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For surface deformation, commonly used energies contain an implicit bending penalty. We present a natural, continuous generalization that incorporates multiple ARAP versions with an implicit, user\u2010controllable bending penalty. We discretize an intuitive variant of the energy and demonstrate that it is independent of mesh resolution and produces comparable results to those of competing methods that include an explicit bending penalty term. We validate our method and demonstrate that, despite its computational overhead, it converges among the fastest of all ARAP variants.<\/jats:p>","DOI":"10.1111\/cgf.70520","type":"journal-article","created":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:17:20Z","timestamp":1786619840000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Bending in the As\u2010Rigid\u2010As\u2010Possible Deformation Energy"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7098-1524","authenticated-orcid":false,"given":"Ugo","family":"Finnendahl","sequence":"first","affiliation":[{"name":"TU Berlin  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9854-8466","authenticated-orcid":false,"given":"Marc","family":"Alexa","sequence":"additional","affiliation":[{"name":"TU Berlin  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,13]]},"reference":[{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03171.x"},{"key":"e_1_2_10_3_2","unstructured":"Br\u00f6nnimann Herv\u00e9 Fabri Andreas Giezeman Geert-Jan Hert Susan Hoffmann Michael Kettner Lutz Pion Sylvain andSchirra Stefan.2D and 3D Linear Geometry Kernel.20238."},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/1833349.1778775"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14790"},{"key":"e_1_2_10_7_2","unstructured":"Guennebaud Ga\u00ebl Jacob Beno\u00eet et al.Eigen v3.http:\/\/eigen.tuxfamily.org.20107."},{"key":"e_1_2_10_8_2","unstructured":"Jacobson Alec Panozzo Daniele et al.libigl: A simple C++ geometry processing library.https:\/\/libigl.github.io\/.20187."},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2359463"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01290.x"},{"key":"e_1_2_10_11_2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/978-3-662-05105-4_2","volume-title":"Visualization and Mathematics III","author":"Meyer Mark","year":"2003"},{"issue":"1","key":"e_1_2_10_12_2","first-page":"198","article-title":"Higher Order Continuity for Smooth As-Rigid-As-Possible Shape Modeling","volume":"14","author":"Oehri Annika","year":"2025","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"key":"e_1_2_10_13_2","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/978-3-662-05105-4_6","volume-title":"Visualization and Mathematics III","author":"Polthier Konrad","year":"2003"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1993.10504266"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1201\/9780849384165"},{"key":"e_1_2_10_16_2","first-page":"109","volume-title":"Proceedings of the Fifth Eurographics Symposium on Geometry Processing","author":"Sorkine Olga","year":"2007"},{"key":"e_1_2_10_17_2","unstructured":"Sharp Nicholas Crane Keenan et al.geometry-central.www.geometry-central.net.20198."},{"key":"e_1_2_10_18_2","unstructured":"Sorkine-Hornung OlgaandRabinovich Michael.Least-Squares Rigid Motion Using SVD. 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