{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T07:58:11Z","timestamp":1767167891424,"version":"build-2238731810"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2000,4]]},"abstract":"<jats:p>We present an algorithm for computing the convex hull of a finite set of points. The algorithm is based on a version of Graham scan with the following additional features:<\/jats:p>\n                  <jats:p>\u2022 If the points are already (single precision) machine numbers, the computation is rounding-error free, that is, the computed hull is the hull that would have been computed if real arithmetic was available.<\/jats:p>\n                  <jats:p>\u2022 If the points are arbitrary numbers, the algorithm renders the smallest possible machine representable convex hull that includes the exact convex hull.<\/jats:p>\n                  <jats:p>\n                    \u2022 The computation time is still O(n log\n                    <jats:sub>2<\/jats:sub>\n                    n).\n                  <\/jats:p>\n                  <jats:p>\u2022 Only floating point arithmetic with double mantissa length is required. No mantissa splitting or other mantissa manipulations are needed; one only has to know the exponent parts of the numbers. Also, no fixed point accumulator is needed.<\/jats:p>\n                  <jats:p>\u2022 Single precision interval arithmetic is recommended for accelerating the computation, but is not necessary.<\/jats:p>\n                  <jats:p>\u2022 All of these aims are achieved with a new method for exact determination of the sign of a sum.<\/jats:p>","DOI":"10.1142\/s0218195900000085","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T04:18:55Z","timestamp":1052281135000},"page":"109-129","source":"Crossref","is-referenced-by-count":14,"title":["EXACT AND OPTIMAL CONVEX HULLS IN 2D"],"prefix":"10.1142","volume":"10","author":[{"given":"HELMUT","family":"RATSCHEK","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of D\u00fcsseldorf,  D\u00fcsseldorf, 40225, Germany"}]},{"given":"JON","family":"ROKNE","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Calgary, Calgary, Alberta, T2N-1N4, Canada"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(78)90003-0"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(79)90072-3"},{"key":"p_8","first-page":"185","year":"1987","journal-title":"New York"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1989.63524"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(72)90045-2"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(87)90207-9"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01891832"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(94)00017-4"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02017351"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1145\/99902.99905"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(98)00010-1"},{"key":"p_26","first-page":"61","author":"Rokne J.","year":"1992","journal-title":"San Diego"},{"key":"p_28","first-page":"361","author":"Seidel R.","year":"1997","journal-title":"Boca Raton"},{"key":"p_29","first-page":"468","author":"Sugihara K.","year":"1992","journal-title":"IEICE Trans. Fundamentals, E75-A"},{"key":"p_30","first-page":"452","author":"Yap C.K.","year":"1995","journal-title":"Singapore"},{"key":"p_31","first-page":"653","author":"Yap C.K.","year":"1997","journal-title":"Boca Raton"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195900000085","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:28:24Z","timestamp":1565080104000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195900000085"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,4]]},"references-count":16,"aliases":["10.1016\/s0218-1959(00)00008-5"],"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2000,4]]}},"alternative-id":["10.1142\/S0218195900000085"],"URL":"https:\/\/doi.org\/10.1142\/s0218195900000085","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,4]]}}}