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03175.x"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024159"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2015.07.014"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03042.x"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12807"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661289"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005292125553"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/PG.2007.43"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766912"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12579"},{"key":"e_1_2_2_24_1","volume-title":"Plummer","author":"Lov\u00e1sz L\u00e1szl\u00f3","year":"2009","unstructured":"L\u00e1szl\u00f3 Lov\u00e1sz and Michael D . 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