{"id":"https://openalex.org/W2056205248","doi":"https://doi.org/10.1137/s1064827501391576","title":"Constrained Centroidal Voronoi Tessellations for Surfaces","display_name":"Constrained Centroidal Voronoi Tessellations for Surfaces","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2056205248","doi":"https://doi.org/10.1137/s1064827501391576","mag":"2056205248"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827501391576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501391576","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max D. Gunzburger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076382628","display_name":"Lili Ju","orcid":"https://orcid.org/0000-0002-6520-582X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lili Ju","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.0772,"has_fulltext":false,"cited_by_count":249,"citation_normalized_percentile":{"value":0.97931034,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"24","issue":"5","first_page":"1488","last_page":"1506"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.994700014591217,"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":0.994700014591217,"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":0.9941999912261963,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9865000247955322,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.8751542568206787},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.8720716834068298},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7737966179847717},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6105793118476868},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5783053636550903},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5273479223251343},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46963879466056824},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4377599060535431},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2928006649017334},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26722919940948486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22043782472610474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14247429370880127},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.08148124814033508}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8751542568206787},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.8720716834068298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7737966179847717},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6105793118476868},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5783053636550903},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5273479223251343},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46963879466056824},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4377599060535431},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2928006649017334},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26722919940948486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22043782472610474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14247429370880127},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.08148124814033508},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827501391576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501391576","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.324.5034","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.324.5034","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.psu.edu/qdu/Res/Pre/dgj03sisc.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2051010753","https://openalex.org/W2051752778","https://openalex.org/W2051808729","https://openalex.org/W2073240454","https://openalex.org/W2092924973","https://openalex.org/W2098290609","https://openalex.org/W2127218421","https://openalex.org/W2131810611","https://openalex.org/W2150593711","https://openalex.org/W2159977720","https://openalex.org/W2162203349","https://openalex.org/W2189887275","https://openalex.org/W2913066018","https://openalex.org/W4252521233","https://openalex.org/W4301756919"],"related_works":["https://openalex.org/W2380539668","https://openalex.org/W1975209811","https://openalex.org/W2056205248","https://openalex.org/W3035747581","https://openalex.org/W2971463366","https://openalex.org/W2077953700","https://openalex.org/W2138130701","https://openalex.org/W112306762","https://openalex.org/W29377594","https://openalex.org/W2105043586"],"abstract_inverted_index":{"Centroidal":[0],"Voronoi":[1,13,65],"tessellations":[2,45,66],"are":[3,17,40,76,95,106,110,127],"useful":[4],"for":[5,43,90,101],"subdividing":[6],"a":[7,26,49,58,71],"region":[8],"in":[9,48],"Euclidean":[10,50],"space":[11,51],"into":[12],"regions":[14],"whose":[15],"generators":[16],"also":[18,41],"the":[19,31,91,104,116,136],"centers":[20],"of":[21,30,46,61,73,83,93,103,119],"mass,":[22],"with":[23],"respect":[24],"to":[25,35,114,129],"prescribed":[27],"density":[28],"function,":[29],"regions.":[32],"Their":[33],"extensions":[34],"general":[36],"spaces":[37],"and":[38,70,87,97,132],"sets":[39,126],"available;":[42],"example,":[44],"surfaces":[47],"may":[52],"be":[53],"considered.":[54],"In":[55],"this":[56],"paper,":[57],"precise":[59],"definition":[60],"such":[62],"constrained":[63],"centroidal":[64],"(CCVTs)":[67],"is":[68],"given":[69],"number":[72],"their":[74,79],"properties":[75],"derived,":[77],"including":[78],"characterization":[80],"as":[81],"minimizers":[82],"an":[84],"\"energy.\"":[85],"Deterministic":[86],"probabilistic":[88],"algorithms":[89,105],"construction":[92],"CCVTs":[94],"presented":[96],"some":[98],"analytical":[99],"results":[100],"one":[102],"given.":[107],"Computational":[108],"examples":[109],"provided":[111],"which":[112],"serve":[113],"illustrate":[115],"high":[117],"quality":[118],"CCVT":[120,124],"point":[121,125],"sets.":[122],"Finally,":[123],"applied":[128],"polynomial":[130],"interpolation":[131],"numerical":[133],"integration":[134],"on":[135],"sphere.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":20}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}