{"id":"https://openalex.org/W2146199242","doi":"https://doi.org/10.1142/s0218195908002763","title":"THE PREDICATES FOR THE EXACT VORONOI DIAGRAM OF ELLIPSES UNDER THE EUCLIDIEAN METRIC","display_name":"THE PREDICATES FOR THE EXACT VORONOI DIAGRAM OF ELLIPSES UNDER THE EUCLIDIEAN METRIC","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2146199242","doi":"https://doi.org/10.1142/s0218195908002763","mag":"2146199242"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195908002763","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195908002763","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087662998","display_name":"Ioannis Z. Emiris","orcid":"https://orcid.org/0000-0002-2339-5303"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"IOANNIS Z. EMIRIS","raw_affiliation_strings":["Department of Informatics and Telecommunications, National Kapodistrian University of Athens, 15784 Panepistimiopolis, Athens, Hellas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications, National Kapodistrian University of Athens, 15784 Panepistimiopolis, Athens, Hellas","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002548887","display_name":"Elias Tsigaridas","orcid":"https://orcid.org/0009-0003-5015-3988"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"ELIAS P. TSIGARIDAS","raw_affiliation_strings":["INRIA-LORIA Lorraine, 615, rue du Jardin Botanique, B.P. 101, 54602 Villers-l\u00e9s-Nancy cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA-LORIA Lorraine, 615, rue du Jardin Botanique, B.P. 101, 54602 Villers-l\u00e9s-Nancy cedex, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283","https://openalex.org/I4210121838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029683844","display_name":"George M. Tzoumas","orcid":null},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"GEORGE M. TZOUMAS","raw_affiliation_strings":["Department of Informatics and Telecommunications, National Kapodistrian University of Athens, 15784 Panepistimiopolis, Athens, Hellas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications, National Kapodistrian University of Athens, 15784 Panepistimiopolis, Athens, Hellas","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.7035,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.95871733,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"18","issue":"06","first_page":"567","last_page":"597"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.9461668729782104},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.8465146422386169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6864478588104248},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43097952008247375},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4284828007221222},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33765214681625366},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.291571706533432},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12900367379188538}],"concepts":[{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.9461668729782104},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8465146422386169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6864478588104248},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43097952008247375},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4284828007221222},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33765214681625366},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.291571706533432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12900367379188538}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195908002763","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195908002763","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321916","display_name":"State Scholarships Foundation","ror":"https://ror.org/023z3dm33"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W45802723","https://openalex.org/W102282416","https://openalex.org/W125503916","https://openalex.org/W578994982","https://openalex.org/W1506764403","https://openalex.org/W1535802299","https://openalex.org/W1565317613","https://openalex.org/W1580997425","https://openalex.org/W1869291234","https://openalex.org/W1977289164","https://openalex.org/W1987221468","https://openalex.org/W1993731062","https://openalex.org/W2006448653","https://openalex.org/W2010201394","https://openalex.org/W2010608836","https://openalex.org/W2031195767","https://openalex.org/W2031953823","https://openalex.org/W2050905577","https://openalex.org/W2067220482","https://openalex.org/W2069254977","https://openalex.org/W2078950386","https://openalex.org/W2103847686","https://openalex.org/W2132812293","https://openalex.org/W2156616818","https://openalex.org/W2171631926","https://openalex.org/W4212788863","https://openalex.org/W4255769949"],"related_works":["https://openalex.org/W3020555194","https://openalex.org/W2371136327","https://openalex.org/W2793256277","https://openalex.org/W2348235448","https://openalex.org/W4360958759","https://openalex.org/W2116218375","https://openalex.org/W4293234107","https://openalex.org/W2389906634","https://openalex.org/W288156810","https://openalex.org/W4297165390"],"abstract_inverted_index":{"This":[0,200],"article":[1,115],"examines":[2],"the":[3,6,20,25,30,35,60,79,97,122,160,163,183,214],"computation":[4,32],"of":[5,14,17,37,46,62,72,81,90,99,140,159,162,185,216],"Delaunay":[7],"graph":[8],"and":[9,110,144,149,167,189],"its":[10],"dual":[11],"Voronoi":[12,88,103],"diagram":[13],"a":[15,53,63,82,87,102,111,179],"set":[16],"ellipses":[18,49,130],"in":[19,133,138,157,171,198],"Euclidean":[21],"plane.":[22],"We":[23,207],"propose":[24],"first":[26],"complete":[27],"methods,":[28],"under":[29],"exact":[31,192],"paradigm,":[33],"for":[34],"predicates":[36],"an":[38,68,191],"incremental":[39],"algorithm:":[40],"\u03ba":[41,57,76,94,147,150,175,203],"1":[42,148],"decides":[43,59,78],"which":[44,195],"one":[45],"two":[47,73],"given":[48,54,74,92,108],"is":[50,116,127,196],"closest":[51],"to":[52,67,86,118,124],"exterior":[55],"point;":[56],"2":[58,151],"position":[61,80],"query":[64,83,112],"ellipse":[65,84],"relative":[66,85],"external":[69],"bitangent":[70],"line":[71],"ellipses;":[75,93],"3":[77,176],"circle":[89],"three":[91],"4":[95,204],"determines":[96],"type":[98],"conflict":[100],"between":[101],"edge,":[104],"defined":[105],"by":[106],"four":[107],"ellipses,":[109,120],"ellipse.":[113],"The":[114,129],"restricted":[117],"non-intersecting":[119,217],"but":[121],"extension":[123],"arbitrary":[125],"ones":[126],"possible.":[128],"are":[131],"input":[132],"parametric":[134],"representation,":[135],"i.e.,":[136],"constructively":[137],"terms":[139,158],"their":[141],"axes,":[142],"center":[143],"rotation.":[145],"For":[146,174],"we":[152,177],"derive":[153],"algebraic":[154,164],"conditions":[155],"optimal":[156],"degree":[161],"numbers":[165],"involved,":[166],"provide":[168],"efficient":[169],"implementations":[170],"C++":[172],".":[173],"compute":[178],"tight":[180],"bound":[181],"on":[182,212],"number":[184],"complex":[186],"tritangent":[187],"circles":[188],"design":[190],"symbolic-numeric":[193],"algorithm,":[194],"implemented":[197],"MAPLE.":[199],"essentially":[201],"answers":[202],"as":[205],"well.":[206],"conclude":[208],"with":[209],"further":[210],"work":[211],"lifting":[213],"condition":[215],"ellipses.":[218]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
