{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T01:14:29Z","timestamp":1781486069501,"version":"3.54.1"},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T00:00:00Z","timestamp":1626652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100023946","name":"NCCR Digital Fabrication","doi-asserted-by":"crossref","award":["51NF40-141853"],"award-info":[{"award-number":["51NF40-141853"]}],"id":[{"id":"10.13039\/501100023946","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":[[2021,8,31]]},"abstract":"<jats:p>In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approximate local congruences on the surface. These symmetries can be exploited to simplify surface paneling of double-curved architectural skins through mold re-use.<\/jats:p>\n          <jats:p>We present an optimization approach to find a Weingarten surface that is close to a given input design. Leveraging insights from differential geometry, our method aligns curvature isolines of the surface in order to contract the curvature diagram from a 2D region into a 1D curve. The unknown functional curvature relation then emerges as the result of the optimization. We show how a robust and efficient numerical shape approximation method can be implemented using a guided projection approach on a high-order B-spline representation. This algorithm is applied in several design studies to illustrate how Weingarten surfaces define a versatile shape space for fabrication-aware exploration in freeform architecture. Our optimization algorithm provides the first practical tool to compute general Weingarten surfaces with arbitrary curvature relation, thus enabling new investigations into a rich, but as of yet largely unexplored class of surfaces.<\/jats:p>","DOI":"10.1145\/3450626.3459939","type":"journal-article","created":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T00:04:27Z","timestamp":1626739467000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":26,"title":["Computational design of weingarten surfaces"],"prefix":"10.1145","volume":"40","author":[{"given":"Davide","family":"Pellis","sequence":"first","affiliation":[{"name":"EPFL, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Kilian","sequence":"additional","affiliation":[{"name":"TU Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Helmut","family":"Pottmann","sequence":"additional","affiliation":[{"name":"KAUST, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark","family":"Pauly","sequence":"additional","affiliation":[{"name":"EPFL, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964996"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2006.164.231"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-011-9653-5"},{"key":"e_1_2_2_4_1","volume-title":"Suris","author":"Bobenko Alexander I.","year":"2008","unstructured":"Alexander I. Bobenko and Yuri B . Suris . 2008 . Discrete differential geometry. Integrable structure. Graduate Studies in Mathematics, Vol. 98 . American Mathematical Society , Providence, RI. Alexander I. Bobenko and Yuri B. Suris. 2008. Discrete differential geometry. Integrable structure. Graduate Studies in Mathematics, Vol. 98. American Mathematical Society, Providence, RI."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1992.10504253"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778782"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01121.x"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417843"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/mana.3210040122"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-013-9830-9"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-019-00098-7"},{"key":"e_1_2_2_12_1","volume-title":"Differentialgeometrie","author":"K\u00fchnel Wolfgang","unstructured":"Wolfgang K\u00fchnel . 2003. Differentialgeometrie ( second ed.). Friedr. Vieweg & Sohn, Braunschweig. viii+256 pages. Kurven---Fl\u00e4chen---Mannigfaltigkeiten . Wolfgang K\u00fchnel. 2003. Differentialgeometrie (second ed.). Friedr. Vieweg & Sohn, Braunschweig. viii+256 pages. Kurven---Fl\u00e4chen---Mannigfaltigkeiten."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2003.07.009"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.difgeo.2019.101564"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185581"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2010.12.013"},{"key":"e_1_2_2_17_1","unstructured":"Davide Pellis Martin Kilian Hui Wang Caigui Jiang Christian M\u00fcller and Helmut Pottmann. 2020a. Architectural freeform surfaces designed for cost-effective paneling through mold re-use. In Advances in Architectural Geometry.  Davide Pellis Martin Kilian Hui Wang Caigui Jiang Christian M\u00fcller and Helmut Pottmann. 2020a. Architectural freeform surfaces designed for cost-effective paneling through mold re-use. In Advances in Architectural Geometry."},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392446"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1993.10504266"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2014.11.002"},{"key":"e_1_2_2_21_1","volume-title":"B\u00e9zier and B-Spline Techniques","author":"Prautzsch Hartmut","unstructured":"Hartmut Prautzsch , Wolfgang Boehm , and Marco Paluszny . 2002. B\u00e9zier and B-Spline Techniques . Springer-Verlag . Hartmut Prautzsch, Wolfgang Boehm, and Marco Paluszny. 2002. B\u00e9zier and B-Spline Techniques. Springer-Verlag."},{"key":"e_1_2_2_22_1","doi-asserted-by":"crossref","unstructured":"Eike Schling. 2018. Repetitive Structures. Ph.D. Dissertation. TU Munich.  Eike Schling. 2018. Repetitive Structures. Ph.D. Dissertation. TU Munich.","DOI":"10.1007\/978-3-030-29829-6_29"},{"key":"e_1_2_2_23_1","volume-title":"Adv. in Architectural Geometry, Lars Hesselgren et al. (Ed.). Klein Publ","author":"Schling Eike","unstructured":"Eike Schling , Martin Kilian , Hui Wang , Denis Schikore , and Helmut Pottmann . 2018. Design and construction of curved support structures with repetitive parameters . In Adv. in Architectural Geometry, Lars Hesselgren et al. (Ed.). Klein Publ . Ltd , 140--165. Eike Schling, Martin Kilian, Hui Wang, Denis Schikore, and Helmut Pottmann. 2018. Design and construction of curved support structures with repetitive parameters. In Adv. in Architectural Geometry, Lars Hesselgren et al. (Ed.). Klein Publ. Ltd, 140--165."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601213"},{"key":"e_1_2_2_26_1","volume-title":"Proceedings Int. Symposium on Conceptual Design of Structures, Madrid.","author":"Tellier Xavier","year":"2019","unstructured":"Xavier Tellier , Cyril Douthe , Laurent Hauswirth , and Olivier Baverel . 2019 . Linear Weingarten surfaces for conceptual design of double-curvature envelopes . In Proceedings Int. Symposium on Conceptual Design of Structures, Madrid. Xavier Tellier, Cyril Douthe, Laurent Hauswirth, and Olivier Baverel. 2019. Linear Weingarten surfaces for conceptual design of double-curvature envelopes. In Proceedings Int. Symposium on Conceptual Design of Structures, Madrid."},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100072765"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(95)00046-1"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01369665"},{"key":"e_1_2_2_30_1","volume-title":"\u00dcber eine Klasse aufeinander abwickelbarer Fl\u00e4chen. J. reine u. angewandte Mathematik 59","author":"Weingarten Julius","year":"1861","unstructured":"Julius Weingarten . 1861. \u00dcber eine Klasse aufeinander abwickelbarer Fl\u00e4chen. J. reine u. angewandte Mathematik 59 ( 1861 ), 382--393. Julius Weingarten. 1861. \u00dcber eine Klasse aufeinander abwickelbarer Fl\u00e4chen. J. reine u. angewandte Mathematik 59 (1861), 382--393."},{"key":"e_1_2_2_31_1","volume-title":"Quintic parametric polynomial minimal surfaces and their properties. Differential Geometry and its Applications 28, 6","author":"Xu Gang","year":"2010","unstructured":"Gang Xu and Guozhao Wang . 2010. Quintic parametric polynomial minimal surfaces and their properties. Differential Geometry and its Applications 28, 6 ( 2010 ), 697 -- 704. Gang Xu and Guozhao Wang. 2010. Quintic parametric polynomial minimal surfaces and their properties. Differential Geometry and its Applications 28, 6 (2010), 697 -- 704."},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.02.065"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3450626.3459939","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3450626.3459939","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:17:21Z","timestamp":1750191441000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3450626.3459939"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,19]]},"references-count":31,"aliases":["10.1145\/3476576.3476680"],"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,8,31]]}},"alternative-id":["10.1145\/3450626.3459939"],"URL":"https:\/\/doi.org\/10.1145\/3450626.3459939","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,19]]},"assertion":[{"value":"2021-07-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}