{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T13:24:11Z","timestamp":1649165051760},"reference-count":9,"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":[[2007,8]]},"abstract":"<jats:p> Given two sets A and B of m non-crossing line segments in the plane, we show how to compute in O(m log m) time a data structure that uses O(m) storage and supports the following query in O( log m) time: Given a parabola \u03b3 : y = ax<jats:sup>2<\/jats:sup> + bx + c, does \u03b3 separate A and B? This structure can be used to build a data structure that stores a simple polygon and allows ray-shooting queries along parabolic trajectories with vertical main axis. For a polygon of complexity n, we can answer such \"stone-throwing\" queries in O( log <jats:sup>2<\/jats:sup> n) time, using O(n log n) storage and O(n log <jats:sup>2<\/jats:sup> n) preprocessing time. This matches the best known bound for circular ray shooting in simple polygons. <\/jats:p>","DOI":"10.1142\/s0218195907002379","type":"journal-article","created":{"date-parts":[[2007,8,21]],"date-time":"2007-08-21T09:39:24Z","timestamp":1187689164000},"page":"349-360","source":"Crossref","is-referenced-by-count":0,"title":["PARABOLA SEPARATION QUERIES AND THEIR APPLICATION TO STONE THROWING"],"prefix":"10.1142","volume":"17","author":[{"given":"OTFRIED","family":"CHEONG","sequence":"first","affiliation":[{"name":"Division of Computer Science, KAIST, Daejeon, South Korea"}]},{"given":"HAZEL","family":"EVERETT","sequence":"additional","affiliation":[{"name":"LORIA &amp; University Nancy 2, Nancy, France"}]},{"given":"HYO-SIL","family":"KIM","sequence":"additional","affiliation":[{"name":"Division of Computer Science, KAIST, Daejeon, South Korea"}]},{"given":"SYLVAIN","family":"LAZARD","sequence":"additional","affiliation":[{"name":"LORIA &amp; INRIA Lorraine, Nancy, France"}]},{"given":"REN\u00c9","family":"SCHOTT","sequence":"additional","affiliation":[{"name":"LORIA &amp; IECN, University Nancy 1, Nancy, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1993.1004"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(02)00167-0"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195906001963"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-004-1098-2"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04245-8"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1995.1017"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-52055-4"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(93)90033-3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2004.10.001"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195907002379","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:30:08Z","timestamp":1565137808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195907002379"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,8]]},"references-count":9,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,8]]}},"alternative-id":["10.1142\/S0218195907002379"],"URL":"https:\/\/doi.org\/10.1142\/s0218195907002379","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,8]]}}}