{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:53:47Z","timestamp":1759838027995,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2011,5,1]],"date-time":"2011-05-01T00:00:00Z","timestamp":1304208000000},"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":[[2011,5]]},"abstract":"<jats:p>In this article we derive an equation for the velocity of an arbitrary time-evolving implicit surface. Strictly speaking, only the normal component of the velocity is unambiguously defined. This is because an implicit surface does not have a unique parametrization. However, by enforcing a constraint on the evolution of the normal field we obtain a unique tangential component. We apply our formulas to surface tracking and to the problem of computing velocity vectors of a motion blurred blobby surface. Other possible applications are mentioned at the end of the article.<\/jats:p>","DOI":"10.1145\/1966394.1966400","type":"journal-article","created":{"date-parts":[[2011,5,24]],"date-time":"2011-05-24T13:04:30Z","timestamp":1306242270000},"page":"1-7","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":20,"title":["On the velocity of an implicit surface"],"prefix":"10.1145","volume":"30","author":[{"given":"Jos","family":"Stam","sequence":"first","affiliation":[{"name":"Autodesk Research, Toronto, Ontario, Canada"}]},{"given":"Ryan","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Autodesk Research, Toronto, Ontario, Canada"}]}],"member":"320","published-online":{"date-parts":[[2011,5,19]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/357306.357310"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1268517.1268521"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/080737617"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7166"},{"key":"e_1_2_2_5_1","first-page":"18","article-title":"Marchingparticles: Fast generation of particles for the sampling of implicit surfaces","volume":"9","author":"Levet F.","year":"2007","unstructured":"Levet , F. , Granier , X. , and Schlick , C. 2007 . Marchingparticles: Fast generation of particles for the sampling of implicit surfaces . Comput. Graph. Geom. 9 , 1, 18 -- 49 . Levet, F., Granier, X., and Schlick, C. 2007. Marchingparticles: Fast generation of particles for the sampling of implicit surfaces. Comput. Graph. Geom. 9, 1, 18--49.","journal-title":"Comput. Graph. Geom."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/37402.37422"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70604"},{"key":"e_1_2_2_8_1","first-page":"394","article-title":"On the reciprocal of the general algebraic matrix","volume":"26","author":"Moore E. H.","year":"1920","unstructured":"Moore , E. H. 1920 . On the reciprocal of the general algebraic matrix . Bull. Amer. Math. Soc. 26 , 394 -- 395 . Moore, E. H. 1920. On the reciprocal of the general algebraic matrix. Bull. Amer. Math. Soc. 26, 394--395.","journal-title":"Bull. Amer. Math. Soc."},{"volume-title":"NSF\/DARPA CARGO Meeting.","author":"Mullan M.","key":"e_1_2_2_9_1","unstructured":"Mullan , M. , Whitaker , R. , and Hart , J . 2004. Procedural level sets . Presented at the NSF\/DARPA CARGO Meeting. Mullan, M., Whitaker, R., and Hart, J. 2004. Procedural level sets. Presented at the NSF\/DARPA CARGO Meeting."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-002-0181-z"},{"volume-title":"Proceedings of the Implicit Surfaces.","author":"Rodrian H.-C.","key":"e_1_2_2_11_1","unstructured":"Rodrian , H.-C. and Moock , H . 1996. Dynamic triangulation of animated skeleton-based implicit surfaces . In Proceedings of the Implicit Surfaces. Rodrian, H.-C. and Moock, H. 1996. Dynamic triangulation of animated skeleton-based implicit surfaces. In Proceedings of the Implicit Surfaces."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.1530289"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192227"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01900346"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1966394.1966400","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1966394.1966400","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:22:26Z","timestamp":1750245746000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1966394.1966400"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["10.1145\/1966394.1966400"],"URL":"https:\/\/doi.org\/10.1145\/1966394.1966400","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2011,5]]},"assertion":[{"value":"2010-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-05-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}