{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T02:12:37Z","timestamp":1774059157917,"version":"3.50.1"},"reference-count":26,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T00:00:00Z","timestamp":1597190400000},"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":[[2020,8,31]]},"abstract":"<jats:p>\n            I present a formulation for Rigid Body Dynamics that is independent of the dimension of the space. I describe the state and equations of motion of rigid bodies using geometric algebra. Using collision detection algorithms extended to\n            <jats:italic toggle=\"yes\">n<\/jats:italic>\n            D I resolve collisions and contact between bodies. My implementation is 4D, but the techniques described here apply to any number of dimensions. I display these four-dimensional rigid bodies by taking a three-dimensional slice through them. I allow the user to manipulate these bodies in real-time.\n          <\/jats:p>","DOI":"10.1145\/3386569.3392483","type":"journal-article","created":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T11:44:27Z","timestamp":1597232667000},"update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["<i>N<\/i>\n            -dimensional rigid body dynamics"],"prefix":"10.1145","volume":"39","author":[{"given":"Marc","family":"ten Bosch","sequence":"first","affiliation":[{"name":"mtb design works, Inc."}]}],"member":"320","published-online":{"date-parts":[[2020,8,12]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Flatland: A Romance of Many Dimensions","author":"Abbott E.A.","year":"1884","unstructured":"E.A. Abbott. 1884. Flatland: A Romance of Many Dimensions. Seeley & Co."},{"key":"e_1_2_2_2_1","volume-title":"Computer Graphics, and Higher Dimensions","author":"Banchoff T.","unstructured":"T. Banchoff. 1990. Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions. Scientific American Library. https:\/\/books.google.com\/books?id=8n55QgAACAAJ"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12272"},{"key":"e_1_2_2_4_1","unstructured":"Jonathan Blow and Atman J Binstock. 2004. How to find the inertia tensor (or other mass properties) of a 3D solid body represented by a triangle mesh. (2004). http:\/\/number-none.com\/blow\/inertia\/"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/70.56661"},{"key":"e_1_2_2_6_1","volume-title":"Physics for Game Programmers : Numerical Methods. (2015). https:\/\/www.gdcvault.com\/play\/1022197\/Physics-for-Game-Programmers-Numerical Presentation at Game Developers Conference","author":"Catto Erin","year":"2015","unstructured":"Erin Catto. 2015. Physics for Game Programmers : Numerical Methods. (2015). https:\/\/www.gdcvault.com\/play\/1022197\/Physics-for-Game-Programmers-Numerical Presentation at Game Developers Conference 2015."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1846.32.119"},{"key":"e_1_2_2_8_1","volume-title":"GL4D: A GPU-based Architecture for Interactive 4D Visualization","author":"Chu Alan","year":"2009","unstructured":"Alan Chu, Chi-Wing Fu, Andrew J. Hanson, and Pheng-Ann Heng. 2009. GL4D: A GPU-based Architecture for Interactive 4D Visualization. IEEE Transactions on Visualization and Computer Graphics (IEEE Visualization 2009) 15, 6 (Nov.-Dec. 2009), 1587--1594."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1006\/icar.1996.0243"},{"key":"e_1_2_2_10_1","volume-title":"Geometric algebra for physicists","author":"Doran Chris","unstructured":"Chris Doran and Anthony Lasenby. 2003. Geometric algebra for physicists. Cambridge University Press."},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"L. Dorst D. Fontijne and S. Mann. 2009. Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry. Elsevier. https:\/\/books.google.com\/books?id=yaEqlAEACAAJ","DOI":"10.1016\/B978-0-12-374942-0.00006-3"},{"key":"e_1_2_2_12_1","volume-title":"Dynamic collision detection using oriented bounding boxes. Geometric Tools","author":"Eberly David","year":"2002","unstructured":"David Eberly. 2002. Dynamic collision detection using oriented bounding boxes. Geometric Tools, Inc (2002)."},{"key":"e_1_2_2_13_1","volume-title":"Real-Time Collision Detection","author":"Ericson Christer","unstructured":"Christer Ericson. 2004. Real-Time Collision Detection. CRC Press, Inc., USA."},{"key":"e_1_2_2_14_1","unstructured":"Stefan Gottschalk. 1996. Separating axis theorem Technical Report TR96-024 Department of Computer Science UNC Chapel Hill. (1996)."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1201775.882358"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.14279\/depositonce-3058"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3305366.3328099"},{"key":"e_1_2_2_18_1","unstructured":"D. Hilbert and S. Cohn-Vossen. 1952. Anschauliche Geometrie. Chelsea Publishing Company. https:\/\/books.google.com\/books?id=d6sBd9h1HbMC"},{"key":"e_1_2_2_19_1","unstructured":"A. Macdonald. 2011. Linear and Geometric Algebra. Alan Macdonald. https:\/\/books.google.com\/books?id=oxhJYgEACAAJ"},{"key":"e_1_2_2_20_1","volume-title":"Geometric Algebra with Applications in Engineering","author":"Perwass Christian","unstructured":"Christian Perwass. 2009. Geometric Algebra with Applications in Engineering (1st ed.). Springer Publishing Company, Incorporated.","edition":"1"},{"key":"e_1_2_2_21_1","unstructured":"Louis Poinsot. 1851. Th\u00e9orie nouvelle de la rotation des corps. Bachelier."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2004.1321"},{"key":"e_1_2_2_23_1","unstructured":"Marc ten Bosch. 2017. 4D Toys. https:\/\/4dtoys.com"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.7151\/dmgaa.1028"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/MC.2012.77"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/11919476_24"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3386569.3392483","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3386569.3392483","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T05:37:36Z","timestamp":1750829856000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3386569.3392483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,12]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,8,31]]}},"alternative-id":["10.1145\/3386569.3392483"],"URL":"https:\/\/doi.org\/10.1145\/3386569.3392483","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,12]]},"assertion":[{"value":"2020-08-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}