{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T08:16:03Z","timestamp":1774685763114,"version":"3.50.1"},"reference-count":46,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T00:00:00Z","timestamp":1690329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>We consider motion effected by shape change. Such motions are ubiquitous in nature and the human made environment, ranging from single cells to platform divers and jellyfish. The shapes may be immersed in various media ranging from the very viscous to air and nearly inviscid fluids. In the absence of external forces these settings are characterized by constant momentum. We exploit this in an algorithm which takes a sequence of changing shapes, say, as modeled by an animator, as input and produces corresponding motion in world coordinates. Our method is based on the geometry of shape change and an appropriate variational principle. The corresponding Euler-Lagrange equations are first order ODEs in the unknown rotations and translations and the resulting time stepping algorithm applies to all these settings without modification as we demonstrate with a broad set of examples.<\/jats:p>","DOI":"10.1145\/3592417","type":"journal-article","created":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T14:29:21Z","timestamp":1690381761000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Motion from Shape Change"],"prefix":"10.1145","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7970-5596","authenticated-orcid":false,"given":"Oliver","family":"Gross","sequence":"first","affiliation":[{"name":"TU Berlin, Berlin, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4023-5026","authenticated-orcid":false,"given":"Yousuf","family":"Soliman","sequence":"additional","affiliation":[{"name":"California Institute of Technology, Pasadena, United States of America"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8962-9355","authenticated-orcid":false,"given":"Marcel","family":"Padilla","sequence":"additional","affiliation":[{"name":"TU Berlin, Berlin, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0191-2859","authenticated-orcid":false,"given":"Felix","family":"Kn\u00f6ppel","sequence":"additional","affiliation":[{"name":"TU Berlin, Berlin, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2087-6435","authenticated-orcid":false,"given":"Ulrich","family":"Pinkall","sequence":"additional","affiliation":[{"name":"TU Berlin, Berlin, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0323-7674","authenticated-orcid":false,"given":"Peter","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"California Institute of Technology, Pasadena, United States of America"}]}],"member":"320","published-online":{"date-parts":[[2023,7,26]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Numerical Geometry of Non-rigid Shapes","author":"Bronstein Alexander M.","unstructured":"Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel. 2008. Numerical Geometry of Non-rigid Shapes. Springer."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925899"},{"key":"e_1_2_2_3_1","unstructured":"Daniel Daye. 2019. Rigged and Animated Scan of Timber Rattlesnake. https:\/\/sketchfab.com\/. CC Attribution-NonCommercial."},{"key":"e_1_2_2_4_1","doi-asserted-by":"crossref","unstructured":"J. Elgeti R. G. Winkler and G. Gompper. 2015. Physics of Microswimmers---Single Particle Motion and Collective Behavior: a Review. Rep. Prog. Phys. 78 (2015).","DOI":"10.1088\/0034-4885\/78\/5\/056601"},{"key":"e_1_2_2_5_1","unstructured":"Leonhard Euler. 1744. Methodus Inveniendi Lineas Curvas Maximi Minive Proprietate Gaudentes. Bousquet Lausanne & Geneva. English translation at WikiSource."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1119\/1.11759"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0380-154"},{"key":"e_1_2_2_8_1","unstructured":"Graphics & Extended Reality Lab. 2022. Large Whip Snake. https:\/\/sketchfab.com\/. CC Attribution."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.32.4.802"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0525"},{"key":"e_1_2_2_11_1","volume-title":"Explicit, Implicit, Symplectic. In Encyclopedia of Applied and Computational Mathematics, Bj\u00f6rn Engquist (Ed.)","author":"Hairer Ernst","unstructured":"Ernst Hairer and Gerhard Wanner. 2015. Euler Methods, Explicit, Implicit, Symplectic. In Encyclopedia of Applied and Computational Mathematics, Bj\u00f6rn Engquist (Ed.). Springer, 451--455."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0812533106"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2516971.2516976"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7683(69)90086-9"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-004-0650-9"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1870.71.237"},{"key":"e_1_2_2_17_1","unstructured":"Gustav Kirchhoff. 1876. Vorlesungen \u00fcber mathematische Physik. Teubner 233--250."},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8928(01)00063-6"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00291937"},{"key":"e_1_2_2_21_1","volume-title":"Course of Theoretical Physics","volume":"1","author":"Landau L. D.","unstructured":"L. D. Landau and E. M. Lifshitz. 1976. Mechanics (third ed.). Course of Theoretical Physics, Vol. 1. Butterworth Heinemann."},{"key":"e_1_2_2_22_1","volume-title":"Powers","author":"Lauga Eric","year":"2009","unstructured":"Eric Lauga and Thomas R. Powers. 2009. The Hydrodynamics of Swimming Microorganisms. Rep. Prog. Phys. 72, 096601 (2009), 36pp."},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.108"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2011.08.010"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1038\/051080a0"},{"key":"e_1_2_2_26_1","volume-title":"Marsden and Matthew West","author":"Jerrold","year":"2001","unstructured":"Jerrold E. Marsden and Matthew West. 2001. Discrete Mechanics and Variational Integrators. Act. Num. 10 (May 2001), 357--514."},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/54852.378508"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356497"},{"key":"e_1_2_2_29_1","volume-title":"Dynamics and Control of Mechanical Systems","author":"Montgomery R.","unstructured":"R. Montgomery. 1993. Dynamics and Control of Mechanical Systems; The Falling Cat and Related Problems. Number 1 in Fields Inst. Commun. Fields Institute, Chapter Gauge Theory of the Falling Cat, 193--218."},{"key":"e_1_2_2_30_1","volume-title":"235--257. Engl. translation https:\/\/arxiv.org\/abs\/physics\/0503066","author":"Noether Emmy","year":"1918","unstructured":"Emmy Noether. 1918. Invariante Variationsprobleme. Nachr. K\u00f6nig. Ges. Wiss. Math. Phys. Klasse (1918), 235--257. Engl. translation https:\/\/arxiv.org\/abs\/physics\/0503066.."},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700701"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322962"},{"key":"e_1_2_2_33_1","unstructured":"Louis Poinsot. 1851. Th\u00e9orie Nouvelle de la Rotation des Corps. Bachelier."},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1119\/1.10903"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-09351-2"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1808675116"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211208900025X"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1119\/1.15986"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s1-4.1.357"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964953"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192170"},{"key":"e_1_2_2_42_1","volume-title":"Life in Moving Fluids","author":"Vogel Steven","unstructured":"Steven Vogel. 1983. Life in Moving Fluids (2nd ed.). Princeton University Press.","edition":"2"},{"key":"e_1_2_2_43_1","volume-title":"Wissenschaftliche Abhandlungen.","author":"von Helmholtz Hermann","unstructured":"Hermann von Helmholtz. 1882. Zur Theorie der station\u00e4ren Str\u00f6me in reibenden Fl\u00fcssigkeiten. In Wissenschaftliche Abhandlungen. Vol. I. J. A. Barth, 223--230."},{"key":"e_1_2_2_44_1","first-page":"1","article-title":"Limbless Movement Simulation with a Particle-Based","volume":"29","author":"Waszak Barlomiej","year":"2018","unstructured":"Barlomiej Waszak. 2018. Limbless Movement Simulation with a Particle-Based System. Comp. Anim. Virt. Worlds 29, 2 (2018), 1--21.","journal-title":"System. Comp. Anim. Virt. Worlds"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185600"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.1510003"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882360"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3592417","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3592417","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:48:59Z","timestamp":1750182539000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3592417"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,26]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1145\/3592417"],"URL":"https:\/\/doi.org\/10.1145\/3592417","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,26]]},"assertion":[{"value":"2023-07-26","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}