{"id":"https://openalex.org/W2051752778","doi":"https://doi.org/10.1137/s0036144599352836","title":"Centroidal Voronoi Tessellations: Applications and Algorithms","display_name":"Centroidal Voronoi Tessellations: Applications and Algorithms","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2051752778","doi":"https://doi.org/10.1137/s0036144599352836","mag":"2051752778"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144599352836","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599352836","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","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/A5056115552","display_name":"Qiang Du","orcid":"https://orcid.org/0000-0002-1067-8937"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA 50011-2064, and","Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA 50011-2064, and","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046440641","display_name":"Vance Faber","orcid":"https://orcid.org/0000-0001-5125-6979"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vance Faber","raw_affiliation_strings":["Communications and Computing Division, Los Alamos National Laboratory, Los Alamos, NM 87545"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communications and Computing Division, Los Alamos National Laboratory, Los Alamos, NM 87545","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Max Gunzburger","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA 50011-2064"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA 50011-2064","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076283476"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":10.7961,"has_fulltext":false,"cited_by_count":2256,"citation_normalized_percentile":{"value":0.98790497,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"41","issue":"4","first_page":"637","last_page":"676"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9894999861717224,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.9711021184921265},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.9699203968048096},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.847965657711029},{"id":"https://openalex.org/keywords/tessellation","display_name":"Tessellation (computer graphics)","score":0.5344611406326294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45715659856796265},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4270259141921997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4214671850204468},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34980446100234985}],"concepts":[{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.9711021184921265},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.9699203968048096},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.847965657711029},{"id":"https://openalex.org/C43817857","wikidata":"https://www.wikidata.org/wiki/Q9357547","display_name":"Tessellation (computer graphics)","level":2,"score":0.5344611406326294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45715659856796265},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4270259141921997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4214671850204468},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34980446100234985}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036144599352836","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599352836","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.407.146","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.407.146","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.sc.fsu.edu/~mgunzburger/files_papers/gunzburger-cvt-siamreview.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.452.2448","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.452.2448","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.personal.psu.edu/qud2/Res/Pre/dfg99sirv.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5306926836","display_name":"Mathematical Sciences:  Analysis, Algorithms, and           Computations for Models of High-Temperature                 Superconductivity","funder_award_id":"9796208","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6779810350","display_name":"Least-Squares Finite Element Methods and Optimization-Based Domain Decomposition Methods for Partial Differential       Equations","funder_award_id":"9806358","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320323537","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W68465796","https://openalex.org/W77371105","https://openalex.org/W1481075119","https://openalex.org/W1511669881","https://openalex.org/W1544918322","https://openalex.org/W1564001778","https://openalex.org/W1578468649","https://openalex.org/W1634005169","https://openalex.org/W1963801390","https://openalex.org/W1964724001","https://openalex.org/W1971784203","https://openalex.org/W1977556410","https://openalex.org/W1981277287","https://openalex.org/W1981743146","https://openalex.org/W1984034733","https://openalex.org/W1985921956","https://openalex.org/W1993823177","https://openalex.org/W1999823999","https://openalex.org/W2000787327","https://openalex.org/W2005314985","https://openalex.org/W2007580079","https://openalex.org/W2011039300","https://openalex.org/W2014564494","https://openalex.org/W2020671618","https://openalex.org/W2043419861","https://openalex.org/W2050744541","https://openalex.org/W2052795606","https://openalex.org/W2053913299","https://openalex.org/W2058182146","https://openalex.org/W2059279601","https://openalex.org/W2060099544","https://openalex.org/W2063379007","https://openalex.org/W2066679806","https://openalex.org/W2069447707","https://openalex.org/W2072031172","https://openalex.org/W2073732659","https://openalex.org/W2073849744","https://openalex.org/W2075224881","https://openalex.org/W2079232128","https://openalex.org/W2086943813","https://openalex.org/W2088387982","https://openalex.org/W2088912280","https://openalex.org/W2091283109","https://openalex.org/W2091291865","https://openalex.org/W2092924973","https://openalex.org/W2122154258","https://openalex.org/W2127218421","https://openalex.org/W2134383396","https://openalex.org/W2142228262","https://openalex.org/W2150593711","https://openalex.org/W2154228396","https://openalex.org/W2156556302","https://openalex.org/W2159508113","https://openalex.org/W2160307327","https://openalex.org/W2187726933","https://openalex.org/W2319660501","https://openalex.org/W2913066018","https://openalex.org/W3000042338","https://openalex.org/W3161697066","https://openalex.org/W4210881201","https://openalex.org/W4238957295","https://openalex.org/W4254197176","https://openalex.org/W4254612649","https://openalex.org/W4285719527","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W2371724110","https://openalex.org/W1997141012","https://openalex.org/W4206423751","https://openalex.org/W2005041861","https://openalex.org/W2059217232","https://openalex.org/W2053576657","https://openalex.org/W1516845492","https://openalex.org/W2013420653","https://openalex.org/W2126647504","https://openalex.org/W2043725094"],"abstract_inverted_index":{"A":[0],"centroidal":[1],"Voronoi":[2,6,20],"tessellation":[3,7],"is":[4],"a":[5],"whose":[8],"generating":[9],"points":[10],"are":[11],"the":[12,18,45,61,64,72],"centroids":[13],"(centers":[14],"of":[15,17,26,39,48,74],"mass)":[16],"corresponding":[19],"regions.":[21],"We":[22,50],"give":[23],"some":[24,57,75],"applications":[25],"such":[27],"tessellations":[28,62],"to":[29],"problems":[30],"in":[31],"image":[32],"compression,":[33],"quadrature,":[34],"finite":[35],"difference":[36],"methods,":[37],"distribution":[38],"resources,":[40],"cellular":[41],"biology,":[42],"statistics,":[43],"and":[44,63],"territorial":[46],"behavior":[47],"animals.":[49],"discuss":[51],"methodsfor":[52],"computing":[53],"these":[54],"tessellations,":[55],"provide":[56],"analyses":[58],"concerning":[59],"both":[60],"methods":[65],"for":[66],"their":[67],"determination,":[68],"and,":[69],"finally,":[70],"present":[71],"results":[73],"numerical":[76],"experiments.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":52},{"year":2025,"cited_by_count":118},{"year":2024,"cited_by_count":123},{"year":2023,"cited_by_count":117},{"year":2022,"cited_by_count":115},{"year":2021,"cited_by_count":134},{"year":2020,"cited_by_count":114},{"year":2019,"cited_by_count":136},{"year":2018,"cited_by_count":118},{"year":2017,"cited_by_count":120},{"year":2016,"cited_by_count":136},{"year":2015,"cited_by_count":122},{"year":2014,"cited_by_count":112},{"year":2013,"cited_by_count":101},{"year":2012,"cited_by_count":106}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}