{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:39:38Z","timestamp":1787503178856,"version":"build-2736575974"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1991,3]]},"abstract":"<jats:p>\n                    In this paper, we investigate the problem of finding the common tangents of two convex polygons that intersect in two (unknown) points. First, we give a \u0398( log\n                    <jats:sup>2<\/jats:sup>\n                    n) bound for algorithms that store the polygons in independent arrays. Second, we show how to beat the lower bound if the vertices of the convex polygons are drawn from a fixed set of n points. We introduce a data structure called a compact interval tree that supports common tangent computations, as well as the standard binary-search-based queries, in O( log n) time apiece. Third, we apply compact interval trees to solve the subpath hull query problem: given a simple path, preprocess it so that we can find the convex hull of a query subpath quickly. With O(n log n) preprocessing, we can assemble a compact interval tree that represents the convex hull of a query subpath in O( log n) time. In order to represent arrangements of Lines implicitly, Edelsbrunner et al. used a less efficient structure, called bridge trees, to solve the subpath hull query problem. Our compact interval trees improve their results by a factor of O( log n). Thus, the present paper replaces the paper on bridge trees referred to by Edelsbrunner et al.\n                  <\/jats:p>","DOI":"10.1142\/s0218195991000025","type":"journal-article","created":{"date-parts":[[2004,11,26]],"date-time":"2004-11-26T20:43:01Z","timestamp":1101501781000},"page":"1-22","source":"Crossref","is-referenced-by-count":25,"title":["COMPACT INTERVAL TREES: A DATA STRUCTURE FOR CONVEX HULLS"],"prefix":"10.1142","volume":"01","author":[{"given":"LEONIDAS","family":"GUIBAS","sequence":"first","affiliation":[{"name":"DEC Systems Research Center,  130 Lytton Avenue, Palo Alto, California 94301, USA"},{"name":"Department of Computer Science,  Stanford University, Stanford, California 94305, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JOHN","family":"HERSHBERGER","sequence":"additional","affiliation":[{"name":"DEC Systems Research Center,  130 Lytton Avenue, Palo Alto, California 94301, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JACK","family":"SNOEYINK","sequence":"additional","affiliation":[{"name":"Department of Computer Science,  Stanford University, Stanford, California 94305, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195991000025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:34:31Z","timestamp":1565116471000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195991000025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[1991,3]]}},"alternative-id":["10.1142\/S0218195991000025"],"URL":"https:\/\/doi.org\/10.1142\/s0218195991000025","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,3]]}}}