{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:30:11Z","timestamp":1787319011886,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"Hong Kong Research Grants Council","award":["2130549"],"award-info":[{"award-number":["2130549"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Computing surface folding maps has numerous applications ranging from computer graphics to material design. In this work we propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization of the existing computational quasi-conformal geometry and allows precise control of the geometry of folding. This property comes from a crucial quantity that occurs as the coefficient of the equation, namely, the alternating Beltrami coefficient. This approach also enables us to solve an inverse problem of parametrizing the folded surface given only partial data with known folding topology. Various interesting applications such as fold sculpting on 3 dimensional models, study of Miura-ori patterns, and self-occlusion reasoning are demonstrated to show the effectiveness of our method.<\/jats:p>","DOI":"10.1137\/18m1220042","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T12:41:26Z","timestamp":1565700086000},"page":"1392-1424","source":"Crossref","is-referenced-by-count":11,"title":["Computing Quasi-Conformal Folds"],"prefix":"10.1137","volume":"12","author":[{"given":"Di","family":"Qiu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ka-Chun","family":"Lam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lok-Ming","family":"Lui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"K. Astala, T. Iwaniec, and G. Martin,\n                      Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)\n                      , Princeton University Press, Princeton, NJ, 2008.","DOI":"10.1515\/9781400830114"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531330"},{"key":"atypb3","first-page":"29","author":"Barnes C.","year":"2010","journal-title":"Berlin"},{"key":"atypb4","first-page":"417","author":"Bertalmio M.","year":"2000","journal-title":"New York"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/130950008"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1080\/02331930412331327157"},{"key":"atypb7","first-page":"8","author":"Daisy M.","year":"2013","journal-title":"New York"},{"key":"atypb8","unstructured":"E. D. Demaine and T. Tachi,\n                      Origamizer: A practical algorithm for folding any polyhedron\n                      , in 33rd International Symposium on Computational Geometry, LIPIcs-Leibniz Int. Proc. Inform. 77, Leibniz-Zentrum fuer Informatik, Schloss Dagstuhl, 201, 34."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00580"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1038\/nmat4540"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2004.831226"},{"key":"atypb12","first-page":"183","author":"Gutlyanskii V.","year":"2012","journal-title":"New York"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360674"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1115\/1.4031023"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566590"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"M. Li,\n                      FoldSketch: Enriching Garments with Physically Reproducible Folds\n                      , PhD thesis, University of British Columbia, Vancouver, Canada, 2018.","DOI":"10.1145\/3197517.3201310"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/120900186"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-011-9506-2"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1993.10504266"},{"key":"atypb20","first-page":"203","author":"Shewchuk J. R.","year":"1996","journal-title":"Berlin"},{"key":"atypb21","first-page":"109","author":"Sorkine O.","year":"2007","journal-title":"Switzerland"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02820441"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.87"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"R. Zayer, C. Rossl, and H.P. Seidel,\n                      Discrete tensorial quasi-harmonic maps\n                      , in Shape Modeling and Applications, 2005 International Conference, IEEE Computer Society, Los Alamitos, CA, 2005, pp. 276-285.","DOI":"10.1109\/SMI.2005.17"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12224"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1220042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:44:23Z","timestamp":1787316263000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1220042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1220042"],"URL":"https:\/\/doi.org\/10.1137\/18m1220042","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}