{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T02:37:03Z","timestamp":1648867023716},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p> In 1926, Jarn\u00edk investigated the drawing of a curve that visits a large number of lattice points relative to its curvature. To this end, he constructed a convex n-gon with vertices on a \u201csmall\u201d integer grid [0, c.n<jats:sup>3\/2<\/jats:sup>]<jats:sup>2<\/jats:sup>, where c &gt; 0 is a constant, and proved that this grid size is optimal up to a constant factor. We consider a similar construction for the double circle of 2n points and prove that it can be embedded in a grid of the same asymptotic size. Moreover, we give an O(n)-time algorithm to generate the corresponding point set. <\/jats:p>","DOI":"10.1142\/s0218195914600061","type":"journal-article","created":{"date-parts":[[2015,3,17]],"date-time":"2015-03-17T07:21:38Z","timestamp":1426576898000},"page":"247-258","source":"Crossref","is-referenced-by-count":2,"title":["EMBEDDING THE DOUBLE CIRCLE IN A SQUARE GRID OF MINIMUM SIZE"],"prefix":"10.1142","volume":"24","author":[{"given":"S.","family":"BEREG","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Texas, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"FABILA-MONROY","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, CINVESTAV, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"FLORES-PE\u00d1ALOZA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, UNAM, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. A.","family":"LOPEZ","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Denver, Denver, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"P\u00c9REZ-LANTERO","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Civil en Inform\u00e1tica, Universidad de Valpara\u00edso, Valparaiso, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,3,16]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2004.02.003"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1963-0143105-7"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-010-0816-0"},{"issue":"2","key":"p_4","first-page":"171","volume":"24","author":"B\u00e1r\u00e1ny I.","journal-title":"Combinatorica"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1137\/0212032"},{"key":"p_7","first-page":"169","volume":"45","author":"Hurtado F.","year":"1997","journal-title":"Ars Combinatoria"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01216795"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-03-03219-7"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195914600061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:47:12Z","timestamp":1565124432000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195914600061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9]]},"references-count":8,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,3,16]]},"published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.1142\/S0218195914600061"],"URL":"https:\/\/doi.org\/10.1142\/s0218195914600061","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9]]}}}