{"id":"https://openalex.org/W1969052304","doi":"https://doi.org/10.1145/2816795.2818076","title":"Efficient construction and simplification of Delaunay meshes","display_name":"Efficient construction and simplification of Delaunay meshes","publication_year":2015,"publication_date":"2015-10-27","ids":{"openalex":"https://openalex.org/W1969052304","doi":"https://doi.org/10.1145/2816795.2818076","mag":"1969052304"},"language":"en","primary_location":{"id":"doi:10.1145/2816795.2818076","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2816795.2818076","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","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/10356/80803/1/Efficient%20Construction%20and%20Simplification%20of%20Delaunay%20Meshes.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008076279","display_name":"Yong\u2010Jin Liu","orcid":"https://orcid.org/0000-0001-5774-1916"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong-Jin Liu","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059342429","display_name":"Chun-Xu Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chun-Xu Xu","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058159208","display_name":"Dian Fan","orcid":"https://orcid.org/0000-0002-2584-3608"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dian Fan","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100389169","display_name":"Ying He","orcid":"https://orcid.org/0000-0002-6749-4485"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Ying He","raw_affiliation_strings":["Nanyang Technological University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.8645,"has_fulltext":true,"cited_by_count":61,"citation_normalized_percentile":{"value":0.99123356,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"34","issue":"6","first_page":"1","last_page":"13"},"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9980000257492065,"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":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8232982754707336},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.815314531326294},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6531383395195007},{"id":"https://openalex.org/keywords/rupperts-algorithm","display_name":"Ruppert's algorithm","score":0.6032814979553223},{"id":"https://openalex.org/keywords/chews-second-algorithm","display_name":"Chew's second algorithm","score":0.5636289119720459},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5407185554504395},{"id":"https://openalex.org/keywords/volume-mesh","display_name":"Volume mesh","score":0.5002315044403076},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.4255217909812927},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4172452688217163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3941151201725006},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3767250180244446},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.3322128653526306},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23227697610855103},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21476152539253235},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11163079738616943}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8232982754707336},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.815314531326294},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6531383395195007},{"id":"https://openalex.org/C99886907","wikidata":"https://www.wikidata.org/wiki/Q105742691","display_name":"Ruppert's algorithm","level":4,"score":0.6032814979553223},{"id":"https://openalex.org/C183342303","wikidata":"https://www.wikidata.org/wiki/Q105742691","display_name":"Chew's second algorithm","level":4,"score":0.5636289119720459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5407185554504395},{"id":"https://openalex.org/C170589453","wikidata":"https://www.wikidata.org/wiki/Q7940896","display_name":"Volume mesh","level":4,"score":0.5002315044403076},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.4255217909812927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4172452688217163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3941151201725006},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3767250180244446},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.3322128653526306},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23227697610855103},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21476152539253235},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11163079738616943},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2816795.2818076","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2816795.2818076","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/80803","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/45017","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/80803/1/Efficient%20Construction%20and%20Simplification%20of%20Delaunay%20Meshes.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"}],"best_oa_location":{"id":"pmh:oai:dr.ntu.edu.sg:10356/80803","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/45017","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/80803/1/Efficient%20Construction%20and%20Simplification%20of%20Delaunay%20Meshes.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":[{"id":"https://metadata.un.org/sdg/11","score":0.5799999833106995,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G7635014514","display_name":null,"funder_award_id":"61432003 & 61322206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8004724926","display_name":null,"funder_award_id":"MOE2013-T2-2-011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8069300600","display_name":null,"funder_award_id":"2011CB302202","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8119831213","display_name":"\u9762\u5411\u5927\u578b\u5de5\u4e1a\u7ea73D\u6253\u5370\u7684\u51e0\u4f55\u6a21\u578b\u53ca\u5185\u5bb9\u9ad8\u6548\u751f\u6210\u7814\u7a76","funder_award_id":"61432003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8323435391","display_name":null,"funder_award_id":"MOE2013-T2-2-011 & AcRF 40/12","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G8525555724","display_name":null,"funder_award_id":"61322206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1969052304.pdf","grobid_xml":"https://content.openalex.org/works/W1969052304.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1585984841","https://openalex.org/W1826955156","https://openalex.org/W1893350195","https://openalex.org/W1967790312","https://openalex.org/W1969549682","https://openalex.org/W1974956622","https://openalex.org/W1981784948","https://openalex.org/W1985270033","https://openalex.org/W1994842413","https://openalex.org/W2006502673","https://openalex.org/W2010328065","https://openalex.org/W2018964608","https://openalex.org/W2020995339","https://openalex.org/W2029041800","https://openalex.org/W2030322781","https://openalex.org/W2047767520","https://openalex.org/W2049153601","https://openalex.org/W2056422961","https://openalex.org/W2057512681","https://openalex.org/W2058077178","https://openalex.org/W2084533748","https://openalex.org/W2085550119","https://openalex.org/W2092924973","https://openalex.org/W2104229632","https://openalex.org/W2105733544","https://openalex.org/W2114288655","https://openalex.org/W2121029369","https://openalex.org/W2126439213","https://openalex.org/W2150593711","https://openalex.org/W2163787581","https://openalex.org/W2166522594","https://openalex.org/W2169574389","https://openalex.org/W2172006071","https://openalex.org/W2235901111","https://openalex.org/W3125178117","https://openalex.org/W3143791812","https://openalex.org/W4239465939"],"related_works":["https://openalex.org/W2353304988","https://openalex.org/W2359979928","https://openalex.org/W330979007","https://openalex.org/W2384614608","https://openalex.org/W2129412583","https://openalex.org/W1989161402","https://openalex.org/W1751078205","https://openalex.org/W2361950850","https://openalex.org/W1600679759","https://openalex.org/W2063329372"],"abstract_inverted_index":{"Delaunay":[0,13,32,69,107],"meshes":[1,108],"(DM)":[2],"are":[3,80],"a":[4,31,58,64,72,118],"special":[5],"type":[6],"of":[7,51,75,168,182],"triangle":[8,27],"mesh":[9,28,136],"where":[10,46],"the":[11,37,49,122,126,140,147,157,165,180,183,204,208],"local":[12],"condition":[14],"holds":[15],"everywhere.":[16],"We":[17,34,61,174],"present":[18],"an":[19,24],"efficient":[20],"algorithm":[21,66,92],"to":[22,67,87,97],"convert":[23],"arbitrary":[25],"manifold":[26],"M":[29,54],"into":[30],"mesh.":[33],"show":[35],"that":[36,146,176],"constructed":[38],"DM":[39,90,119,169],"has":[40,120,153],"O":[41,99],"(":[42,100],"Kn":[43],")":[44,104],"vertices,":[45],"n":[47],"is":[48,57],"number":[50],"vertices":[52],"in":[53],"and":[55,85,113,129],"K":[56,103],"model-dependent":[59],"constant.":[60],"also":[62,93],"develop":[63],"novel":[65],"simplify":[68],"meshes,":[70],"allowing":[71],"smooth":[73],"choice":[74],"detail":[76],"levels.":[77],"Our":[78],"methods":[79],"conceptually":[81],"simple,":[82],"theoretically":[83],"sound":[84],"easy":[86],"implement.":[88],"The":[89],"construction":[91],"scales":[94],"well":[95],"due":[96],"its":[98],"nK":[101],"log":[102],"time":[105],"complexity.":[106],"have":[109],"many":[110],"favorable":[111],"geometric":[112],"numerical":[114,166],"properties.":[115],"For":[116],"example,":[117],"exactly":[121],"same":[123],"geometry":[124,160],"as":[125,195],"input":[127,209],"mesh,":[128],"it":[130],"can":[131,163,178],"be":[132],"encoded":[133],"by":[134],"any":[135,172],"data":[137],"structure.":[138],"Moreover,":[139],"empty":[141],"geodesic":[142,188],"circumcircle":[143],"property":[144],"implies":[145],"commonly":[148],"used":[149],"cotangent":[150],"Laplace-Beltrami":[151],"operator":[152],"non-negative":[154],"weights.":[155],"Therefore,":[156],"existing":[158],"digital":[159],"processing":[161],"algorithms":[162],"benefit":[164],"stability":[167],"without":[170],"changing":[171],"codes.":[173],"observe":[175],"DMs":[177,205],"improve":[179],"accuracy":[181],"heat":[184],"method":[185],"for":[186],"computing":[187],"distances.":[189],"Also,":[190],"popular":[191],"parameterization":[192],"techniques,":[193],"such":[194],"discrete":[196],"harmonic":[197],"mapping,":[198],"produce":[199],"more":[200],"stable":[201],"results":[202],"on":[203,207],"than":[206],"meshes.":[210]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}