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Graph."],"published-print":{"date-parts":[[2020,10,31]]},"abstract":"<jats:p>\n            The unsigned p-Willmore functional introduced in the work of Mondino [2011] generalizes important geometric functionals, which measure the area and Willmore energy of immersed surfaces. Presently, techniques from the work of Dziuk [2008] are adapted to compute the first variation of this functional as a weak-form system of equations, which are subsequently used to develop a model for the p-Willmore flow of closed surfaces in R\n            <jats:sup>3<\/jats:sup>\n            . This model is amenable to constraints on surface area and enclosed volume and is shown to decrease the p-Willmore energy monotonically. In addition, a penalty-based regularization procedure is formulated to prevent artificial mesh degeneration along the flow; inspired by a conformality condition derived in the work of Kamberov et al. [1996], this procedure encourages angle-preservation in a closed and oriented surface immersion as it evolves. Following this, a finite-element discretization of both procedures is discussed, an algorithm for running the flow is given, and an application to mesh editing is presented.\n          <\/jats:p>","DOI":"10.1145\/3369387","type":"journal-article","created":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T22:12:02Z","timestamp":1597097522000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["Computational p-Willmore Flow with Conformal Penalty"],"prefix":"10.1145","volume":"39","author":[{"given":"Anthony","family":"Gruber","sequence":"first","affiliation":[{"name":"Texas Tech University, Lubbock, Texas"}]},{"given":"Eugenio","family":"Aulisa","sequence":"additional","affiliation":[{"name":"Texas Tech University, Lubbock, Texas"}]}],"member":"320","published-online":{"date-parts":[[2020,8,10]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1137\/S0895479899358194"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.1016\/j.parco.2005.07.004"},{"key":"e_1_2_1_3_1","first-page":"93","article-title":"Willmore-type energies and Willmore-type surfaces in space forms","volume":"18","author":"Athukorallage B.","year":"2015","journal-title":"JP J. Geom. Topol."},{"unstructured":"E. Aulisa S. Bna and G. Bornia. 2014. FEMuS Finite Element Multiphysics Solver. Retrieved from https:\/\/github.com\/eaulisa\/MyFEMuS.  E. Aulisa S. Bna and G. Bornia. 2014. FEMuS Finite Element Multiphysics Solver. Retrieved from https:\/\/github.com\/eaulisa\/MyFEMuS.","key":"e_1_2_1_4_1"},{"doi-asserted-by":"crossref","unstructured":"J. L. Barbosa M. Do Carmo and J. Eschenburg. 2012. Stability of hypersurfaces of constant mean curvature in Riemannian manifolds. In Manfredo P. do Carmo\u2013Selected Papers. Springer 291--306.  J. L. Barbosa M. Do Carmo and J. Eschenburg. 2012. Stability of hypersurfaces of constant mean curvature in Riemannian manifolds. In Manfredo P. do Carmo\u2013Selected Papers. Springer 291--306.","key":"e_1_2_1_5_1","DOI":"10.1007\/978-3-642-25588-5_22"},{"volume-title":"Discrete Differential Geometry","author":"Bobenko A.","key":"e_1_2_1_6_1"},{"volume-title":"ACM SIGGRAPH 2005 Courses. 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I a Mat.(NS) B"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3369387","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3369387","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:23:30Z","timestamp":1750202610000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3369387"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,10]]},"references-count":37,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,10,31]]}},"alternative-id":["10.1145\/3369387"],"URL":"https:\/\/doi.org\/10.1145\/3369387","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2020,8,10]]},"assertion":[{"value":"2019-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-08-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}