{"id":"https://openalex.org/W3084262744","doi":"https://doi.org/10.1109/tvcg.2021.3070046","title":"Deterministic Linear Time Constrained Triangulation Using Simplified Earcut","display_name":"Deterministic Linear Time Constrained Triangulation Using Simplified Earcut","publication_year":2021,"publication_date":"2021-03-31","ids":{"openalex":"https://openalex.org/W3084262744","doi":"https://doi.org/10.1109/tvcg.2021.3070046","mag":"3084262744","pmid":"https://pubmed.ncbi.nlm.nih.gov/33788688"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2021.3070046","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2021.3070046","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2009.04294","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050783045","display_name":"Marco Livesu","orcid":"https://orcid.org/0000-0002-4688-7060"},"institutions":[{"id":"https://openalex.org/I4210137033","display_name":"Istituto di Matematica Applicata e Tecnologie Informatiche","ror":"https://ror.org/03m0n3c07","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210137033","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marco Livesu","raw_affiliation_strings":["Mathematics and Computer Science, CNR IMATI, Genoa, Italy","Mathematics & Computer Science, CNR IMATI, Genoa, GE, Italy, (e-mail: marco.livesu@gmail.com)"],"raw_orcid":"https://orcid.org/0000-0002-4688-7060","affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science, CNR IMATI, Genoa, Italy","institution_ids":["https://openalex.org/I4210137033"]},{"raw_affiliation_string":"Mathematics & Computer Science, CNR IMATI, Genoa, GE, Italy, (e-mail: marco.livesu@gmail.com)","institution_ids":["https://openalex.org/I4210137033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006227713","display_name":"Gianmarco Cherchi","orcid":"https://orcid.org/0000-0003-2029-1119"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianmarco Cherchi","raw_affiliation_strings":["Mathematics and Computer Science, University of Cagliari, Cagliari, CA, Italy","[Mathematics & Computer Science, University of Cagliari, 3111 Cagliari, CA, Italy, (e-mail: cherchi.gianmarco@gmail.com)]"],"raw_orcid":"https://orcid.org/0000-0003-2029-1119","affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science, University of Cagliari, Cagliari, CA, Italy","institution_ids":["https://openalex.org/I172446870"]},{"raw_affiliation_string":"[Mathematics & Computer Science, University of Cagliari, 3111 Cagliari, CA, Italy, (e-mail: cherchi.gianmarco@gmail.com)]","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003406070","display_name":"Riccardo Scateni","orcid":"https://orcid.org/0000-0002-0950-7372"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Riccardo Scateni","raw_affiliation_strings":["Mathematics and Computer Science, University of Cagliari, Cagliari, CA, Italy","Mathematics & Computer Science, University of Cagliari, 3111 Cagliari, CA, Italy, 09123 (e-mail: riccardo@unica.it)"],"raw_orcid":"https://orcid.org/0000-0002-0950-7372","affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science, University of Cagliari, Cagliari, CA, Italy","institution_ids":["https://openalex.org/I172446870"]},{"raw_affiliation_string":"Mathematics & Computer Science, University of Cagliari, 3111 Cagliari, CA, Italy, 09123 (e-mail: riccardo@unica.it)","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076347394","display_name":"Marco Attene","orcid":"https://orcid.org/0000-0002-9012-7245"},"institutions":[{"id":"https://openalex.org/I4210137033","display_name":"Istituto di Matematica Applicata e Tecnologie Informatiche","ror":"https://ror.org/03m0n3c07","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210137033","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Attene","raw_affiliation_strings":["Mathematics and Computer Science, CNR IMATI, Genoa, Italy","Mathematics and Computer Science, IMATI CNR Genova, 308019 Genova, Liguria, Italy, (e-mail: marco.attene@ge.imati.cnr.it)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science, CNR IMATI, Genoa, Italy","institution_ids":["https://openalex.org/I4210137033"]},{"raw_affiliation_string":"Mathematics and Computer Science, IMATI CNR Genova, 308019 Genova, Liguria, Italy, (e-mail: marco.attene@ge.imati.cnr.it)","institution_ids":["https://openalex.org/I4210137033"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5050783045"],"corresponding_institution_ids":["https://openalex.org/I4210137033"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01457827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"12","first_page":"5172","last_page":"5177"},"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9876999855041504,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/polygon","display_name":"Polygon (computer graphics)","score":0.6852062940597534},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.6695642471313477},{"id":"https://openalex.org/keywords/minimum-weight-triangulation","display_name":"Minimum-weight triangulation","score":0.6268153190612793},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6210683584213257},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5936635732650757},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48477381467819214},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.4763636589050293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4691511392593384},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44867444038391113},{"id":"https://openalex.org/keywords/convex-polygon","display_name":"Convex polygon","score":0.44410327076911926},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.44120293855667114},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4397144615650177},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4297712743282318},{"id":"https://openalex.org/keywords/star-shaped-polygon","display_name":"Star-shaped polygon","score":0.4144861102104187},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.368982195854187},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3179068863391876},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.2987254858016968},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.14950504899024963},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1016608476638794}],"concepts":[{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6852062940597534},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.6695642471313477},{"id":"https://openalex.org/C39969762","wikidata":"https://www.wikidata.org/wiki/Q6865406","display_name":"Minimum-weight triangulation","level":4,"score":0.6268153190612793},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6210683584213257},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5936635732650757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48477381467819214},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.4763636589050293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4691511392593384},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44867444038391113},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.44410327076911926},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.44120293855667114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4397144615650177},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4297712743282318},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.4144861102104187},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.368982195854187},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3179068863391876},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.2987254858016968},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.14950504899024963},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1016608476638794},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tvcg.2021.3070046","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2021.3070046","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:33788688","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33788688","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on visualization and computer graphics","raw_type":null},{"id":"pmh:oai:arXiv.org:2009.04294","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.04294","pdf_url":"https://arxiv.org/pdf/2009.04294","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2009.04294","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2009.04294","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:3084262744","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2009.04294","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.04294","pdf_url":"https://arxiv.org/pdf/2009.04294","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W102262102","https://openalex.org/W131654247","https://openalex.org/W1825136300","https://openalex.org/W1971748934","https://openalex.org/W1971842242","https://openalex.org/W1983487792","https://openalex.org/W1999011824","https://openalex.org/W2001351033","https://openalex.org/W2004988621","https://openalex.org/W2015568644","https://openalex.org/W2027440570","https://openalex.org/W2036773635","https://openalex.org/W2047178754","https://openalex.org/W2050417465","https://openalex.org/W2073058919","https://openalex.org/W2094472302","https://openalex.org/W2106413026","https://openalex.org/W2116179136","https://openalex.org/W2119352997","https://openalex.org/W2124677557","https://openalex.org/W2129412583","https://openalex.org/W2170083611","https://openalex.org/W2200785014","https://openalex.org/W2396935036","https://openalex.org/W2800234772","https://openalex.org/W2970048909","https://openalex.org/W3109028501","https://openalex.org/W4249353371","https://openalex.org/W6605397754","https://openalex.org/W6712518083"],"related_works":["https://openalex.org/W119195015","https://openalex.org/W2483636719","https://openalex.org/W2084668024","https://openalex.org/W3011179386","https://openalex.org/W1793184581","https://openalex.org/W1518406227","https://openalex.org/W2044916959","https://openalex.org/W2896844293","https://openalex.org/W2008012883","https://openalex.org/W1506835786","https://openalex.org/W2925504816","https://openalex.org/W2174232782","https://openalex.org/W2185518273","https://openalex.org/W2015042527","https://openalex.org/W2798624557","https://openalex.org/W3021223474","https://openalex.org/W2093937220","https://openalex.org/W2126670031","https://openalex.org/W2784798536","https://openalex.org/W2020225160"],"abstract_inverted_index":{"Triangulation":[0],"algorithms":[1],"that":[2,45,63,68,101],"conform":[3],"to":[4,78,88,118,126,140],"a":[5,25,115],"set":[6],"of":[7,114,147],"non-intersecting":[8],"input":[9],"segments":[10],"typically":[11],"proceed":[12],"in":[13,81,153],"an":[14,82,127],"incremental":[15],"fashion,":[16,84],"by":[17],"inserting":[18],"points":[19,93],"first,":[20],"and":[21,156],"then":[22],"segments.":[23],"Inserting":[24],"segment":[26,49],"amounts":[27],"to:":[28],"(1)":[29],"deleting":[30],"all":[31,69],"the":[32,38,47,86,112,145],"triangles":[33,80],"it":[34,152,158],"intersects;":[35],"(2)":[36],"filling":[37],"so":[39],"generated":[40],"hole":[41],"with":[42,159],"two":[43,74],"polygons":[44,65],"have":[46],"wanted":[48],"as":[50],"shared":[51],"edge;":[52],"(3)":[53],"triangulate":[54],"each":[55,97],"polygon":[56,92,104],"separately.":[57],"In":[58],"this":[59,124],"article":[60],"we":[61],"prove":[62,144],"these":[64],"are":[66,94],"such":[67,135],"their":[70],"convex":[71,109],"vertices":[72,110],"but":[73,134],"can":[75],"be":[76],"used":[77],"form":[79],"earcut":[83],"without":[85],"need":[87],"check":[89],"whether":[90],"other":[91],"located":[95],"within":[96],"ear.":[98],"The":[99],"fact":[100],"any":[102],"simple":[103],"contains":[105],"at":[106],"least":[107],"three":[108],"guarantees":[111],"existence":[113],"valid":[116],"ear":[117],"cut,":[119],"ensuring":[120],"convergence.":[121],"Not":[122],"only":[123],"translates":[125],"optimal":[128],"deterministic":[129],"linear":[130],"time":[131],"triangulation":[132],"algorithm,":[133],"algorithm":[136],"is":[137],"also":[138,150],"trivial":[139],"implement.":[141],"We":[142],"formally":[143],"correctness":[146],"our":[148],"approach,":[149],"validating":[151],"practical":[154],"applications":[155],"comparing":[157],"prior":[160],"art.":[161]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}