{"id":"https://openalex.org/W1993731062","doi":"https://doi.org/10.1145/1137856.1137891","title":"The predicates for the Voronoi diagram of ellipses","display_name":"The predicates for the Voronoi diagram of ellipses","publication_year":2006,"publication_date":"2006-06-05","ids":{"openalex":"https://openalex.org/W1993731062","doi":"https://doi.org/10.1145/1137856.1137891","mag":"1993731062"},"language":"en","primary_location":{"id":"doi:10.1145/1137856.1137891","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137891","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-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":["National and Kapodistrian University of Athens, Greece","National and Kapodistrian University of Athens, GREECE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National and Kapodistrian University of Athens, Greece","institution_ids":["https://openalex.org/I200777214"]},{"raw_affiliation_string":"National and Kapodistrian University of Athens, GREECE","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/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":"Elias P. Tsigaridas","raw_affiliation_strings":["National and Kapodistrian University of Athens, Greece","National and Kapodistrian University of Athens, GREECE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National and Kapodistrian University of Athens, Greece","institution_ids":["https://openalex.org/I200777214"]},{"raw_affiliation_string":"National and Kapodistrian University of Athens, GREECE","institution_ids":["https://openalex.org/I200777214"]}]},{"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":["National and Kapodistrian University of Athens, Greece","National and Kapodistrian University of Athens, GREECE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National and Kapodistrian University of Athens, Greece","institution_ids":["https://openalex.org/I200777214"]},{"raw_affiliation_string":"National and Kapodistrian University of Athens, GREECE","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.6869,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.95404664,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"227","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9990000128746033,"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":0.9990000128746033,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12549","display_name":"Image and Object Detection Techniques","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.9681401252746582},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.8442624807357788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4728814959526062},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.44689705967903137},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.445316344499588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4241240620613098},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42101335525512695},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31030893325805664}],"concepts":[{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.9681401252746582},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8442624807357788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4728814959526062},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.44689705967903137},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.445316344499588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4241240620613098},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42101335525512695},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31030893325805664},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1137856.1137891","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137891","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.105.8883","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.8883","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.loria.fr/~petitjea/Arcadia/docs/voronoi-ellipses.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.464.9492","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.464.9492","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sop.inria.fr/galaad/personnel/Elias.Tsigaridas/papers/confs/ett-voronoi-socg.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.2280","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.2280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cgi.di.uoa.gr/~geotz/papers/EmiTsiTzo-SoCG06-PredVorEll.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W102282416","https://openalex.org/W125503916","https://openalex.org/W1483218536","https://openalex.org/W1506764403","https://openalex.org/W1535802299","https://openalex.org/W1548072019","https://openalex.org/W1565317613","https://openalex.org/W1580997425","https://openalex.org/W1869291234","https://openalex.org/W1964712205","https://openalex.org/W1977289164","https://openalex.org/W1987221468","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/W2073751737","https://openalex.org/W2078950386","https://openalex.org/W2103847686","https://openalex.org/W2114174667","https://openalex.org/W2132812293","https://openalex.org/W2156616818","https://openalex.org/W2171631926","https://openalex.org/W2224227196","https://openalex.org/W4212788863","https://openalex.org/W6604152061","https://openalex.org/W6605220680","https://openalex.org/W6630178116","https://openalex.org/W6635510123","https://openalex.org/W6688595986","https://openalex.org/W7063904013"],"related_works":["https://openalex.org/W2908074373","https://openalex.org/W4250008887","https://openalex.org/W2962789953","https://openalex.org/W1492333335","https://openalex.org/W2042426695","https://openalex.org/W2189603398","https://openalex.org/W2154887871","https://openalex.org/W4299527166","https://openalex.org/W2084691280","https://openalex.org/W889844791"],"abstract_inverted_index":{"This":[0,182],"paper":[1,106],"examines":[2],"the":[3,6,15,20,25,30,53,71,88,113,155,163,167],"computation":[4,27],"of":[5,9,12,32,40,55,65,73,82,90,157,166],"Voronoi":[7,80,94],"diagram":[8],"a":[10,47,56,74,79,93,102,151],"set":[11],"ellipses":[13,43,121,168],"in":[14,124,145,169,200],"Euclidean":[16],"plane.":[17],"We":[18,189],"propose":[19],"first":[21],"complete":[22],"algorithms,":[23],"under":[24],"exact":[26,174],"paradigm,":[28],"for":[29],"predicates":[31],"an":[33,61,173],"incremental":[34],"algorithm:":[35],"\u03ba1":[36,130],"decides":[37,52,70],"which":[38,177],"one":[39],"2":[41,66],"given":[42,48,67,84,99],"is":[44,107,118,178],"closest":[45],"to":[46,60,78,109,115,171],"exterior":[49],"point;":[50],"\u03ba2":[51,132],"position":[54,72],"query":[57,75,103],"ellipse":[58,76],"relative":[59,77],"external":[62],"bitangent":[63],"line":[64],"ellipses;":[68,85],"\u03ba3":[69,148,196],"circle":[81],"3":[83],"\u03ba4":[86,186],"determines":[87],"type":[89],"conflict":[91],"between":[92],"edge,":[95],"defined":[96],"by":[97],"4":[98],"ellipses,":[100,111],"and":[101,131,141,161,197],"ellipse.":[104],"The":[105,120],"restricted":[108],"non-intersecting":[110],"but":[112],"extension":[114],"arbitrary":[116],"ones":[117],"straightforward.":[119],"are":[122],"input":[123],"parametric":[125,164],"representation":[126],"or":[127],"constructively.":[128],"For":[129,147],"we":[133,149],"derive":[134],"optimal":[135],"algebraic":[136],"conditions,":[137],"solve":[138],"them":[139],"exactly":[140],"provide":[142],"efficient":[143],"implementations":[144],"C++.":[146,201],"compute":[150],"tight":[152],"bound":[153],"on":[154,180,194],"number":[156],"complex":[158],"tritangent":[159],"circles":[160],"use":[162],"form":[165],"order":[170],"design":[172],"subdivision-based":[175],"algorithm,":[176],"implemented":[179],"Maple.":[181],"approach":[183],"essentially":[184],"answers":[185],"as":[187],"well.":[188],"conclude":[190],"with":[191],"current":[192],"work":[193],"optimizing":[195],"implementing":[198],"it":[199]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
