{"id":"https://openalex.org/W2172006071","doi":"https://doi.org/10.1137/s1064827503428527","title":"Anisotropic Centroidal Voronoi Tessellations and Their Applications","display_name":"Anisotropic Centroidal Voronoi Tessellations and Their Applications","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2172006071","doi":"https://doi.org/10.1137/s1064827503428527","mag":"2172006071"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827503428527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503428527","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":true,"oa_status":"green","oa_url":"https://dr.ntu.edu.sg/bitstream/10356/98741/1/dwacvt.pdf","any_repository_has_fulltext":true},"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/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":["Department of Mathematics, Penn State University, University Park, PA 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Penn State University, University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100733741","display_name":"Desheng Wang","orcid":"https://orcid.org/0000-0001-8288-2657"},"institutions":[{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]},{"id":"https://openalex.org/I97429440","display_name":"University of Wales","ror":"https://ror.org/01se4f844","country_code":"GB","type":"education","lineage":["https://openalex.org/I97429440"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Desheng Wang","raw_affiliation_strings":["Civil and Computational Engineering Centre, School of Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Civil and Computational Engineering Centre, School of Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK","institution_ids":["https://openalex.org/I39586589","https://openalex.org/I97429440"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100733741"],"corresponding_institution_ids":["https://openalex.org/I39586589","https://openalex.org/I97429440"],"apc_list":null,"apc_paid":null,"fwci":7.5123,"has_fulltext":true,"cited_by_count":156,"citation_normalized_percentile":{"value":0.9697246,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"26","issue":"3","first_page":"737","last_page":"761"},"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9916999936103821,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9854000210762024,"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/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.8850734233856201},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.7840322256088257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7742631435394287},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.7683764100074768},{"id":"https://openalex.org/keywords/surface-triangulation","display_name":"Surface triangulation","score":0.6805299520492554},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.6385279893875122},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.5529862642288208},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5432814359664917},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5272666215896606},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.48112908005714417},{"id":"https://openalex.org/keywords/metric-tensor","display_name":"Metric tensor","score":0.4771568179130554},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.42956140637397766},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38662752509117126},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3449859023094177},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.07590919733047485},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.06440341472625732}],"concepts":[{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.8850734233856201},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.7840322256088257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742631435394287},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7683764100074768},{"id":"https://openalex.org/C50285192","wikidata":"https://www.wikidata.org/wiki/Q15713605","display_name":"Surface triangulation","level":4,"score":0.6805299520492554},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.6385279893875122},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.5529862642288208},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5432814359664917},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5272666215896606},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.48112908005714417},{"id":"https://openalex.org/C8466233","wikidata":"https://www.wikidata.org/wiki/Q757269","display_name":"Metric tensor","level":3,"score":0.4771568179130554},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.42956140637397766},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38662752509117126},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3449859023094177},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.07590919733047485},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.06440341472625732},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s1064827503428527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503428527","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:dr.ntu.edu.sg:10356/98741","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/6047","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/98741/1/dwacvt.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.112.1094","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.1094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.scs.fsu.edu/~burkardt/pdf/du_wang2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.330.9320","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.9320","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.spms.ntu.edu.sg/~desheng/dwacvt.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.352.7770","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.352.7770","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/dw04sisc.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:dr.ntu.edu.sg:10356/98741","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/6047","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/98741/1/dwacvt.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4213711566","display_name":"Analysis, Algorithms and Computations for Model Problems in Material Sciences","funder_award_id":"0196522","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6234456375","display_name":"ITR: Computational Tools for Multicomponent Materials Design","funder_award_id":"0205232","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2172006071.pdf","grobid_xml":"https://content.openalex.org/works/W2172006071.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W140937755","https://openalex.org/W188919190","https://openalex.org/W1525169043","https://openalex.org/W1965906701","https://openalex.org/W1967005434","https://openalex.org/W2001099600","https://openalex.org/W2002423590","https://openalex.org/W2004250781","https://openalex.org/W2019856220","https://openalex.org/W2029336492","https://openalex.org/W2031003742","https://openalex.org/W2031140167","https://openalex.org/W2032350951","https://openalex.org/W2033838452","https://openalex.org/W2046053182","https://openalex.org/W2051752778","https://openalex.org/W2056205248","https://openalex.org/W2065139213","https://openalex.org/W2073240454","https://openalex.org/W2092924973","https://openalex.org/W2117377495","https://openalex.org/W2128878012","https://openalex.org/W2129757752","https://openalex.org/W2129819199","https://openalex.org/W2131810611","https://openalex.org/W2135397228","https://openalex.org/W2142228262","https://openalex.org/W2150593711","https://openalex.org/W2158086285","https://openalex.org/W2162203349","https://openalex.org/W2950200454","https://openalex.org/W3106306093","https://openalex.org/W4239339957","https://openalex.org/W4254197176"],"related_works":["https://openalex.org/W4233285229","https://openalex.org/W2085351143","https://openalex.org/W2379205232","https://openalex.org/W1967229461","https://openalex.org/W1996451305","https://openalex.org/W1568423349","https://openalex.org/W2354869996","https://openalex.org/W2360914760","https://openalex.org/W2024358741","https://openalex.org/W3013087716"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"a":[5,17],"novel":[6],"definition":[7,30],"of":[8,49,65,73,89],"the":[9,29,33,40,43,47,54,63,71,87,90],"anisotropic":[10,50,67],"centroidal":[11],"Voronoi":[12],"tessellation":[13],"(ACVT)":[14],"corresponding":[15],"to":[16,31,38,62,70],"given":[18,55],"Riemann":[19],"metric":[20],"tensor.":[21],"A":[22],"directional":[23],"distance":[24],"function":[25],"is":[26,60],"used":[27],"in":[28],"simplify":[32],"computation.":[34],"We":[35],"provide":[36],"algorithms":[37],"approximate":[39],"ACVT":[41,59],"using":[42],"Lloyd":[44],"iteration":[45],"and":[46,76],"construction":[48],"Delaunay":[51,68],"triangulation":[52],"under":[53],"Riemannian":[56],"metric.":[57],"The":[58],"applied":[61],"optimization":[64],"two-dimensional":[66],"triangulation,":[69],"generation":[72],"surface":[74],"CVT,":[75],"high-quality":[77],"triangular":[78],"mesh":[79],"on":[80],"general":[81],"surfaces.":[82],"Various":[83],"numerical":[84],"examples":[85],"demonstrating":[86],"effectiveness":[88],"proposed":[91],"method":[92],"are":[93],"presented.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}