{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:20:38Z","timestamp":1698538838692},"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":[[1993,12]]},"abstract":"<jats:p> The main concern of this paper is the detection of double contact configurations for some polygons moving in translation in a polygonal environment. We first establish some general properties about such configurations and give conditions of existence of double contacts for two or three objects. <\/jats:p><jats:p> For three convex polygons moving in a polygonal environment or three simple polygons moving in a rectangle there always exists a double contact. Two examples without possibility of double contacts are given, one with three polygons (not convex) moving in a polygonal environment, and one with four convex polygons moving in a rectangle. We deduce an algorithm detecting a double contact position in time O(n<jats:sup>2<\/jats:sup>) (resp. O(n<jats:sup>3<\/jats:sup>)) for two (resp. three) convex polygons of constant sizes moving in a non-convex polygon of size n. <\/jats:p>","DOI":"10.1142\/s0218195993000270","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T03:29:30Z","timestamp":1101180570000},"page":"429-442","source":"Crossref","is-referenced-by-count":1,"title":["SIMULTANEOUS CONTAINMENT OF SEVERAL POLYGONS: ANALYSIS OF THE CONTACT CONFIGURATIONS"],"prefix":"10.1142","volume":"03","author":[{"given":"OLIVIER","family":"DEVILLERS","sequence":"first","affiliation":[{"name":"INRIA, B.P. 93 06561 Sophia-Antipolis cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195993000270","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:36:42Z","timestamp":1565192202000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195993000270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":0,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,12]]}},"alternative-id":["10.1142\/S0218195993000270"],"URL":"https:\/\/doi.org\/10.1142\/s0218195993000270","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}