{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T02:16:23Z","timestamp":1774059383388,"version":"3.50.1"},"reference-count":51,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2009,7,27]],"date-time":"2009-07-27T00:00:00Z","timestamp":1248652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"publisher","award":["200021-117756"],"award-info":[{"award-number":["200021-117756"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"],"award-info":[{"award-number":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000145","name":"Division of Information and Intelligent Systems","doi-asserted-by":"publisher","award":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"],"award-info":[{"award-number":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"]}],"id":[{"id":"10.13039\/100000145","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000144","name":"Division of Computer and Network Systems","doi-asserted-by":"publisher","award":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"],"award-info":[{"award-number":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"]}],"id":[{"id":"10.13039\/100000144","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"],"award-info":[{"award-number":["MSPA Award No. IIS-05-28402CSR Award No. CNS-06-14770CAREER Award No. CCF-06-43268"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2009,7,27]]},"abstract":"<jats:p>\n            We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by customdesigned basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in\n            <jats:italic>enrichment textures<\/jats:italic>\n            , which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose\n            <jats:italic>harmonic enrichment functions<\/jats:italic>\n            to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of\n            <jats:italic>C<\/jats:italic>\n            <jats:sup>1<\/jats:sup>\n            continuous basis functions and thus allows for simpler,\n            <jats:italic>C<\/jats:italic>\n            <jats:sup>0<\/jats:sup>\n            continuous XFEM enrichment functions.\n          <\/jats:p>","DOI":"10.1145\/1531326.1531356","type":"journal-article","created":{"date-parts":[[2009,7,28]],"date-time":"2009-07-28T12:43:55Z","timestamp":1248785035000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":55,"title":["Enrichment textures for detailed cutting of shells"],"prefix":"10.1145","volume":"28","author":[{"given":"Peter","family":"Kaufmann","sequence":"first","affiliation":[{"name":"ETH Zurich"}]},{"given":"Sebastian","family":"Martin","sequence":"additional","affiliation":[{"name":"ETH Zurich"}]},{"given":"Mario","family":"Botsch","sequence":"additional","affiliation":[{"name":"Bielefeld University"}]},{"given":"Eitan","family":"Grinspun","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Markus","family":"Gross","sequence":"additional","affiliation":[{"name":"ETH Zurich"}]}],"member":"320","published-online":{"date-parts":[[2009,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2007.11.001"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(96)01087-0"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.39"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280821"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00325"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882364"},{"key":"e_1_2_2_9_1","volume-title":"Proc. of Symp. on Computer Animation '03","author":"Bridson R.","unstructured":"Bridson , R. , Marino , S. , and Fedkiw , R . 2003. Simulation of clothing with folds and wrinkles . In Proc. of Symp. on Computer Animation '03 , 28--36. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In Proc. of Symp. on Computer Animation '03, 28--36."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566624"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.200310088"},{"key":"e_1_2_2_13_1","first-page":"9","article-title":"Simulating 2D tearing phenomena for interactive medical surgery simulators","volume":"2000","author":"De Casson F. B.","year":"2000","unstructured":"De Casson , F. B. , and Laugier , C. 2000 . Simulating 2D tearing phenomena for interactive medical surgery simulators . In Computer Animation 2000 , 9 -- 14 . De Casson, F. B., and Laugier, C. 2000. Simulating 2D tearing phenomena for interactive medical surgery simulators. In Computer Animation 2000, 9--14.","journal-title":"Computer Animation"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-005-0317-z"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360665"},{"key":"e_1_2_2_16_1","volume-title":"Proc. of IEEE Computer Animation, 225--229","author":"Forest C.","unstructured":"Forest , C. , Delingette , H. , and Ayache , N . 2002. Removing tetrahedra from a manifold mesh . In Proc. of IEEE Computer Animation, 225--229 . Forest, C., Delingette, H., and Ayache, N. 2002. Removing tetrahedra from a manifold mesh. In Proc. of IEEE Computer Animation, 225--229."},{"key":"e_1_2_2_17_1","unstructured":"Gingold Y. Secord A. Han J. Y. Grinspun E. and Zorin D. 2004. A discrete model for inelastic deformation of thin shells. Tech. rep. Courant Institute of Mathematical Sciences New York University.  Gingold Y. Secord A. Han J. Y. Grinspun E. and Zorin D. 2004. A discrete model for inelastic deformation of thin shells. Tech. rep. Courant Institute of Mathematical Sciences New York University."},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276438"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2217"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566578"},{"key":"e_1_2_2_21_1","volume-title":"Proc. of Symp. on Computer Animation'03","author":"Grinspun E.","year":"2003","unstructured":"Grinspun , E. , Hirani , A. N. , Desbrun , M. , and Schr &amp;#246;der, P. 2003 . Discrete shells . In Proc. of Symp. on Computer Animation'03 , 62--67. Grinspun, E., Hirani, A. N., Desbrun, M., and Schr&amp;#246;der, P. 2003. Discrete shells. In Proc. of Symp. on Computer Animation'03, 62--67."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566589"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.52"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2003.08.001"},{"key":"e_1_2_2_25_1","volume-title":"The Finite Element Method. Linear Static and Dynamic Finite Element Analysis","author":"Hughes T. J. R.","unstructured":"Hughes , T. J. R. 2000. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis . Dover Publications . Hughes, T. J. R. 2000. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Dover Publications."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2009.32"},{"key":"e_1_2_2_27_1","volume-title":"Proc. of Symp. on Computer Animation, 105--115","author":"Kaufmann P.","unstructured":"Kaufmann , P. , Martin , S. , Botsch , M. , and Gross , M . 2008. Flexible simulation of deformable models using discontinuous Galerkin FEM . In Proc. of Symp. on Computer Animation, 105--115 . Kaufmann, P., Martin, S., Botsch, M., and Gross, M. 2008. Flexible simulation of deformable models using discontinuous Galerkin FEM. In Proc. of Symp. on Computer Animation, 105--115."},{"key":"e_1_2_2_28_1","unstructured":"Kaufmann P. Martin S. Botsch M. and Gross M. 2009. Implementation of discontinuous Galerkin Kirchhoff-Love shells. Tech. Rep. no. 622 Department of Computer Science ETH Zurich.  Kaufmann P. Martin S. Botsch M. and Gross M. 2009. Implementation of discontinuous Galerkin Kirchhoff-Love shells. Tech. Rep. no. 622 Department of Computer Science ETH Zurich."},{"key":"e_1_2_2_29_1","first-page":"1521","article-title":"Polyhedral finite elements using harmonic basis functions. Computer Graphics Forum (Proc","volume":"27","author":"Martin S.","year":"2008","unstructured":"Martin , S. , Kaufmann , P. , Botsch , M. , Wicke , M. , and Gross , M. 2008 . Polyhedral finite elements using harmonic basis functions. Computer Graphics Forum (Proc . of Symp. on Geometry Processing) 27 , 5, 1521 -- 1529 . Martin, S., Kaufmann, P., Botsch, M., Wicke, M., and Gross, M. 2008. Polyhedral finite elements using harmonic basis functions. Computer Graphics Forum (Proc. of Symp. on Geometry Processing) 27, 5, 1521--1529.","journal-title":"of Symp. on Geometry Processing)"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.429"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015734"},{"key":"e_1_2_2_33_1","volume-title":"Proc. of Virtual Reality Interactions and Physical Simulations.","year":"2008","unstructured":"M&amp;#252;ller, M. 2008 . Hierarchical position based dynamics . In Proc. of Virtual Reality Interactions and Physical Simulations. M&amp;#252;ller, M. 2008. Hierarchical position based dynamics. In Proc. of Virtual Reality Interactions and Physical Simulations."},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2008.01.018"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2489"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311550"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566579"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073296"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1283"},{"key":"e_1_2_2_40_1","volume-title":"Level Set Methods and Fast Marching Methods","author":"Sethian J.","unstructured":"Sethian , J. 1999. Level Set Methods and Fast Marching Methods . Cambridge University Press . Sethian, J. 1999. Level Set Methods and Fast Marching Methods. Cambridge University Press."},{"key":"e_1_2_2_41_1","volume-title":"Proc. of Symp. on Computer Animation, 73--80","author":"Sifakis E.","unstructured":"Sifakis , E. , Der , K. G. , and Fedkiw , R . 2007. Arbitrary cutting of deformable tetrahedralized objects . In Proc. of Symp. on Computer Animation, 73--80 . Sifakis, E., Der, K. G., and Fedkiw, R. 2007. Arbitrary cutting of deformable tetrahedralized objects. In Proc. of Symp. on Computer Animation, 73--80."},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-002-0391-2"},{"key":"e_1_2_2_43_1","volume-title":"Proc. of Symp. on Computer Animation, 63--72","author":"Steinemann D.","unstructured":"Steinemann , D. , Otaduy , M. A. , and Gross , M . 2006. Fast arbitrary splitting of deforming objects . In Proc. of Symp. on Computer Animation, 63--72 . Steinemann, D., Otaduy, M. A., and Gross, M. 2006. Fast arbitrary splitting of deforming objects. In Proc. of Symp. on Computer Animation, 63--72."},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/54852.378522"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/37401.37427"},{"key":"e_1_2_2_46_1","volume-title":"Proc. of Symp. on Computer Animation, 107--116","author":"Thomaszewski B.","unstructured":"Thomaszewski , B. , Wacker , M. , and Strasser , W . 2006. A consistent bending model for cloth simulation with corotational subdivision finite elements . In Proc. of Symp. on Computer Animation, 107--116 . Thomaszewski, B., Wacker, M., and Strasser, W. 2006. A consistent bending model for cloth simulation with corotational subdivision finite elements. In Proc. of Symp. on Computer Animation, 107--116."},{"key":"e_1_2_2_47_1","volume-title":"Taucs: A library of sparse linear solvers","author":"Toledo S.","year":"2003","unstructured":"Toledo , S. , Chen , D. , and Rotkin , V. , 2003 . Taucs: A library of sparse linear solvers . http:\/\/www.tau.ac.il\/~stoledo\/taucs. Toledo, S., Chen, D., and Rotkin, V., 2003. Taucs: A library of sparse linear solvers. http:\/\/www.tau.ac.il\/~stoledo\/taucs."},{"key":"e_1_2_2_48_1","doi-asserted-by":"crossref","unstructured":"Wempner G. and Talaslidis D. 2003. Mechanics of solids and shells: theories and approximations. CRC Press.  Wempner G. and Talaslidis D. 2003. Mechanics of solids and shells: theories and approximations . CRC Press.","DOI":"10.1201\/9781420036428"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2005.00891.x"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01058.x"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.849"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1531326.1531356","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1531326.1531356","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:30:23Z","timestamp":1750253423000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1531326.1531356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,27]]},"references-count":51,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,7,27]]}},"alternative-id":["10.1145\/1531326.1531356"],"URL":"https:\/\/doi.org\/10.1145\/1531326.1531356","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,27]]},"assertion":[{"value":"2009-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}