{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:41:22Z","timestamp":1771702882692,"version":"3.50.1"},"reference-count":83,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2008,10,1]],"date-time":"2008-10-01T00:00:00Z","timestamp":1222819200000},"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":[[2008,10]]},"abstract":"<jats:p>The spatial deformation methods are a family of modeling and animation techniques for indirectly reshaping an object by warping the surrounding space, with results that are similar to molding a highly malleable substance. They have the virtue of being computationally efficient (and hence interactive) and applicable to a variety of object representations.<\/jats:p>\n          <jats:p>In this article we survey the state of the art in spatial deformation. Since manipulating ambient space directly is infeasible, deformations are controlled by tools of varying dimension\u2014points, curves, surfaces and volumes\u2014and it is on this basis that we classify them. Unlike previous surveys that concentrate on providing a single underlying mathematical formalism, we use the user-centered criteria of versatility, ease of use, efficiency and correctness to compare techniques.<\/jats:p>","DOI":"10.1145\/1409625.1409629","type":"journal-article","created":{"date-parts":[[2008,11,6]],"date-time":"2008-11-06T13:49:43Z","timestamp":1225979383000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":99,"title":["A survey of spatial deformation from a user-centered perspective"],"prefix":"10.1145","volume":"27","author":[{"given":"James","family":"Gain","sequence":"first","affiliation":[{"name":"University of Cape Town"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dominique","family":"Bechmann","sequence":"additional","affiliation":[{"name":"LSIIT, University of Strasbourg"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,11,4]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the 12th Pacific Conference on Computer Graphics and Applications (PG'04)","author":"Angelidis A."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/998687.1007036"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2005.08.002"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00142"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(97)00040-X"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/964965.808573"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-8493(94)90071-X"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of EUROGRAPHICS'. State of the Art Reports (STARs).","author":"Bechmann D.","year":"1998"},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of Computer Networks and ISDN Systems (Compugraphics'96)","author":"Bechmann D."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/vis.4340040305"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/vis.4340060104"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/776350.776353"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-002-0191-x"},{"key":"e_1_2_1_14_1","volume-title":"Numerical Control: Mathematics and Applications","author":"Bezier P.","year":"1972"},{"key":"e_1_2_1_15_1","volume-title":"Proceedings of Pacific Graphics. 49--61","author":"Blanc C."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/357346.357349"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195991000281"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/176579.176581"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2005.00886.x"},{"key":"e_1_2_1_20_1","unstructured":"Boullion T. L. and Odell P. L. 1971. Generalized Inverse Matrix. Wiley Interscience New York.  Boullion T. L. and Odell P. L. 1971. Generalized Inverse Matrix. Wiley Interscience New York."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566622"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(78)90110-0"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/74334.74358"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192220"},{"key":"e_1_2_1_25_1","volume-title":"Computer Graphics","author":"Comninos P."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/97880.97900"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/127719.122720"},{"key":"e_1_2_1_28_1","unstructured":"Crespin B. 1999. Implicit free-form deformations. In Implicit Surfaces. 17--23.  Crespin B. 1999. Implicit free-form deformations. In Implicit Surfaces. 17--23."},{"key":"e_1_2_1_29_1","first-page":"181","article-title":"Free-form deformation as an interactive modeling tool","volume":"17","author":"Davis O. R.","year":"1991","journal-title":"J. Imag. Tech."},{"key":"e_1_2_1_30_1","volume-title":"Proceedings of Graphics Interface. 55--60","author":"Decaudin P.","year":"1996"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/2945.620488"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(90)90036-Q"},{"key":"e_1_2_1_33_1","volume-title":"Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide","author":"Farin G.","edition":"4"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-8493(96)00025-8"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-005-0351-x"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2005.36"},{"key":"e_1_2_1_38_1","volume-title":"Proceedings of Eurographics, 7--18","author":"Gain J. E."},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/311625.312132"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/2945.965344"},{"key":"e_1_2_1_41_1","unstructured":"Greissmair J. and Purgathofer W. 1989. Deformation of solids with trivariate B-Splines. Comput. Graph. Forum 137--148.  Greissmair J. and Purgathofer W. 1989. Deformation of solids with trivariate B-Splines. Comput. Graph. Forum 137--148."},{"key":"e_1_2_1_42_1","series-title":"SIAM Revue II, 15--22","volume-title":"Some applications of the pseudo-inverse of a matrix","author":"Greville T."},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4485(98)00019-0"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/304012.304036"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/142920.134036"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1007\/s003710100114"},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1080\/10867651.2000.10487521"},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073229"},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.1130059"},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/1230100.1230107"},{"key":"e_1_2_1_51_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2006.03.014"},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(86)90039-7"},{"key":"e_1_2_1_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/781606.781641"},{"key":"e_1_2_1_54_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.329096"},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(94)90103-1"},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218501"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882323"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060244.1060255"},{"key":"e_1_2_1_59_1","doi-asserted-by":"crossref","unstructured":"MacCracken R. and Joy K. I. 1996. Free-form deformations with lattices of arbitrary topology. Comput. Graph. 181--188.  MacCracken R. and Joy K. I. 1996. Free-form deformations with lattices of arbitrary topology. Comput. Graph. 181--188.","DOI":"10.1145\/237170.237247"},{"key":"e_1_2_1_60_1","volume-title":"Blendeforming: Ray traceable localized flodover-free space deformation. Comput. Graph. Int. 183--190.","author":"Mason D.","year":"2001"},{"key":"e_1_2_1_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183294"},{"key":"e_1_2_1_62_1","volume-title":"Proceedings of the 12th Spring Conference on Computer Graphics. 183--191","author":"Mikita M.","year":"1996"},{"key":"e_1_2_1_63_1","doi-asserted-by":"publisher","DOI":"10.1145\/504789.504791"},{"key":"e_1_2_1_65_1","volume-title":"Proceedings of the Conference on Computer Animation. IEEE Computer Society, 93--102","author":"Moccozet L."},{"key":"e_1_2_1_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/1201775.882308"},{"key":"e_1_2_1_67_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276429"},{"key":"e_1_2_1_69_1","volume-title":"Proceedings of IEEE Cyberworlds. IEEE Computer Society, 472--479","author":"Ono Y."},{"key":"e_1_2_1_71_1","volume-title":"Proceedings of the Conference on Computer Animation. IEEE Computer Society, 87--93","author":"Peng Q."},{"key":"e_1_2_1_72_1","volume-title":"Proceedings of Shape Modeling International. 165--174","author":"Pernot J.-P."},{"key":"e_1_2_1_73_1","doi-asserted-by":"publisher","DOI":"10.1007\/s003710050005"},{"key":"e_1_2_1_74_1","doi-asserted-by":"publisher","DOI":"10.1145\/218013.218086"},{"key":"e_1_2_1_75_1","first-page":"2","article-title":"Introduction to the special issue on interactive sculpting","volume":"13","author":"Rossignac J.","year":"1994","journal-title":"ACM Trans. Graph."},{"key":"e_1_2_1_76_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-8493(94)00122-F"},{"key":"e_1_2_1_77_1","volume-title":"Proceedings of the 12th Pacific Conference on Computer Graphics and Applications (PG '04)","author":"Schein S."},{"key":"e_1_2_1_78_1","doi-asserted-by":"publisher","DOI":"10.1109\/MC.1983.1654471"},{"key":"e_1_2_1_79_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882295"},{"key":"e_1_2_1_80_1","doi-asserted-by":"publisher","DOI":"10.1145\/15886.15903"},{"key":"e_1_2_1_81_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280946"},{"key":"e_1_2_1_82_1","volume-title":"Proceedings of Graphies Interface. 35--42","author":"Singh K."},{"key":"e_1_2_1_83_1","doi-asserted-by":"publisher","DOI":"10.1145\/364338.364382"},{"key":"e_1_2_1_84_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-004-0277-8"},{"key":"e_1_2_1_85_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1142002"},{"key":"e_1_2_1_86_1","doi-asserted-by":"publisher","DOI":"10.1109\/PG.2007.22"},{"key":"e_1_2_1_87_1","doi-asserted-by":"publisher","DOI":"10.1145\/545261.545283"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1409625.1409629","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1409625.1409629","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:29:53Z","timestamp":1750253393000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1409625.1409629"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,10]]},"references-count":83,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,10]]}},"alternative-id":["10.1145\/1409625.1409629"],"URL":"https:\/\/doi.org\/10.1145\/1409625.1409629","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,10]]},"assertion":[{"value":"2006-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-11-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}