{"id":"https://openalex.org/W1484846518","doi":"https://doi.org/10.1145/2999532","title":"Constructing Intrinsic Delaunay Triangulations from the Dual of Geodesic Voronoi Diagrams","display_name":"Constructing Intrinsic Delaunay Triangulations from the Dual of Geodesic Voronoi Diagrams","publication_year":2017,"publication_date":"2017-04-14","ids":{"openalex":"https://openalex.org/W1484846518","doi":"https://doi.org/10.1145/2999532","mag":"1484846518"},"language":"en","primary_location":{"id":"doi:10.1145/2999532","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2999532","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/10356/87052/1/Constructing%20Intrinsic%20Delaunay%20Triangulations%20from%20the%20Dual%20of%20Geodesic%20Voronoi%20Diagrams.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, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China","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, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China","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, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China","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, Singapore","Nanyang Technological University (Singapore)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Nanyang Technological University (Singapore)","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":10.8524,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.98163302,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"36","issue":"2","first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9918000102043152,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.93052077293396},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.8979371786117554},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.7594450116157532},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.674798846244812},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.6278359889984131},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.5929886102676392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5743346214294434},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5696483254432678},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.5602766275405884},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5250311493873596},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.49154195189476013},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.47999924421310425},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4553412199020386},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.38936126232147217},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35827523469924927},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3278799057006836},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3270780146121979},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.27689671516418457},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21373453736305237},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.10868340730667114}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.93052077293396},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.8979371786117554},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.7594450116157532},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.674798846244812},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.6278359889984131},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.5929886102676392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5743346214294434},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5696483254432678},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.5602766275405884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5250311493873596},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.49154195189476013},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.47999924421310425},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4553412199020386},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38936126232147217},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35827523469924927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3278799057006836},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3270780146121979},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27689671516418457},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21373453736305237},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.10868340730667114}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2999532","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2999532","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:10356/87052","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/45219","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/87052/1/Constructing%20Intrinsic%20Delaunay%20Triangulations%20from%20the%20Dual%20of%20Geodesic%20Voronoi%20Diagrams.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:10356/87052","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/45219","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/87052/1/Constructing%20Intrinsic%20Delaunay%20Triangulations%20from%20the%20Dual%20of%20Geodesic%20Voronoi%20Diagrams.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/G3794609071","display_name":null,"funder_award_id":"61661130156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4443897377","display_name":null,"funder_award_id":"61432003, 61521002 and 61661130156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G797295151","display_name":null,"funder_award_id":"61521002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation 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"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1484846518.pdf","grobid_xml":"https://content.openalex.org/works/W1484846518.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1957318557","https://openalex.org/W1969052304","https://openalex.org/W1985270033","https://openalex.org/W2008581147","https://openalex.org/W2024403957","https://openalex.org/W2026778346","https://openalex.org/W2066612780","https://openalex.org/W2084533748","https://openalex.org/W2090903187","https://openalex.org/W2092924973","https://openalex.org/W2099963367","https://openalex.org/W2103723796","https://openalex.org/W2104229632","https://openalex.org/W2105207001","https://openalex.org/W2105733544","https://openalex.org/W2108567935","https://openalex.org/W2124036531","https://openalex.org/W2126439213","https://openalex.org/W2163787581","https://openalex.org/W2169574389","https://openalex.org/W2244240907","https://openalex.org/W4239339957"],"related_works":["https://openalex.org/W2371448287","https://openalex.org/W2054943762","https://openalex.org/W2358109229","https://openalex.org/W2795062835","https://openalex.org/W2354869996","https://openalex.org/W1967229461","https://openalex.org/W2106536058","https://openalex.org/W2058313718","https://openalex.org/W1967060523","https://openalex.org/W105410060"],"abstract_inverted_index":{"Intrinsic":[0],"Delaunay":[1,6],"triangulation":[2,7,134],"(IDT)":[3],"naturally":[4],"generalizes":[5],"from":[8],"R":[9],"2":[10,240],"to":[11,15,54,66,94,130],"curved":[12],"surfaces.":[13],"Due":[14],"many":[16],"favorable":[17],"properties,":[18],"the":[19,38,46,127,141,148,164,185,188,212,216,249,255],"IDT":[20,44],"whose":[21],"vertex":[22],"set":[23],"includes":[24],"all":[25,112,137],"mesh":[26,34,113,195],"vertices":[27,114],"is":[28,45,61,135,157,225,248],"of":[29,187,251],"particular":[30],"interest":[31],"in":[32,68,176,254,264],"polygonal":[33],"processing.":[35],"To":[36,146],"date,":[37],"only":[39,85],"way":[40],"for":[41,126],"constructing":[42],"such":[43],"edge-flipping":[47],"algorithm,":[48],"which":[49,177],"iteratively":[50],"flips":[51],"non-Delaunay":[52],"edges":[53],"become":[55],"locally":[56],"Delaunay.":[57],"Although":[58],"this":[59],"algorithm":[60],"conceptually":[62],"simple":[63],"and":[64,77,117,220],"guarantees":[65],"terminate":[67],"finite":[69],"steps,":[70],"it":[71,261],"has":[72,231],"no":[73],"known":[74],"time":[75,235,266],"complexity":[76,236],"may":[78],"also":[79],"produce":[80],"triangulations":[81],"containing":[82],"faces":[83],"with":[84,196],"two":[86],"edges.":[87],"This":[88],"article":[89],"develops":[90],"a":[91,105,132,153,194,226,232],"new":[92],"method":[93,230],"obtain":[95],"proper":[96,133,227],"IDTs":[97],"on":[98,267],"manifold":[99],"triangle":[100],"meshes.":[101],"We":[102],"first":[103],"compute":[104],"geodesic":[106],"Voronoi":[107,138,160,189],"diagram":[108,190],"(GVD)":[109],"by":[110,171,202],"taking":[111],"as":[115],"generators":[116],"then":[118],"find":[119],"its":[120,222],"dual":[121,128,223],"graph.":[122],"The":[123],"sufficient":[124],"condition":[125],"graph":[129,224],"be":[131,181],"that":[136,162,201,260],"cells":[139,161],"satisfy":[140],"so-called":[142],"closed":[143,149,165,217],"ball":[144,150,166,218],"property.":[145],"guarantee":[147],"property":[151],"everywhere,":[152],"certain":[154],"sampling":[155],"criterion":[156],"required.":[158],"For":[159],"violate":[163],"property,":[167,219],"we":[168,199],"fix":[169],"them":[170],"computing":[172],"topologically":[173],"safe":[174],"regions,":[175],"auxiliary":[178,210],"sites":[179],"can":[180],"added":[182],"without":[183],"changing":[184],"topology":[186],"beyond":[191],"them.":[192],"Given":[193],"n":[197,208,239,244],"vertices,":[198],"prove":[200],"adding":[203],"at":[204],"most":[205],"O":[206,237],"(":[207,238],")":[209],"sites,":[211],"computed":[213],"GVD":[214],"satisfies":[215],"hence":[221],"IDT.":[228],"Our":[229],"theoretical":[233],"worst-case":[234],"+":[241],"tn":[242],"log":[243],"),":[245],"where":[246],"t":[247],"number":[250],"obtuse":[252],"angles":[253],"mesh.":[256],"Computational":[257],"results":[258],"show":[259],"empirically":[262],"runs":[263],"linear":[265],"real-world":[268],"models.":[269]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
