{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T10:28:50Z","timestamp":1761560930382},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1991,12]]},"abstract":"<jats:p> This paper presents a new technique for computing space deformations that interpolate a set of user-defined constraints. Constraints are specified by indicating the images of selected points. The deformation is formulated as the product of a polynomial function f of \u211d<jats:sup>n<\/jats:sup> into a higher-dimensional space, \u211d<jats:sup>m<\/jats:sup>, with a linear projection from \u211d<jats:sup>m<\/jats:sup> back to \u211d<jats:sup>n<\/jats:sup>. The projection matrix is computed using a pseudo-inverse technique. For sufficient m, the degrees of freedom may be used to optimize potential functions controlled by attracting and repulsing points. A prototype implementation is presented, which demonstrates the application of this technique to the interactive design of free-form shapes (when n=3) and of deformation processes in space-time domain (when n=4). <\/jats:p>","DOI":"10.1142\/s0218195991000281","type":"journal-article","created":{"date-parts":[[2004,11,27]],"date-time":"2004-11-27T01:43:01Z","timestamp":1101519781000},"page":"427-453","source":"Crossref","is-referenced-by-count":37,"title":["DEFORMATION OF N-DIMENSIONAL OBJECTS"],"prefix":"10.1142","volume":"01","author":[{"given":"PAUL","family":"BORREL","sequence":"first","affiliation":[{"name":"Interactive Geometric Modeling, IBM Research Division, Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DOMINIQUE","family":"BECHMANN","sequence":"additional","affiliation":[{"name":"D\u00e9partement d'lnformatique, Universit\u00e9 Louis Pasteur, 7. rue Ren\u00e9 Descartes, 67084 Strasbourg cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195991000281","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:33:49Z","timestamp":1565130829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195991000281"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,12]]},"references-count":0,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[1991,12]]}},"alternative-id":["10.1142\/S0218195991000281"],"URL":"https:\/\/doi.org\/10.1142\/s0218195991000281","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,12]]}}}