{"id":"https://openalex.org/W2149362108","doi":"https://doi.org/10.1007/978-3-642-00212-0_2","title":"The Voronoi Diagram of Circles and Its Application to the Visualization of the Growth of Particles","display_name":"The Voronoi Diagram of Circles and Its Application to the Visualization of the Growth of Particles","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2149362108","doi":"https://doi.org/10.1007/978-3-642-00212-0_2","mag":"2149362108"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-00212-0_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-00212-0_2","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5045073378","display_name":"Fran\u00e7ois Anton","orcid":"https://orcid.org/0000-0003-1558-4611"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Anton","raw_affiliation_strings":["Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, DK-2800, Kongens Lyngby, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, DK-2800, Kongens Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107860337","display_name":"Darka Mioc","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Darka Mioc","raw_affiliation_strings":["Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick, Canada, E3B 5A3"],"affiliations":[{"raw_affiliation_string":"Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick, Canada, E3B 5A3","institution_ids":["https://openalex.org/I106938459"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109231266","display_name":"Christopher Gold","orcid":null},"institutions":[{"id":"https://openalex.org/I128993996","display_name":"University of South Wales","ror":"https://ror.org/02mzn7s88","country_code":"GB","type":"education","lineage":["https://openalex.org/I128993996"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Christopher Gold","raw_affiliation_strings":["School of Computing, University of Glamorgan, Pontypridd, CF37 1DL, UK"],"affiliations":[{"raw_affiliation_string":"School of Computing, University of Glamorgan, Pontypridd, CF37 1DL, UK","institution_ids":["https://openalex.org/I128993996"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045073378"],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.4782,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.67752443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"20","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991000294685364,"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":0.9991000294685364,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9695000052452087,"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/T11106","display_name":"Data Management and Algorithms","score":0.9692000150680542,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.977030336856842},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.7961490154266357},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.7632455229759216},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.7133684158325195},{"id":"https://openalex.org/keywords/weighted-voronoi-diagram","display_name":"Weighted Voronoi diagram","score":0.6934800148010254},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5632209777832031},{"id":"https://openalex.org/keywords/graph-drawing","display_name":"Graph drawing","score":0.48591771721839905},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.4654771685600281},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.46292778849601746},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4513605237007141},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.44865933060646057},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.43233931064605713},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33345234394073486},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3178979754447937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30040615797042847},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.22316190600395203},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1916481852531433},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.09407103061676025}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.977030336856842},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.7961490154266357},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.7632455229759216},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7133684158325195},{"id":"https://openalex.org/C20468658","wikidata":"https://www.wikidata.org/wiki/Q17130624","display_name":"Weighted Voronoi diagram","level":3,"score":0.6934800148010254},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5632209777832031},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.48591771721839905},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.4654771685600281},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.46292778849601746},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4513605237007141},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.44865933060646057},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.43233931064605713},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33345234394073486},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3178979754447937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30040615797042847},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.22316190600395203},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1916481852531433},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.09407103061676025},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-00212-0_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-00212-0_2","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.atira.dk:publications/c563ebd5-4b5a-43dd-a019-882c44802d34","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/c563ebd5-4b5a-43dd-a019-882c44802d34","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Anton , F , Mioc , D & Gold , C M 2009 , ' The Voronoi diagram of circles and its application to the visualization of the growth of particles ' , Transactions on Computational Science , pp. 20-54 . https://doi.org/10.1007/978-3-642-00212-0_2","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W21857574","https://openalex.org/W175214484","https://openalex.org/W1481075119","https://openalex.org/W1483218536","https://openalex.org/W1520127302","https://openalex.org/W1550331971","https://openalex.org/W1555471913","https://openalex.org/W1596015817","https://openalex.org/W1608422328","https://openalex.org/W1869291234","https://openalex.org/W1969568644","https://openalex.org/W2002558490","https://openalex.org/W2006279327","https://openalex.org/W2031195767","https://openalex.org/W2048475323","https://openalex.org/W2050905577","https://openalex.org/W2052165970","https://openalex.org/W2066181227","https://openalex.org/W2092924973","https://openalex.org/W2093528056","https://openalex.org/W2115675360","https://openalex.org/W2313120994","https://openalex.org/W2493051178","https://openalex.org/W2899519211","https://openalex.org/W2978212472","https://openalex.org/W3043060850","https://openalex.org/W4210881201","https://openalex.org/W4214609516","https://openalex.org/W4231553787","https://openalex.org/W4241950961","https://openalex.org/W4242733942","https://openalex.org/W4243473751","https://openalex.org/W4243579654","https://openalex.org/W4252614677","https://openalex.org/W4292096448","https://openalex.org/W4300166240","https://openalex.org/W4301168154","https://openalex.org/W6602828855"],"related_works":["https://openalex.org/W2369399365","https://openalex.org/W1992160534","https://openalex.org/W2185378562","https://openalex.org/W2384419600","https://openalex.org/W2002507856","https://openalex.org/W4239527536","https://openalex.org/W2129618641","https://openalex.org/W1562406979","https://openalex.org/W1483512156","https://openalex.org/W1967060523"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}