{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:32Z","timestamp":1750308152490,"version":"3.41.0"},"reference-count":7,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2005,9,1]],"date-time":"2005-09-01T00:00:00Z","timestamp":1125532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:p>\n            Determining the topology of an algebraic surface is not only an interesting mathematical problem, but also a key issue in computer graphics and CAGD. An algorithm is proposed to determine the intrinsic topology of an implicit real algebraic surface\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>x,y,z<\/jats:italic>\n            ) = 0 in R\n            <jats:sup>3<\/jats:sup>\n            , where\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>x,y,z<\/jats:italic>\n            ) \u2208\n            <jats:italic>Q<\/jats:italic>\n            [\n            <jats:italic>x,y,z<\/jats:italic>\n            ] and\n            <jats:italic>Q<\/jats:italic>\n            is the field of rational numbers. There exist algorithms to determine the topology for algebraic surfaces of special type [2, 3, 4, 7]. The CAD method proposed by Collins [1] can divide the space into cylindrical parts. But it does not give the connection information neither the intrinsic representation.\n          <\/jats:p>","DOI":"10.1145\/1113439.1113444","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"80-81","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Intrinsic topological representation of real algebraic surfaces"],"prefix":"10.1145","volume":"39","author":[{"given":"Jin-San","family":"Cheng","sequence":"first","affiliation":[{"name":"KLMM, Institute of Systems Science, Academia Sinica, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Shan","family":"Gao","sequence":"additional","affiliation":[{"name":"KLMM, Institute of Systems Science, Academia Sinica, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"Cardiff University, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,9]]},"reference":[{"volume-title":"Cylindrical algebraic decomposition I: the basic algorithm. Quantifier Elimination and Cylindrical Algebraic Decomposition","author":"Arnon D. S.","key":"e_1_2_1_1_1"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(88)90013-1"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2004.08.001"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(03)00085-3"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.5555\/1648394.1648503"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(96)00034-1"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1186562.1015769"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1113439.1113444","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1113439.1113444","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:18:47Z","timestamp":1750263527000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1113439.1113444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1145\/1113439.1113444"],"URL":"https:\/\/doi.org\/10.1145\/1113439.1113444","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[2005,9]]},"assertion":[{"value":"2005-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}