{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T13:16:20Z","timestamp":1760706980157},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1999,2]]},"abstract":"<jats:p> Let S be a set of points in the plane. The width (resp. roundness) of S is defined as the minimum width of any slab (resp. annulus) that contains all points of S. We give a new characterization of the width of a point set. Also, we give a rigorous proof of the fact that either the roundness of S is equal to the width of S, or the center of the minimum-width annulus is a vertex of the closest-point Voronoi diagram of S, the furthest-point Voronoi diagram of S, or an intersection point of these two diagrams. This proof corrects the characterization of roundness used extensively in the literature. <\/jats:p>","DOI":"10.1142\/s021819599900008x","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T06:35:01Z","timestamp":1053585301000},"page":"97-108","source":"Crossref","is-referenced-by-count":8,"title":["ON THE WIDTH AND ROUNDNESS OF A SET OF POINTS IN THE PLANE"],"prefix":"10.1142","volume":"09","author":[{"given":"MICHIEL","family":"SMID","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Magdeburg, D-39106 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RAVI","family":"JANARDHAN","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Univeristy of Minnesota, Minneapolis, MN\u00a055455, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","first-page":"358","author":"Agarwal P.K.","year":"1994","journal-title":"Proc. 10th Annu. ACM Sympos. Gomput Geom."},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02712871"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1994.1038"},{"key":"p_6","first-page":"139","author":"Garcia-Lopez J.","year":"1997","journal-title":"Proc Annu. ACM Sympos. Gomput. Geom."},{"key":"p_9","first-page":"129","author":"Mehlhorn K.","year":"1997","journal-title":"Proc. 13th Annu. ACM Sympos. Comput. Geom."},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02253130"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(95)00004-6"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819599900008X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:32:07Z","timestamp":1565137927000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819599900008X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,2]]},"references-count":7,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,2]]}},"alternative-id":["10.1142\/S021819599900008X"],"URL":"https:\/\/doi.org\/10.1142\/s021819599900008x","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,2]]}}}