{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:12:19Z","timestamp":1750306339869,"version":"3.41.0"},"reference-count":38,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T00:00:00Z","timestamp":1468195200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2016,7,11]]},"abstract":"<jats:p>Patterns play a central role in 2D graphic design. A critical step in the design of patterns is evaluating multiple design alternatives. Exploring these alternatives with existing tools is challenging because most tools force users to work with a single fixed representation of the pattern that encodes a specific set of geometric relationships between pattern elements. However, for most patterns, there are many different interpretations of its regularity that correspond to different design variations. The exponential nature of this variation space makes the problem of finding all variations intractable. We present a method called PATEX to characterize and efficiently identify distinct and valid pattern variations, allowing users to directly navigate the variation space. Technically, we propose a novel linear approximation to handle the complexity of the problem and efficiently enumerate suitable pattern variations under proposed element movements. We also present two pattern editing interfaces that expose the detected pattern variations as suggested edits to the user. We show a diverse collection of pattern edits and variations created with PATEX. The results from our user study indicate that our suggested variations can be useful and inspirational for typical pattern editing tasks.<\/jats:p>","DOI":"10.1145\/2897824.2925950","type":"journal-article","created":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T16:04:33Z","timestamp":1468253073000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["PATEX"],"prefix":"10.1145","volume":"35","author":[{"given":"Paul","family":"Guerrero","sequence":"first","affiliation":[{"name":"University College London"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gilbert","family":"Bernstein","sequence":"additional","affiliation":[{"name":"Stanford University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wilmot","family":"Li","sequence":"additional","affiliation":[{"name":"Adobe Research"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Niloy J.","family":"Mitra","sequence":"additional","affiliation":[{"name":"University College London"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,7,11]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601102"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1054972.1055014"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766980"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/15922.15912"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185574"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595289108"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/218013.218021"},{"key":"e_1_2_2_8_1","doi-asserted-by":"crossref","unstructured":"Daniel M. and Lucas M. 1997. Towards declarative geometric modelling in mechanics. In Integrated Design and Manufacturing in Mechanical Engineering P. Chedmail J.-C. Bocquet and D. Dornfeld Eds. Springer Netherlands 427--436.  Daniel M. and Lucas M. 1997. Towards declarative geometric modelling in mechanics. In Integrated Design and Manufacturing in Mechanical Engineering P. Chedmail J.-C. Bocquet and D. Dornfeld Eds. Springer Netherlands 427--436.","DOI":"10.1007\/978-94-011-5588-5_43"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964961"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12311"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601185"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531339"},{"key":"e_1_2_2_13_1","unstructured":"Gleicher M. and Witkin A. 1991. Differential manipulation. In Graphics Interface 61--67.  Gleicher M. and Witkin A. 1991. Differential manipulation. In Graphics Interface 61--67."},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/142750.143074"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2591010"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218443"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01567.x"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/263407.263525"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882353"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/2024156.2024219"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/325334.325241"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.48"},{"volume-title":"PATEX project website","key":"e_1_2_2_23_1","unstructured":"2016. PATEX project website . http:\/\/geometry.cs.ucl.ac.uk\/projects\/2016\/pattern-variations\/. Accessed: 2016-19-04. 2016. PATEX project website. http:\/\/geometry.cs.ucl.ac.uk\/projects\/2016\/pattern-variations\/. Accessed: 2016-19-04."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/325165.325240"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508409"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/263407.263521"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618513"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/2817721.2817729"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01636.x"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01885.x"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1576246.1531341"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/2642918.2647398"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/2702123.2702198"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01411.x"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185552"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/2421636.2421639"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12008-008-0047-3"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185595"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2897824.2925950","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2897824.2925950","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:55:04Z","timestamp":1750222504000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2897824.2925950"}},"subtitle":["exploring pattern variations"],"short-title":[],"issued":{"date-parts":[[2016,7,11]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,7,11]]}},"alternative-id":["10.1145\/2897824.2925950"],"URL":"https:\/\/doi.org\/10.1145\/2897824.2925950","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2016,7,11]]},"assertion":[{"value":"2016-07-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}