{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:42:27Z","timestamp":1758814947410},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1999,4]]},"abstract":"<jats:p>Let shape P be any simply-connected set in the plane, bounded by a Jordan curve, that is not a circular disk. We say that a set of points I on the boundary of P immobilize the shape if any rigid motion of P in the plane causes at least one point of I to penetrate the interior of P. We prove that four points always suffice to immobilize any shape. For a large class of shapes, which includes polygons without parallel edges, three points are sufficient to immobilize. An O(n log \u00a0n) algorithm is given that finds a set 3 points that immobilize a given polygon without parallel edges. The algorithm becomes linear for convex polygons. Some results are generalized for d-dimensional polytopes, where 2d points are always sufficient and sometimes necessary to immobilize.<\/jats:p>","DOI":"10.1142\/s0218195999000133","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T06:35:01Z","timestamp":1053585301000},"page":"181-206","source":"Crossref","is-referenced-by-count":26,"title":["IMMOBILIZING A SHAPE"],"prefix":"10.1142","volume":"09","author":[{"given":"JUREK","family":"CZYZOWICZ","sequence":"first","affiliation":[{"name":"D\u00e9partement d' Informatique, Universit\u00e9 du Qu\u00e9bec \u00e0 Hull, Hull, Qu\u00e9bec, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"IVAN","family":"STOJMENOVIC","sequence":"additional","affiliation":[{"name":"Computer Science Department, University of Ottawa, Ottawa, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JORGE","family":"URRUTIA","sequence":"additional","affiliation":[{"name":"Computer Science Department, University of Ottawa, Ottawa, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187749"},{"key":"p_3","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1515\/9780773591134-050","author":"Czyzowicz J.","year":"1996","journal-title":"Proc. 8-th Canadian Conference on Computational Geometry, Ottawa"},{"key":"p_4","first-page":"41","author":"Czyzowicz J.","year":"1991","journal-title":"Proc. 3rd Canad. Conf. on Comput. Geometry"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900102"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1177\/027836498900800202"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1109\/21.35342"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1145\/379139.379167"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187890"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195999000133","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,6]],"date-time":"2024-01-06T01:53:45Z","timestamp":1704506025000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195999000133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,4]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,4]]}},"alternative-id":["10.1142\/S0218195999000133"],"URL":"https:\/\/doi.org\/10.1142\/s0218195999000133","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,4]]}}}