{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T02:57:54Z","timestamp":1767841074333,"version":"3.49.0"},"reference-count":46,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2018,12,4]],"date-time":"2018-12-04T00:00:00Z","timestamp":1543881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["51NF40-141853"],"award-info":[{"award-number":["51NF40-141853"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2018,12,31]]},"abstract":"<jats:p>Interlocking assemblies have a long history in the design of puzzles, furniture, architecture, and other complex geometric structures. The key defining property of interlocking assemblies is that all component parts are immobilized by their geometric arrangement, preventing the assembly from falling apart. Computer graphics research has recently contributed design tools that allow creating new interlocking assemblies. However, these tools focus on specific kinds of assemblies and explore only a limited space of interlocking configurations, which restricts their applicability for design.<\/jats:p>\n          <jats:p>\n            In this paper, we propose a new general framework for designing interlocking assemblies. The core idea is to represent part relationships with a family of base\n            <jats:italic>Directional Blocking Graphs<\/jats:italic>\n            and leverage efficient graph analysis tools to compute an interlocking arrangement of parts. This avoids the exponential complexity of brute-force search. Our algorithm iteratively constructs the geometry of assembly components, taking advantage of all existing blocking relations for constructing successive parts. As a result, our approach supports a wider range of assembly forms compared to previous methods and provides significantly more design flexibility. We show that our framework facilitates efficient design of complex interlocking assemblies, including new solutions that cannot be achieved by state of the art approaches.\n          <\/jats:p>","DOI":"10.1145\/3272127.3275034","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T19:16:10Z","timestamp":1543432570000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":28,"title":["DESIA"],"prefix":"10.1145","volume":"37","author":[{"given":"Ziqi","family":"Wang","sequence":"first","affiliation":[{"name":"EPFL"}]},{"given":"Peng","family":"Song","sequence":"additional","affiliation":[{"name":"EPFL"}]},{"given":"Mark","family":"Pauly","sequence":"additional","affiliation":[{"name":"EPFL"}]}],"member":"320","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882352"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12608"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2015.07.003"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818087"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2537852"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461932"},{"key":"e_1_2_2_7_1","volume-title":"Sustainable Dry Interlocking Block Masonry Construction. In 15th International Brick and Block Masonry Conference.","author":"Deepak Bansal","year":"2012","unstructured":"Bansal Deepak . 2012 . Sustainable Dry Interlocking Block Masonry Construction. In 15th International Brick and Block Masonry Conference. Bansal Deepak. 2012. Sustainable Dry Interlocking Block Masonry Construction. In 15th International Brick and Block Masonry Conference."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661266"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982402"},{"key":"e_1_2_2_10_1","volume-title":"Tom Van Mele, and Philippe Block","author":"Frick Ursula","year":"2015","unstructured":"Ursula Frick , Tom Van Mele, and Philippe Block . 2015 . Decomposing Three-Dimensional Shapes into Self-supporting, Discrete-Element Assemblies. In Modelling Behaviour . 187--201. Ursula Frick, Tom Van Mele, and Philippe Block. 2015. Decomposing Three-Dimensional Shapes into Self-supporting, Discrete-Element Assemblies. 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The Armadillo Vault: Computational design and digital fabrication of a freeform stone shell. In Advances in Architectural Geometry . 344--363. Matthias Rippmann, Tom Van Mele, Mariana Popescu, Edyta Augustynowicz, Tom\u00e1s M\u00e9ndez Echenagucia, Cristi\u00e1n Calvo Barentin, Ursula Frick, and Philippe Block. 2016. The Armadillo Vault: Computational design and digital fabrication of a freeform stone shell. In Advances in Architectural Geometry. 344--363."},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12051"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982416"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818128"},{"key":"e_1_2_2_30_1","volume-title":"Systems of Linear Inequalities","author":"Solodovnikov A. S.","unstructured":"A. S. Solodovnikov . 1979. Systems of Linear Inequalities . Mir Publishers . A. S. Solodovnikov. 1979. Systems of Linear Inequalities. 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