{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T13:11:33Z","timestamp":1790687493257,"version":"4.1.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"5","license":[{"start":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T00:00:00Z","timestamp":1259625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee, Hong Kong","doi-asserted-by":"publisher","award":["HKUST618208"],"award-info":[{"award-number":["HKUST618208"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001475","name":"Nanyang Technological University","doi-asserted-by":"publisher","award":["M58020007.500000"],"award-info":[{"award-number":["M58020007.500000"]}],"id":[{"id":"10.13039\/501100001475","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p>\n            This paper presents a computer-aided geometric design approach to realize a new genre of 3D puzzle, namely the\n            <jats:italic>3D Polyomino puzzle<\/jats:italic>\n            . We base our puzzle pieces on the family of 2D shapes known as\n            <jats:italic>polyominoes<\/jats:italic>\n            in recreational mathematics, and construct the 3D puzzle model by covering its geometry with polyominolike shapes. We first apply quad-based surface parametrization to the input solid, and tile the parametrized surface with polyominoes. Then, we construct a nonintersecting offset surface inside the input solid and shape the puzzle pieces to fit inside a thick shell volume. Finally, we develop a family of associated techniques for precisely constructing the geometry of individual puzzle pieces, including the ring-based ordering scheme, the motion space analysis technique, and the tab and blank construction method. The final completed puzzle model is guaranteed to be not only buildable, but also interlocking and maintainable.\n          <\/jats:p>","DOI":"10.1145\/1618452.1618503","type":"journal-article","created":{"date-parts":[[2009,12,8]],"date-time":"2009-12-08T20:53:14Z","timestamp":1260305594000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":54,"title":["3D polyomino puzzle"],"prefix":"10.1145","volume":"28","author":[{"given":"Kui-Yip","family":"Lo","sequence":"first","affiliation":[{"name":"The Hong Kong University of Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Wing","family":"Fu","sequence":"additional","affiliation":[{"name":"Nanyang Technological University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongwei","family":"Li","sequence":"additional","affiliation":[{"name":"The Hong Kong University of Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2009,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/563732.1138362"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057459"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/502122.502124"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2004.07.005"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141993"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218440"},{"key":"e_1_2_1_7_1","unstructured":"Floater M. S. and Hormann K. 2004. Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling Springer N. A. Dodgson M. S. Floater and M. A. Sabin Eds. 259--284.  Floater M. S. and Hormann K. 2004. Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling Springer N. A. Dodgson M. S. Floater and M. A. Sabin Eds. 259--284."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0557-150"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1954.11988548"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1515\/9780691215051"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345022"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1278780.1278874"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/PG.2007.46"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015711"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276433"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276475"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015773"},{"key":"e_1_2_1_18_1","unstructured":"Putter G. 1998. Gerard's universal polyomino solver 1.4. http:\/\/www.xs4all.nl\/~gp\/PolyominoSolver\/Polyomino.html.  Putter G. 1998. Gerard's universal polyomino solver 1.4. http:\/\/www.xs4all.nl\/~gp\/PolyominoSolver\/Polyomino.html."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-006-0067-6"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1186562.1015810"},{"key":"e_1_2_1_22_1","volume-title":"Proc. of Eurographics symp. on geom. proc., 201--210","author":"Tong Y.","unstructured":"Tong , Y. , Alliez , P. , Cohen-Steiner , D. , and Desbrun , M . 2006. Designing quadrangulations with discrete harmonic forms . In Proc. of Eurographics symp. on geom. proc., 201--210 . Tong, Y., Alliez, P., Cohen-Steiner, D., and Desbrun, M. 2006. Designing quadrangulations with discrete harmonic forms. In Proc. of Eurographics symp. on geom. proc., 201--210."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276417"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1618452.1618503","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1618452.1618503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:23:23Z","timestamp":1750249403000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1618452.1618503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":23,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1145\/1618452.1618503"],"URL":"https:\/\/doi.org\/10.1145\/1618452.1618503","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]},"assertion":[{"value":"2009-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}