{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T18:31:21Z","timestamp":1791311481470,"version":"4.3.1"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T00:00:00Z","timestamp":1446422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Visual Computing Center (VCC) at KAUST"},{"name":"Austrian Science Fund","award":["P23735-N13"],"award-info":[{"award-number":["P23735-N13"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,11,4]]},"abstract":"<jats:p>We study the design and optimization of polyhedral patterns, which are patterns of planar polygonal faces on freeform surfaces. Working with polyhedral patterns is desirable in architectural geometry and industrial design. However, the classical tiling patterns on the plane must take on various shapes in order to faithfully and feasibly approximate curved surfaces. We define and analyze the deformations these tiles must undertake to account for curvature, and discover the symmetries that remain invariant under such deformations. We propose a novel method to regularize polyhedral patterns while maintaining these symmetries into a plethora of aesthetic and feasible patterns.<\/jats:p>","DOI":"10.1145\/2816795.2818077","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T12:36:39Z","timestamp":1445949399000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":45,"title":["Polyhedral patterns"],"prefix":"10.1145","volume":"34","author":[{"given":"Caigui","family":"Jiang","sequence":"first","affiliation":[{"name":"King Abdullah University of Science and Technology (KAUST)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengcheng","family":"Tang","sequence":"additional","affiliation":[{"name":"King Abdullah University of Science and Technology (KAUST)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amir","family":"Vaxman","sequence":"additional","affiliation":[{"name":"TU Wien \/ Utrecht University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Wonka","sequence":"additional","affiliation":[{"name":"KAUST"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Helmut","family":"Pottmann","sequence":"additional","affiliation":[{"name":"TU Wien \/ KAUST"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,11,2]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Abas S. J. Salman A. S. Moustafa A. and Atiyah M. 1995. Symmetries of Islamic geometrical patterns vol. 3. World Scientific.  Abas S. J. Salman A. S. Moustafa A. and Atiyah M. 1995. Symmetries of Islamic geometrical patterns vol. 3. World Scientific.","DOI":"10.1142\/2301"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMI.2005.40"},{"key":"e_1_2_2_3_1","doi-asserted-by":"crossref","unstructured":"Bobenko A. and Suris Yu. 2008. Discrete differential geometry: Integrable Structure. American Math. Soc.  Bobenko A. and Suris Yu. 2008. Discrete differential geometry: Integrable Structure. American Math. Soc.","DOI":"10.1090\/gsm\/098"},{"key":"e_1_2_2_4_1","unstructured":"Botsch M. Steinberg S. Bischoff S. and Kobbelt L. 2002. Openmesh - a generic and efficient polygon mesh data structure.  Botsch M. Steinberg S. Bischoff S. and Kobbelt L. 2002. Openmesh - a generic and efficient polygon mesh data structure."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03171.x"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015817"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2014.01.004"},{"key":"e_1_2_2_8_1","doi-asserted-by":"crossref","unstructured":"Huard M. Bompas P. and Eigensatz M. 2014. Planar panelization with extreme repetition. In Advances in Architectural Geometry 2014 P. Block et al. Eds. Springer.  Huard M. Bompas P. and Eigensatz M. 2014. Planar panelization with extreme repetition. In Advances in Architectural Geometry 2014 P. Block et al. Eds. Springer.","DOI":"10.1007\/978-3-319-11418-7_17"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12444"},{"key":"e_1_2_2_10_1","unstructured":"Krieg O. D. Schwinn T. Menges A. Li J.-M. Knippers J. Schmitt A. and Schwieger V. 2003. Taucs. In A Library of Sparse Linear Solvers. TAU.  Krieg O. D. Schwinn T. Menges A. Li J.-M. Knippers J. Schmitt A. and Schwieger V. 2003. Taucs. In A Library of Sparse Linear Solvers. TAU."},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Krieg O. D. Schwinn T. Menges A. Li J.-M. Knippers J. Schmitt A. and Schwieger V. 2014. Biomimetic lightweight timber plate shells: Computational integration of robotic fabrication architectural geometry and structural design. In Advances in Architectural Geometry. Springer 109--125.  Krieg O. D. Schwinn T. Menges A. Li J.-M. Knippers J. Schmitt A. and Schwieger V. 2014. Biomimetic lightweight timber plate shells: Computational integration of robotic fabrication architectural geometry and structural design. In Advances in Architectural Geometry. Springer 109--125.","DOI":"10.1007\/978-3-319-11418-7_8"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2322367"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141941"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024174"},{"key":"e_1_2_2_15_1","doi-asserted-by":"crossref","unstructured":"Lu P. J. and Steinhardt P. J. 2007. Decagonal and quasi-crystalline tilings in medieval islamic architecture. Science 315 5815 1106--1110.  Lu P. J. and Steinhardt P. J. 2007. Decagonal and quasi-crystalline tilings in medieval islamic architecture. Science 315 5815 1106--1110.","DOI":"10.1126\/science.1135491"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12005"},{"key":"e_1_2_2_17_1","doi-asserted-by":"crossref","unstructured":"Sauer R. 1970. Differenzengeometrie. Springer.  Sauer R. 1970. Differenzengeometrie. Springer.","DOI":"10.1007\/978-3-642-86411-7"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618485"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778783"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601213"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01776.x"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03040.x"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2816795.2818077","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2816795.2818077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:48:18Z","timestamp":1750225698000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2816795.2818077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,2]]},"references-count":22,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,11,4]]}},"alternative-id":["10.1145\/2816795.2818077"],"URL":"https:\/\/doi.org\/10.1145\/2816795.2818077","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,2]]},"assertion":[{"value":"2015-11-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}